Operation of Traffic Signal Systems in Oversaturated Conditions, Volume 2 – Final Report (2014)

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Chapter 2: Research Approach This research project resulted in several significant findings and developments: • Development of new quantitative measures of oversaturation • A research methodology for developing signal timing plans for oversaturated conditions • A software tool that can select pre-planned mitigation strategies based on the new quantitative measures • Evaluation of many combinations of strategies in real world examples • Development of guidance and a process to help practitioners identify which strategies apply when and where In this chapter, we will present the following: • A series of definitions and framing concepts • The motivation and theory for calculation of quantitative metrics of oversaturation • The multi-objective methodology for developing and evaluating signal timing plans for oversaturated operation • The design and concept of the online software tool for selection of strategies In Chapter 3, we will summarize the findings and test cases of these research and development efforts: • Testing and evaluation of the multi-objective development and evaluation methodology • Testing and evaluation of the quantitative measures of oversaturation • Testing and evaluation of a heuristic for green time re-allocation using quantitative measurement of oversaturation • Testing and evaluation of the online strategy selection framework Chapter 4 presents the findings, conclusions, and directions for future research. Definitions Oversaturated conditions can be described according to the following attributes: • Spatial extent • Temporal extent • Recurrence • Cause(s) • Symptoms Operation of traffic signal systems in oversaturated conditions Page 25

The details of these five dimensions comprise a specific “scenario” of traffic conditions that warrant some mitigation strategies. To further clarify these dimensions, we present a series of definitions. The terms “scenario” and “situation” will be used interchangeably to describe the combination of spatial and temporal traffic conditions that describe the oversaturated traffic control problem. A strategy is a specific component or combination of traffic control actions applied to mitigate the symptoms of a scenario. We will assume that the reader has an understanding of general North American traffic engineering terminology (cycle, split, offset, sequence, rings, movements, etc.) and will use these terms without definition. A glossary is included in Appendix B of this report. As summarized in Chapter 1, a survey of expert practitioners was conducted. This survey produced a range of definitions for the concept of “oversaturation”. All of the offered definitions considered that oversaturation is directly related to both the traffic demand exceeding the capacity of the intersection and the traffic control strategy in place. From these offered suggestions and our own experience, we settled on a definition of oversaturation which we tried to identify as the most basic “building block” definition. From this basic definition, further definitions will be presented. First, we assert that the traffic movement is the lowest level building block of traffic control and operations at an intersection. Movements can have green time specifically allocated to them, such as a protected left turn. Movements can also be grouped together into phases for the purpose of allocation of green time, or movements can borrow green time from other movements or phases by using overlaps. Thus, we define: A traffic movement is oversaturated when the traffic demand for the movement exceeds the green-time capacity such that a queue that exists at the beginning of the green time is not fully dissipated at the end of the green time for that movement. This basic definition of oversaturation does not immediately imply that a change in traffic control strategy is necessary or that any action is required at all. It simply describes the condition at its lowest common denominator in the context of traffic signal control. An example of this basic scenario is shown in Figure 1. The example on the left shows a queue of vehicles waiting to turn left at an intersection. Vehicles intending to turn left have been shown in green color. A “subject vehicle” is marked in the queue for reference. The illustration on the right then shows the resulting traffic condition after the left-turn green time has elapsed. The “subject vehicle” highlighted has made some progress towards the stop bar of the left turn bay, but did not proceed through the intersection on the green light. This illustrates the concept of an oversaturated movement at an intersection. An overflow queue is defined as a minimum of one vehicle that is left over from a queue that could not be fully discharged during the previous green phase. Operation of traffic signal systems in oversaturated conditions Page 26

Common sense dictates that a scenario where a queue of vehicles is dispersed and one or two vehicles are remaining after the termination of the green time is probably not a serious issue to address with alternative traffic control strategies, at least if it only lasts for one or two cycles. However, from general queuing theory we know that a sustained arrival rate (traffic demand) that exceeds the service rate (green time) of any process will result in queues that grow until the arrival rate is reduced. This can occur naturally as fewer vehicles arrive or the arriving traffic begins taking alternate routes because of the downstream congestion. Figure 3. An oversaturated traffic movement Additional qualifying conditions are necessary to extend this basic definition of oversaturation before changes in traffic control actions are typically required. These conditions can include: • The degree to which the movement is oversaturated (i.e. the length of the overflow queue). • The rate at which the oversaturation level is growing (the growth rate of the overflow queue). • The effect of the oversaturation on other movements, approaches, and intersections. • The length of time that the oversaturation persists. Subject Vehicle Start of Green Subject Vehicle End of Green An Oversaturated Movement: vehicle in queue does not clear intersection Operation of traffic signal systems in oversaturated conditions Page 27

Significantly oversaturated conditions existing on a single movement can be handled by re-timing the signal to shift green time from other under-saturated phases to the phase serving the oversaturated movement. Extension of the Definition for Spatial Extent From this basic condition of oversaturation on a movement, the next level of characterization of oversaturation is oversaturation on an approach to an intersection. An approach is defined as a combination of compatible traffic movements that serve traffic in the same direction of travel. A traffic movement is compatible with another movement if they do not inherently conflict (i.e. they could be served by the same traffic phase). An approach is oversaturated if all movements of the approach are oversaturated or if an oversaturated movement causes “detrimental effects” to one or more of the other movements served by the approach. Figure 4. An oversaturated approach for both through and left-turn movements Subject Vehicle Start of Green Subject Vehicle Subject Vehicle End of Green An Oversaturated Approach: vehicles in queues of multiple movements do not clear Subject vehicle Operation of traffic signal systems in oversaturated conditions Page 28

Figure 4 illustrates the case where both the through movement and the left-turn movement are oversaturated. The “subject vehicle” tags in the figure indicate that both movements are oversaturated since neither vehicle proceeds through the intersection during the green signal. For the purpose of this illustration, and the definition it is not necessary that both movements are served by one traffic phase or separately by two phases. The oversaturation is defined on the “approach”. Detrimental Effects A detrimental effect or a symptom is a situation where the oversaturation on one movement causes reduction in the ability of traffic on a compatible movement (or any other movement) to utilize all of the green time allocated for that movement due to starvation or blocking. Starvation is the condition where the light is green but there is no associated vehicle flow for that direction of travel. Figure 5 illustrates the condition where the oversaturated condition on the left-turn movement creates starvation for the through movement because the vehicles that intend to turn left have blocked the ability of the through vehicles to proceed to the stop line. Thus, perhaps if the left turning movement was not oversaturated, the through movement would not have been impeded and the green time might have been adequate to satisfy the through demand. Operation of traffic signal systems in oversaturated conditions Page 29

Figure 5. Illustration of oversaturated approach due to starvation A traffic control phase would be considered oversaturated if all movements that are served by the phase are oversaturated. Oversaturated conditions that exist on single approaches or single phases can typically be addressed with re-allocation of green time from other under-saturated phases or by changes to the phase sequence. Once the oversaturated condition grows to extend past a single movement or approach, the problem trade-offs become more challenging. An intersection is considered to be oversaturated if two or more incompatible traffic movements at the intersection are oversaturated. Blocking and Non-Blocking Conditions Oversaturation at an intersection can have blocking or non-blocking conditions. A blocking condition exists when the queues on one movement prevent one or more other movements at the intersection from proceeding through the intersection during its associated green time. Subject Vehicle Start of Green Subject Vehicle End of Green An Oversaturated Approach: vehicles in queue for one movement blocks/ starves others (detrimental effects) Starvation due to blocking Operation of traffic signal systems in oversaturated conditions Page 30

Figure 6 below illustrates an oversaturated intersection where the vehicles in the northbound left turn bay are blocking the movement of the vehicles on the eastbound approach. In a non-blocking situation at an oversaturated intersection, there is no impedance of one approach flow by another incompatible flow. Figure 6. Oversaturation at an intersection caused by blocking An intersection with a blocking condition is more complex to address than a scenario where blocking does not occur. More careful consideration of the effects of green-time re-allocation must be taken into account before a specific mitigation action can be taken when there is blocking. In most locales, blocking the intersection is illegal and most drivers will comply with these common sense rules. Oversaturation on a Route A route is a useful building block definition to identify oversaturation problems that are larger than an individual intersection. The term “route” is not meant to construe an origin-destination pair or any considerable distance from the beginning point to the ending point. Figure 7 illustrates an oversaturated route comprised of a northbound through movement (intersection GF), a northbound left turn movement (intersection FB), and then an eastbound through movement (intersection B). These three movements comprise an oversaturated route when they are Ov ers atu rat ed mo ve me nt Oversaturated approach An Oversaturated Intersection (blocking) Operation of traffic signal systems in oversaturated conditions Page 31

oversaturated at the same time. Oversaturation on a route can also be a source of blocking conditions at intersections. A route is considered to be oversaturated if two or more compatible movements on a single travel path through a series of intersections simultaneously have oversaturated conditions. Figure 7. Oversaturated condition on a route Oversaturation on a Network Multiple routes that are oversaturated at the same time and that interact with each other define an oversaturated network. An example of this type of situation is illustrated in shows an example of several routes and approaches that are oversaturated Figure 8. Figure 8 at the same time including all of the intersections in the figure except intersections C and D. Oversaturated Route F GC B Operation of traffic signal systems in oversaturated conditions Page 32

Figure 8. Illustration of an oversaturated network Special Cases of Network Oversaturation Several special cases of oversaturated scenarios on networks can be defined. Two examples are freeway-arterial diamond interchanges and arterials with heavy traffic on the arterial and minor flows on side streets. These special cases as listed in Table 2. Oversaturated Sub-Network F H G E D C B A Operation of traffic signal systems in oversaturated conditions Page 33

Table 2. Special cases of network oversaturation Special Case Description Two-way arterial Two or more consecutive approaches in both travel directions that are simultaneously oversaturated. Interchange Two or more oversaturated routes at the junction of an arterial and a freeway. Grid Two or more oversaturated routes in a network of signals that have regular spacing and typically are run together on a common cycle time in central business districts. Coordination in both directions of travel is typically considered. Figure 9 illustrates the special case of an oversaturated condition on a two-way arterial. In this example, both directions of north and south travel are oversaturated with traffic at the same time along the route from EFGH and from HGFE. Oversaturated conditions existing on routes and networks are complex problems requiring careful consideration of green-time re-allocation, sequence, offsets, and cycle selection. Operation of traffic signal systems in oversaturated conditions Page 34

Figure 9. Illustration of oversaturated condition on a two-way arterial Large-Scale Problems and Gridlock Wide-spread or regional oversaturated conditions are the most complicated situations to be handled by any mitigation strategy. Situations can arise where a mitigating action in one area of the network exacerbates the congestion in other areas. Multiple interacting areas of oversaturated conditions define a regional oversaturated network as illustrated in Figure 10. Gridlock is defined as a special case of oversaturated conditions where simultaneous blocking of several movements causes traffic to remain unable to proceed in any direction. During gridlock, the green time is provided to a movement when the vehicles served by that traffic phase are unable to proceed. Oversaturated two-way arterial F H G E D C B A Operation of traffic signal systems in oversaturated conditions Page 35

Figure 10. A challenging regional network scenario Strategic restriction of demand to the network (i.e. “metering”) might be expected to be the only reasonable mitigating action that can resolve gridlock situations. Duration of Oversaturation The series of definitions in the previous section categorized the spatial extent of an oversaturated condition. The other dimension defining an oversaturated condition is the duration. Of course these two elements are continually interacting as traffic moves through the system, perhaps creating oversaturation in one area that was previously in a different part of the network. The problem may grow continually larger as flows at one or more critical points create shockwaves that move upstream. The existence of a persistent (or growing) queue for two or more cycles on a facility (movement, approach, intersection, etc.) defines an oversaturated condition. This is a minimum level of Oversaturated Network F H G E D C B A Operation of traffic signal systems in oversaturated conditions Page 36

occurrence that provides the definition. As the condition persists for more cycles continuously the condition would be considered to be more severe when combined with the severity level presented by the length of the persistent queue with respect to the storage area for the movement or approach. An oversaturated condition is thus considered to be dissipated when a queue that was persistent from the previous cycle is cleared during the following green time. However, the nature of traffic is a random process that is influenced by variations in driver behavior and inherent randomness in aggregate arrival rates of traffic due to individual decisions on departure time and route. As such, a condition may be dissipated for one or two cycles only to return in the next cycle due to surge in traffic demand. As shown in Table 2, there are four terms to describe time conditions on the extent of oversaturated conditions: Table 3. Duration of oversaturation Duration Description Situational Oversaturated conditions characterized by several consecutive cycles in which the condition persists but is naturally dissipated due to removal of exogenous factors that caused the condition. Intermittent Oversaturated conditions characterized by frequent transition between over- and under-saturated conditions. Persistent Oversaturated conditions characterized by a considerable number of consecutive cycles in which the oversaturated condition continues. A “considerable number of cycles” might be defined, at a minimum, to be a duration during which it would not be considered typical to modify a signal timing pattern based on a time-of-day pattern schedule. For example, it would not be common to modify signal timing plan parameters more often than once per 30 minutes. At a maximum, the duration of a persistent condition might be dissipated within the time where it would be typical to make a pattern change based on a time-of-day schedule. For example, many agencies might be expected to change signal timing parameters in 2 to 3 hours increments. Prolonged Extensive duration of oversaturation that extends for time periods that would encompass the duration of more than one pattern in a typical time-of-day schedule. At a minimum, more than one to one and a half hours in duration. We have tried to stay away from defining “crisp” criteria for definitions of temporal duration such as 15 minutes, 1 hour, or five cycles. Causal Factors A wide range of influencing or causal factors can cause oversaturated conditions. As shown in Table 3, the basic categories of causal factors are: Operation of traffic signal systems in oversaturated conditions Page 37

Table 4. Causal factors Factor Description Traffic Demand Heavier traffic flow than can be processed by the traffic signal system regardless of modifications and enhancements to geometrics, signal timings, or both. Variations in demand level can also lead to intermittent oversaturation. Geometrics Physical design characteristics of a traffic facility that exacerbate the ability of the traffic signal system to move traffic efficiently. Traffic signal operations Signal timing practices and inefficiencies that contribute to oversaturation due to “sub-optimal” operating policies and principles. Other travel modes Service of other travel modes (buses, trains, bikes, pedestrians) by the traffic signal system and modal operations (bus stops, train crossings, etc.) that exacerbate the ability of the traffic signal system to move traffic efficiently. Anomalous events Atypical events and conditions including crashes, work zones, weather conditions, and other incidents that exacerbate the ability of the signal system to move traffic efficiently since the saturation flow rates and travel behaviors of drivers are modified significantly. Planned Special Events Events that are known to happen at a specific time, such as concerts or athletic events. Ingress and egress to the facility or facilities exacerbates the ability of the traffic system to operate efficiently. Start of oversaturation at ingress is typically difficult to determine, although end time of oversaturation typically occurs shortly after start time of the event. Conversely, start of egress is sometimes less of a certain event (for example, overtime at a sporting event) but the “beginning of the end” might be easier to identify since when the parking lot at the event is empty, the end of the event is known. A specific condition can, of course, be caused by a combination of these influencing factors. Combinations of factors will increase the intensity of the situation negatively. Occurrence Frequency The final component that is necessary for categorizing an oversaturated condition is the frequency in which the oversaturation occurs. Occurrence frequency is divided into two basic categories: recurrent and non-recurrent as described in Table 4. Recurrent situations are easier to study and analyze due to their repeatable nature. Strategies can be applied that are pre-planned and use fixed modifications to signal timings. Non-recurrent conditions can require automated responses based on detector monitoring. Operation of traffic signal systems in oversaturated conditions Page 38

Table 5. Frequency of oversaturation Frequency Description Recurrent Oversaturated conditions characterized by relatively predictable and repeatable occurrences at certain times of day and days of the week. Geometric physical capacity, peak travel demand rates, traffic signal timing operations, and other modal effects (buses, trains, bicycles, and pedestrians) can be considered as recurrent causes. Situations can include all or any combination of factors. Non-recurrent Oversaturated conditions that occur on a traffic facility because of atypical exogenous factors that are not predictable or repeatable. Factors could include crashes and incidents, significant demand pattern shifts, and work zones as well as atypical influence of other modes (buses, trains, bicycles, pedestrians) such as heavy pedestrian crossings due to a special event. Situations can include all or any combination of factors. Specific Symptoms on Routes and at Intersections The definitions presented above for spatial and temporal extent represent a high-level view of the extent of queuing in a traffic signal system network. At a more detailed level, from a link-by-link perspective, it is important to quantify the specific type of problem being experienced. Overflow queues must be considered relative to the amount of storage capacity on the particular movement, phase, or approach. For example, a long persistent queue on a long approach may not be a direct cause for alarm. This situation may actually be the most appropriate mitigation to a particular scenario by storing vehicles where there is the most capacity. However, a relatively short queue that consistently fills a short link might cause a ripple effect. An important step in the process is to consider the extent of overflow queues versus the storage available. In particular, increasing green time at an upstream signal to disperse additional vehicles queued upstream will further exacerbate the downstream situation when there is limited storage available on the downstream link. A straightforward procedure for minimizing the two kinds of overflow queuing problems is presented in Chapter 3. In addition to overflow queuing, the following symptoms contribute additional complexity to the design and application of mitigation strategies: • Spillback • Starvation • Storage blocking • Cross blocking The combination of these effects in oversaturated routes, sub-networks, and networks is what makes the management of oversaturated conditions one of the most challenging problems in traffic signal control. Operation of traffic signal systems in oversaturated conditions Page 39

Spillback occurs when a queue from a downstream intersection uses up all the space on a link and prevents vehicles from entering the upstream link on green. Some literature has defined this condition as causing “de facto red” to the upstream movement since no progression is possible. This is illustrated in Figure 11. Figure 11. Approach spillback (de facto red) Starvation occurs when a phase is green, but the phase cannot service at full capacity efficiently due to storage blocking, spillback blocking, or perhaps because the upstream signal is red. Starvation due to sub-optimal signal timing is illustrated in Figure 12. Starvation Figure 12. Approach starvation due to signal timing Spillback BA BA Operation of traffic signal systems in oversaturated conditions Page 40

Storage bay spillback, shown in Figure 13, occurs when turning traffic uses up the entire space of the storage lane and blocks the through traffic. The blocked through movement then experiences starvation. Figure 13. Storage bay spillback Turning storage blocking, shown in Figure 14, occurs when queues extend beyond the opening of the storage bay. In this situation, the turning movement will experience starvation since the turn signal is green, but the vehicles that intend to turn left are blocked from reaching the turn bay. If there are no vehicles in the left turn bay, the left turn can also be skipped completely. Figure 14. Storage bay blocking Cross intersection blocking, illustrated in Figure 15, occurs when queues extend into an intersection blocking the progression of crossing vehicles. While most jurisdictions have “don’t block the box” laws or policies, these types of situations are not uncommon in grids and networks with short link lengths. Carefully controlled settings of green times and signal offsets are necessary to mitigate these types of situations. Storage spillback Storage blocking Operation of traffic signal systems in oversaturated conditions Page 41

Figure 15. Cross blocking effects Identification of these symptoms of oversaturated conditions is an important component of the identification of appropriate mitigation strategies. Summary of Characteristics that Define an Oversaturated Scenario A particular oversaturated scenario is defined as a combination of the attributes summarized in Table 6. The purpose of this categorization matrix is to identify what type of problem is occurring in order to identify the appropriate mitigation strategies that are applicable. In the next section, each mitigation strategy will be categorized according to which elements in Table 6 are applicable to that strategy. Table 6. Summary of characteristics of oversaturated scenario Cross Blocking Extent Duration Causation Recurrence Symptoms Movement Situational Signal Timing Recurrent Starvation Approach Intermittent Geometrics Non-recurrent Spillback Intersection Persistent Other modes Storage Blocking Route Prolonged Demand Cross Blocking One-way arterial Unplanned Events Two-way arterial Planned Events Interchange Grid Network Operation of traffic signal systems in oversaturated conditions Page 42

Oversaturation Problem Characterization and System Dynamics Oversaturated conditions might be characterized as being both easy and hard to identify. A motorist that takes a specific route on a daily basis might easily predict where the oversaturated links will occur on their route and knows almost instinctively when the conditions on certain parts of their route are more heavily congested than normal. Similarly, with extended experience in a particular agency and location, traffic engineers become accustomed to the trouble areas of their jurisdiction and this is not only contained to situations that are recurrent. Special event patterns and intermittent situations (such as those created by bus or train schedules) can certainly be identified. The first step to characterization is observing and identifying which type of scenario is being experienced. In many situations, with good local knowledge or limited problem extent, identifying the elements in each column of the table is straight forward. In other more complex situations it will be important to collect field data and analyze how the data helps to identify the appropriate element in each column of Table 6. As part of the scenario definition you will need to define what is “in” the system and what is not “in” the system. This is a subjective decision. A general rule of thumb might be to include intersections that are affected by the oversaturation at some point during the scenario, but no more. Certain mitigation strategies such as gating may cause approaches becoming oversaturated that were not initially oversaturated for the explicit purpose of alleviating downstream conditions. High-Level System Dynamics From a high-level perspective, it is well known that daily traffic and recurrent events have repeatable patterns. No traffic system is continually in oversaturated operation and thus any scenario evolves into three regimes of operation: • Loading • Oversaturated operation (or “processing”) • Recovery This concept is illustrated in Figure 16. Operation of traffic signal systems in oversaturated conditions Page 43

Figure 16. Loading, oversaturation, and recovery regimes of operation During the loading regime, the traffic volumes are increasing, route proportions are changing, and in the case of non-recurrent events, the triggering event(s) have started. During loading, overflow queuing and other symptoms such as storage blocking and starvation begin to emerge. Early application of mitigation strategies can delay the onset of oversaturated operation. During the loading phase, shifting one’s operational objectives from minimizing user delay to maximizing throughput can provide a measurable improvement in performance on the approaches, routes, and networks that will shortly become oversaturated. This principle is confirmed in many of the test cases presented in Chapter 3. Early application of mitigation strategies is easier to conceptualize when the causal factors are recurrent. If the condition is non-recurrent or if it is difficult to predict when the condition will starts or how long it will last, then it may necessary to use an online tool to identify and then apply a mitigation strategy. During the oversaturated operation regime, the traffic volumes and route proportions are such that queues and congestion are not going to be dissipated until either (a) the traffic volumes are reduced, (b) the route proportions are changed (i.e. drivers’ avoid the area, adjust their routes, decide to travel later, etc.) or (c) both. This is the operational situation that many practitioners might characterize as “there is nothing that can be done”. While we disagree that this is the case for all situations, it is true that it is difficult to discern the difference between different mitigation strategies when the overflow queuing and downstream blockages hinder the ability of traffic to be moved (anywhere). Applying queue management approaches (e.g. decreasing green time or truncating phases when a downstream link is blocked) can provide enhanced service to non-saturated movements and approaches that can increase total system throughput. Mitigation LOADING OVERSATURATED OPERATION RECOVERY TIME TRAFFIC LOAD Operation of traffic signal systems in oversaturated conditions Page 44

strategies applied during this phase also serve to help the system return to steady-state operation sooner during the recovery phase than continuing to apply the “normal” operational strategies. During the recovery regime, traffic volumes, route proportions, or restrictive downstream capacity (e.g. clearance of crash, opening of additional toll booths, removal of construction, reduction in traffic flow) have been adjusted so that the overflow queues begin to dissipate. In this phase of operation, mitigation strategies are especially effective in returning the system to a steady state sooner than continuing to apply the “normal” operational strategies. Summary An oversaturated traffic scenario is described by its attributes: • Extent • Duration • Causation • Recurrence • Symptoms The duration and extent attributes of a scenario are further characterized by three regimes of operation: • Loading (growth of queues) • Processing (persistence of queues) • Recovery (dissipation of queues) In order to identify appropriate mitigation strategies and signal timing plan parameters, the scenario must first be adequately characterized. Direct measurement of queue lengths is the primary method for doing this. Historically, this has been challenging to accomplish in the field due to the need for deployment of extensive sensor networks. In the next section, we describe a novel technique for estimation of queue lengths from typical “advance” detector loops or zones when combined with high-resolution (second-by-second) signal timing phase data. From this basic technique, two derived measures of the type of oversaturation are developed which can directly measure problematic symptoms. Differentiation of the two common symptoms in oversaturation is a key step in determining which mitigation strategies and signal timing approaches are appropriate for a given scenario. Operation of traffic signal systems in oversaturated conditions Page 45

Measuring Length of Queue and Overflow Queuing Effects In the previous section, we defined the key qualitative characteristics of an oversaturated traffic scenario. To characterize the nature of an oversaturated problem quantitatively, the primary method is to measure queue lengths. Historically, this has been challenging to accomplish in the field due to the need for deployment of extensive sensor networks. This project, we have developed one direct and two derived measurements of oversaturation at the movement or approach level. The direct measurement of oversaturation is the length of the overflow queue relative to the length of the approach. For this project, we have shown that length of overflow queue can be reasonably estimated using second-by-second detector volume and occupancy data from upstream detectors and second-by-second phase timing information. This method uses a fairly simple traffic flow model correlated to the time when the phase that serves the queue is green or red to determine if a queue is growing or shrinking. The key characteristic of this model is that queue lengths much further upstream from the detection point can be reasonably estimated. This allows the approach to be applied in typical arterials with dilemma zone or extension detection. Typical stop-bar detectors that are 25’+ in length do not do an adequate job of capturing the gaps between traffic to estimate these measures. Furthermore, this method can capture the overflow queue, or the amount of queue remaining after the light turns red, that was not dispersed during the green time. This is the key distinction between oversaturated operation and operation of the signal during congested, but still undersaturated conditions. If a long queue is generated during the red light but is dissipated fully during the ensuing green phase, this may indicated heavy approach demand, but it is not oversaturated. Quantitative Characterization of the Severity of Oversaturation The amount and cause of overflow queuing is the key distinction in determining which mitigation strategies are appropriate for a given traffic scenario. If the overflow queue is created because of not enough green time, then essentially more green time is required. However if the overflow queue is created because of a downstream restriction, then more green time for this phase may only worsen the problem. Two quantitative indicators characterize overflow queuing: • TOSI – temporal oversaturation severity dimension • SOSI – spatial oversaturation severity dimension Detrimental effects in the temporal dimension are characterized by an overflow queue at the end of the signal cycle. These overflow vehicles that did not pass through the intersection during the current cycle, cannot be discharged due to insufficient green time. This overflow queue must now be served in the next cycle. Operation of traffic signal systems in oversaturated conditions Page 46

The amount of green time that is now used to service the overflow queue is quantified by TOSI, ranging from 0% to 100%. When TOSI = 100%, all of the green time for the phase is used to disperse the overflow queue. If the arrival rate is still constant (or increasing), the queue will continue to grow so that TOSI could conceptually be 120%, 140%, 200%, and so on. The values of TOSI indicate directly how much additional green is needed to disperse the overflow queue. Detrimental effects in the spatial dimension are characterized by the inability of upstream traffic to proceed due to blockage at the downstream intersection. In this case, vehicles are not discharged from the upstream intersection even though the signal is green. Therefore, some portion of the green time of the upstream intersection becomes unusable. The amount of green time that is unusable is quantified by SOSI, ranging from 0% to 100%. When SOSI = 100%, all of the green time for the phase is wasted because the downstream vehicles cannot move. SOSI = 100% is a distinctly different situation than TOSI = 100%. When TOSI = 100% and there is downstream capacity to receive vehicles, this phase can benefit greatly from increasing the green time. When SOSI is 100%, there is no need to allocate more green time to the phase, unless the downstream blockage is dissipated. The values of SOSI essentially indicate how much additional green time is needed at the downstream intersection to disperse traffic so that upstream traffic can move. SOSI is also affected by the offset relationship between the upstream and downstream intersections. TOSI is related to how the upstream intersection and the downstream intersection are related. Poor offsets can create TOSI effects if the upstream platoon is released too early. Therefore, in most situations it is important to consider more than one intersection at a time when considering mitigation strategies. In the next section we provide a brief summary of the motivation for the queue estimation technique followed by the theory and examples of TOSI and SOSI computation measures. Motivation for the Measurement of Queue Length and Oversaturation Severity An oversaturated traffic facility, is generally defined as demand exceeds the capacity. The degree of saturation, i.e. the volume/capacity ratio, is defined as: i i i vX c = Equation (Eq.) 1 where Xi is the degree of saturation for lane group i; vi and ci are demand flow rate and capacity for lane group i, respectively. A lane group or approach is oversaturated when Xi >1. For a single intersection with two competing Eq. 2 streams, Gazis (1964) expanded this oversaturation concept by proposing the following inequality: 1 ( )a b a b q q L s s C+ > − Eq. 2 Operation of traffic signal systems in oversaturated conditions Page 47

where qa and qb are arrival rates for two conflicting directions; sa and sb are saturation flow rates for two directions; L is the total lost time; and C is the cycle length. Direct application of these definitions to detect the onset and quantify the duration and extent of oversaturation is difficult partly because of the uncertainty of the capacity and saturation flow, and partly due to the difficulty to measure the arrival flow. Using current data collection systems for oversaturated situations, the detectors typically cannot distinguish the true arrival rate because a queue grows past their fixed-point locations. Traffic demand is simply not measurable when a fixed-location detector is occupied with vehicular queue. Alternatively, oversaturation has also been characterized as “a stopped queue cannot be completely dissipated during a green cycle” (Gazis, 1964), or “traffic queues persist from cycle to cycle either due to insufficient green splits or because of blockage” (Abu-Lebdeh & Benekohal, 2003). These definitions were discussed in the previous section of this report. The key concept in the definitions is not only the estimation of the queue length, but also the portion of the queue that is residual or overflow from the previous cycle. Many other alternative measures have been defined (refer to Appendix A of this report for a comprehensive literature review) for degree of saturation, but they do not provide enough information on the oversaturated condition for accurate decision making. Methods such as green utilization can indicate the need for more green, but not quantify how much. To the best of our knowledge, previous research studies using traffic data from signal systems to diagnose and identify oversaturation are mostly qualitative and incomplete. Conceptual definitions discussed in the literature review are either not applicable in the real world or have other deficiencies. Since detection of the onset of oversaturation as well as quantifying the severity of oversaturation is a critical step before applying appropriate mitigation strategies, it becomes imperative to have an implementable and quantifiable measure of oversaturation and a coherent methodology to identify the situation. This component of the research project is intended to fill that gap. This section is organized as follows. First we discuss overflow queue length as a quantifiable measure of oversaturation. Overflow queue is measurable from typical vehicle-actuated traffic signal systems with advanced detection on the subject approach and access to second-by-second detector and phase timing data. Next, the methodology for identification and quantification of oversaturation is then described. Finally, the section concludes with the results from field testing of the methodology in the real world and a summary of the implications for the other components of the research project. Conclusions and directions for future work are summarized in Chapter 4. A Quantifiable Measure of Oversaturation Since the general definition of oversaturation, i.e. traffic demand exceeding the capacity of a facility, cannot be applied directly to detect the occurrence of oversaturation, we propose a Operation of traffic signal systems in oversaturated conditions Page 48

measure of oversaturation by quantifying its detrimental effects. The detrimental effect of oversaturation can be described in temporal and/or spatial dimensions, both of which lead to the reduction of usable green time in a cycle for a signalized approach. Detrimental effects of oversaturation in the temporal dimension are characterized by an overflow queue at the end of a cycle. These overflow vehicles were intended to pass through the intersection during the current cycle. Because of insufficient green splits, these overflow vehicles were not able to be discharged and must be serviced in the next cycle. The portion of next green time phase that is used to discharge the overflow queue becomes “unusable” for the traffic arrivals during that cycle. If the arrival rate remains the same and the green time remains inadequate, eventually all of the green time is spent serving the overflow queue and the queue continues to grow longer. Detrimental effects of oversaturation in the spatial dimension can be characterized by a spillover from downstream traffic. When spillover happens on an approach, the downstream link is blocked and vehicles cannot be discharged from the intersection during the green phase. Therefore a portion of the green time becomes unusable, because while the light is green the vehicles at the stop-bar cannot proceed. The most common cause of spillover is that the downstream link is fully occupied by a queue when the light turns green. Therefore the condition of oversaturation is characterized by an overflow queue at the end of a cycle creating detrimental effects on the following cycle, or by a downstream spillover within a cycle creating detrimental effects on the upstream approach. To quantify the detrimental effects in either the temporal or spatial dimensions, we introduce the oversaturation severity index (OSI) by using the ratio between unusable green time and total available green time in a cycle. OSI will be a non-negative percentage value between 0 and 100, with 0 indicating no detrimental effect for signal operation, and 100 indicating that all available green time becomes unusable. We further differentiate OSI into TOSI and SOSI. TOSI describes the detrimental effects created by overflow queue, i.e. the detrimental effect in the temporal dimension. SOSI describes the detrimental effects caused by spillover, i.e. the detrimental effect in the spatial dimension. Although both TOSI and SOSI can be calculated using the ratio between unusable green time and total available green time, the meanings of “unusable” are distinctly different. For TOSI, the “unusable” green time is the equivalent green time to discharge the overflow queue in the following cycle while for SOSI, the “unusable” green time is the time period during which a downstream link is blocked and the upstream discharge rate is zero. Since TOSI quantifies the detrimental effect of oversaturation on the following cycle, the duration and frequency of TOSI greater than zero becomes a fundamental indicator of traffic congestion at the intersection level. On the other hand, SOSI describes the detrimental effect of oversaturation caused by a downstream queue spillover, indicating a route-level problem. From a practical Operation of traffic signal systems in oversaturated conditions Page 49

perspective, the presence of TOSI >0 and SOSI>0 in a series of compatible approaches is the primary method by which to judge a critical route in an oversaturated system. The differentiation of TOSI and SOSI identifies the causal relationship of arterial traffic congestion. Positive TOSI indicates that the available green time is insufficient for queue discharge and an overflow queue is generated at the end of a cycle. Subsequently, in the following cycles, the queue may grow and spillover to an upstream intersection creating a positive SOSI at the upstream intersection. Clearly in this case a positive S-OSI at the upstream intersection is caused by the downstream bottleneck. Note that a downstream bottleneck may lead to the situation that both SOSI and TOSI of the upstream intersection are greater than zero because a portion of the green time is wasted due to downstream blockage (i.e. SOSI> 0) and an overflow queue may be generated (i.e. TOSI> 0) due to the inability to fully discharge the queue. With the TOSI and SOSI oversaturation severity indices, the focus of the identification algorithm shifts from measuring travel demand to quantifying detrimental effects. The classification and quantification of detrimental effects created by oversaturation are very important for traffic management, because different oversaturated situations call for different mitigation strategies For example, an isolated intersection with positive TOSI values on one or more approaches can be mitigated by extending green times. An arterial corridor with multiple intersections having positive TOSI and SOSI values requires the adjustment of green times as well as offsets to prevent further deterioration of oversaturation. A heuristic methodology for directly using TOSI and SOSI values to adjust green times on an oversaturated route is presented later in this Chapter. In the following section, we describe two algorithms for the identification and quantification of oversaturated conditions. The first algorithm estimates the overflow queue length (and correspondingly, TOSI), and the second algorithm detects spillover conditions and estimates SOSI. Algorithms for Identification of Oversaturation The identification algorithms discussed in the following section will work with typical detector (6’x6’) configurations for a vehicle-actuated signalized intersection, i.e., with either short stop-line detectors for vehicle presence detection or advance detectors that are a few hundred feet upstream from the stop line for green extension. Throughout this section, we will assume advance detectors are available and will note the necessary changes if the only available detector is located at the stop-bar. We also assume that high-resolution (i.e. second-by-second or event-based) traffic signal interval (i.e. green, yellow, red) data can be collected. The availability of high-resolution traffic signal data has been increased in recent years. For example, second-by-second detector data has been used by ACS-Lite (Luyanda et al., 2003). Continuous event-based signal data, including both vehicle-detector actuation events and signal phase change events, has been collected and archived by the SMART-Signal system (Systematic Operation of traffic signal systems in oversaturated conditions Page 50

Monitoring of Arterial Road Traffic and Signals) developed at the University of Minnesota (Liu & Ma, 2009; Liu et al., 2009a, 2009b). Phase timing and detector data is also stored on the ASC3 controller and can be retrieved via FTP (Smaglik, et al, 2007). Although the algorithms presented in this section are demonstrated by using event-based data from the SMART-Signal system, they are also applicable to second-by-second signal and detector data coming from any other traffic signal management system. Algorithm for Overflow Queue Length Estimation An overflow queue at an intersection refers to those vehicles that are part of the discharging platoon that cannot pass through the intersection during the green time. An overflow queue also represents the minimum queue length at the end of a cycle as additional vehicles may join the queue from side street turning movements. Vehicles in the overflow queue then occupy a portion of green time in the next cycle. The ratio between the overflow queue discharge time and the total available green time is then denoted as TOSI. Estimation of overflow queue length requires the reconstruction of queue length profiles within a cycle. As the traditional input-output approach for queue length estimation can only handle queues that are shorter than the distance between the vehicle detector and the intersection stop line, in this section we adopt the queue length estimation method developed by Liu et al. (2009a). Both maximum and minimum queue lengths can be calculated using this method. In the following discussion we provide a brief discussion of the queue length estimation algorithm, focusing on the application of this method to the estimation of both oversaturated conditions measured by TOSI and SOSI. The queue estimation method is based on the identification of traffic state changes and the associated shockwaves that occur during each cycle. The information in Figure 17. Shockwave profile within a cycle , assumes there is no overflow queue from past cycles, so at the beginning of the red signal, the vehicles that arrive at the intersection are forced to stop which creates a queuing shockwave (v1) spreading backward from the stop line. At the beginning of the effective green time, vehicles begin to discharge at the saturation flow rate (assuming there is no blockage downstream) forming the discharge shockwave (v2), again spreading upstream from the stop-line. The discharge shockwave (v2) usually has higher speed than (v1), so the two waves will meet some time after the start of the green time, which is the time that the maximum queue length is reached. As soon as the two shockwaves meet, a departure shockwave (v3 in Figure 17. Shockwave profile within a cycle ) is generated, spreading toward the stop line. Here the front of the departure shockwave reflects the discontinuity between the saturated discharging traffic flow and the new traffic arrivals after the maximum queue length is reached. An overflow queue is formed sometime after the start of the red signal of the next cycle when the departure shockwave (v3) meets the compression Operation of traffic signal systems in oversaturated conditions Page 51

shockwave (v4). The compression shockwave (v4) is similar to the queuing shockwave (v1), as both shockwaves form a stationary queue. The difference between the two shockwaves is that the compression shockwave represents traffic discontinuity from saturated traffic flow to the “jammed” traffic condition, while the queuing shockwave represents a change to the jammed traffic condition from arriving traffic, which is not necessary in a saturated state. The shockwave motions described above will repeat from cycle to cycle. Distance Time 1v 2v n gT n rT nTmax 1+ngT 3v nTmin 5v 1+n rT 4v A B CLoop Detector H AT BT CT dL nLmax D nLmin 1v A' Trajectory of Shockwave Residual Queue Figure 17. Shockwave profile within a cycle Intuitively, the queuing profile including the maximum queue length ( max nL , i.e., the maximum queue length for the cycle n) and the minimum queue length ( min nL , i.e., the overflow queue length for the cycle n) can be easily derived if the times when the shockwaves cross the detector location can be identified (indicated as “break points” A, B, and C in Figure 17. Shockwave profile within a cycle). High-resolution detector data, which provides at least second-by-second detector occupancy time and gaps between consecutive vehicles, implies the changes of traffic state and can therefore be utilized to identify these break points. Figure 18 presents an example of detector occupancy time (see Figure 18a) and vehicle gaps (see Figure 18b) within a cycle. This sample data was collected from an advance detector at one intersection at the SMART-Signal test-bed on TH55 in Minneapolis, MN. As shown in the figure, a sudden increase of occupancy time indicates that queue (v1) spills back to the advance detector. The time of break point A (TA) can then be identified as the time when the occupancy is significantly increased. Similarly, the time of break point B (TB) can be identified as when the occupancy drops to the normal value. This change indicates that the discharge shockwave (v2) spreads back to the advanced detector and the vehicles begin to move. Operation of traffic signal systems in oversaturated conditions Page 52

Break point C (TC)represents the time when the departure shockwave (v3) crosses the detector line. Before break point C appears, vehicles discharge at the saturation flow rate, i.e., the saturation traffic state (qm, km); and after (TC), the traffic condition changes back to the arrival traffic state (qa, ka). The change of these two traffic states (from saturation to free-flow arrival) is indicated by the variation of the time gaps. As indicated in Figure 18b, before TC, the time gaps between vehicles are consistently small (less than 2.5 seconds), meaning that most of the vehicles are discharged at the saturation flow rate. But after TC, the vehicle gaps become much larger and their variances are significantly increased. Therefore a threshold value of a time gap can be used to identify the break point C time TC. Case 1 - Long Queue 0 10 20 30 40 50 7:26:07 7:26:50 7:27:33 7:28:16 7:29:00 Case 1 - Long Queue 0 2.5 5 7.5 10 7:26:07 7:26:50 7:27:33 7:28:16 7:29:00 Detector Occupancy Time Break Point A Break Point B Time Gap Between Consecutive Vehicles ),( mm kq ),( na n a kq Pattern I: Saturation condition Pattern II: Free flow arrival Break Point C (Sec) (Sec) Time Time a) b) Figure 18. a) detector occupancy profile in a cycle; b) time gap between consecutive vehicles in a cycle. Once break points (A, B, and C) have been identified, the flow and density of each traffic state (i.e. the arrival traffic state (qa, ka), saturation traffic state (qm, km), and jammed traffic state (0, kj)) can be calculated based on detector occupancy times and time gaps between vehicles. Then the wave speeds of v1, v2, and v3 can be estimated using following equation: 2 1 2 1 q qqv k k k −∆ = = ∆ − Eq. 3 where q1, k1 are the flow and density of the upstream traffic and q2, k2 are the flow and density Operation of traffic signal systems in oversaturated conditions Page 53

of the downstream traffic. Using the estimated shockwave speeds from the above equation, the maximum queue (both length max nL and time max nT ) and the minimum queue (both length min nL and time min nT ) during the nth cycle can be calculated based on the shockwave profile (see Figure 17) by the following equations: max 2 3 max max 2 ( ) 1 1 ( ) n C B d n n d B T TL L v v L LT T v − = +   +       − = +  Eq. 4 1max max 3 min 3 4 1 min min 4 1 1 n n n g n n n n g L T T vL v v LT T v + +    + −     =   +      = +  Eq. 5 where Ld is the distance from the stop line to the loop detector; and Tgn+1 is the end of green of the (n+1)th cycle. It is necessary to identify whether an overflow queue is present at the end of the cycle before the calculation of the minimum queue length: 1max max 3 1max max 3 Without Residual Queue With Residual Queue n n n g n n n g L T T v L T T v + +  + <    + ≥ Eq. 6 For severely congested traffic conditions, the break point C may not be able to be found during the green phase. In addition, large trucks may make it difficult to identify break point C. In such cases, the traffic pattern does not change during the green phase and vehicles keep discharging at the saturation flow rate (see Figure 19). Then an overflow queue must exist, at least, between the detector location and the stop line. Eq. 4 cannot be applied to calculate the maximum queue length since the shockwave speed (v3) cannot be calculated. Operation of traffic signal systems in oversaturated conditions Page 54

Under such conditions, the complete queue profile cannot be recovered from the detector data. However, since the entire green time has been used for queue discharge the number of vehicles passing the detector location during the green time can be counted (between TB and Tgn+1), so that a minimum of the maximum queue length, i.e. min( max nL ), can be estimated by simply taking the end of cycle (Tgn+1) as TC (see Figure 20). Since the space headway (ljam) and the velocity of the discharge wave (v2) can be assumed constant at jammed traffic conditions, the following equation can be used to identify the minimum overflow queue: ( ) max max max 2 min( ) If Point cannot be identified: min min( ) n jam d n n n r L l N L C L T T v  = ⋅ +   = +  Eq. 7 where N is the traffic count between TB and Tgn+1; ljam is the space headway at jammed traffic conditions (assumed as a known constant); and Trn is the end of the red phase of the nth cycle. Occupation Time 0 20 40 60 80 17:27:06 17:27:49 17:28:32 17:29:15 17:29:59 Gap 0 3 6 9 12 17:27:06 17:27:49 17:28:32 17:29:15 17:29:59 Detector Occupancy Time Break Point A Break Point B Time Gap Between Consecutive Vehicles(Sec) (Sec) Time Time No pattern changes, always discharge at saturation flow rate; Point C cannot be identified a) b) Figure 19. Break points identification (Point C cannot be identified) Operation of traffic signal systems in oversaturated conditions Page 55

Distance Time 1v 2v n gT n rT maxmin( ) nT 1( )ng CT T + 3v minmin( ) nT 5v 1+n rT 4v A B CLoop Detector H AT BT dL maxmin( ) nL D minmin( ) nL 1v A' Trajectory of Shockwave Figure 20. Calculation of overflow queue length when Point C cannot be found Then v3 can be calculated by Eq. 8: ( ) ( ) max 3 1 max min If point C cannot be identified: min n d n n g L L v T T+ − = − Eq. 8 The coordinate of the minimum of the overflow queue length, i.e. min( min nL ) and min( min nT ) for Point D, can then be estimated using Eq. 5. If an overflow queue exists at the end of a signal cycle, some portion of the green time in the following cycle will be utilized to discharge the overflow vehicles and therefore becomes the unusable green time for that cycle. The unusable green time can be determined by calculating the number of vehicles in the overflow queue multiplied by the saturation discharge headway (~2 seconds). The detrimental effect caused by the overflow queue therefore can be quantified by the oversaturation severity index in the temporal dimension (T-OSI): min / T-OSI 100% 100% n jamL l hunusable green time total available green time G ⋅ = × = × Eq. 9 where G is the effective green time, and h is the saturation discharge headway. We should note that, when only stop-line detection is available, an overflow queue can be detected if break point C cannot be identified within the green time. Although the length of the Operation of traffic signal systems in oversaturated conditions Page 56

overflow queue cannot be measured with stop-line detection only, it is sufficient to say that oversaturation may have occurred at this intersection for this cycle, i.e. TOSI > 0. This assumes the stop-line detector is sufficiently short enough to capture the gaps between successive vehicles at discharge speeds. Algorithm for Identification of Spillover Spillover creates detrimental effects for the operation of upstream traffic signals. Identification of spillover is particularly important because it indicates that traffic congestion has started to spread out in the network involving multiple intersections. To identify spillover using traffic signal phase and detector data, we first need to illustrate the concept of Queue-Over-Detector (QOD), i.e. the complete occupation of a detector for a relatively long time due to a vehicular queue. Generally, there are two types of QOD. One is caused by red signal phases. Due to the normal cyclical signal timing, vehicles slow down and stop due to the red light and then resume traveling as the light turns green. If a vehicle in the queue stays on the detector because of a red light, detector occupancy time increases continuously, creating the first type of QOD. The second type of QOD is caused by spillover. When a queue spills back from a downstream intersection to an upstream intersection, the upstream intersection may be blocked and vehicles cannot be discharged even when the signal is green. Some vehicles will stay on the detector for a while creating a prolonged detector occupancy time after the traffic light turns green. Conceptually, the duration of the second type of QOD is equivalent to “the time period within a signal cycle in which the vehicles would be moving at the location of the detector during the green time in the absence of disturbances”, which was briefly discussed in Mueck (2002). Therefore, the detrimental effect of a spillover can be quantified by measuring the duration of the second type of QOD. It is not difficult to identify QOD using high-resolution phase and detector data since it is simply indicated by a relatively large occupancy time (or percentage occupancy value keeping at 100% for an extended period). In our implementation, a threshold value of 3 seconds (which is roughly equivalent to 5mph of speed assuming a 22ft. effective vehicle length) is used for the identification of QOD. We now need to differentiate between the two types of QOD. Figure 21 demonstrates both types of QOD by drawing each vehicle trajectory starting from upstream to downstream. Since the first type of QOD is caused by the red signal, the maximum occupancy time is the red interval. Considering the overflow queue from the last cycle and queue propagation at the green start, the first type of QOD can only happen within the range between the compression shockwave )v4) and the discharge shockwave (v2), which have the same velocity (see Figure 21). Therefore if QOD occurs between 4( / ) n g dT L v+ and 2( / ) n r dT L v+ , it is the first type of “normal” QOD. Operation of traffic signal systems in oversaturated conditions Page 57

The second type of QOD, which occurs outside of the time interval 4 2[ / , / ] n n g d r dT L v T L v+ + , indicates that a spillover has happened at a downstream location. This creates unusable green time, meaning that vehicles cannot be discharged during the green time because of the downstream queue. Therefore when a QOD event is identified, spillover occurs when the QOD starting time QODstartT or ending time QOD endT falls outside of the time interval 4 2[ / , / ] n n g d r dT L v T L v+ + . An example case of the second type of QOD is demonstrated in Figure 21. QOD caused by red interval Distance Time A SC QOD ST OCC St QOD ET 4v 2v QOD caused by spillover Stop-bar detector Advance detector n gT n rT 1ngT +OCC Et E Downstream Upstream Figure 21. Queue-over-detector phenomena The oversaturation severity index in the spatial dimension (S-OSI) can then be calculated as: ( ), , S-OSI 100% 100% QOD QOD end i start iT Tunusable green time total available green time G − = × = × ∑ Eq. 10 where , QOD start iT and , QOD end iT are the starting and ending times of the thi occurrence of the second type of QOD. In order to improve the robustness of the identification of the spillover condition, the maximum queue length of the downstream intersection should also be estimated using the method discussed previously. If the estimated maximum queue length at the downstream approach is longer than or equal to the link length, then oversaturation on that link is confirmed. This can be used to avoid some diagnosis errors caused by incidents (for example, the detector is occupied by a disabled Operation of traffic signal systems in oversaturated conditions Page 58

vehicle for a relatively long period of time or the detector is placed at or near a bus stop and a transit vehicle stays on the detector for some time). These “incidents” may generate the second type of QOD, but it does not necessarily indicate an oversaturated condition on the downstream link. Here we should note that the queue length estimation method discussed previously cannot be applied directly to an intersection with queue spillover from a downstream link. With spillover, queued vehicles can only be discharged when the downstream blockage is cleared and the signal light remains green. For the example shown in Figure 22, when the traffic light turns green at intersection i (Trn), queued vehicles begin to discharge, but the discharging process is disturbed because the queue at the downstream intersection i+1 grows and eventually spills over to the upstream intersection i. A second type of QOD will be identified by the advance detector, starting at time QODstartT . QOD ends when the spillover is cleared, i.e. at the time QOD endT . Under this condition, the queue estimation method needs to be modified because break points A, B, and C need to be updated as A’, B’, and C’, as shown in the Figure 22. Eq. 4 through Eq. 8 remain valid after updating the definitions of A, B, and C. Distance Time 1v 2v n gT n rT 3v QOD endT 1+n rT A B C Loop Detector H AT BT dL max nL D min nL 1v Time 4v B' QOD startT 2v 2v 2v 1v C' QOD Caused by Spillover 4v A' Intersection i Intersection i+1 Figure 22. Updated breakpoints A’, B’, and C’ Example: Field-test Results Trunk Highway 55 (TH55), a major arterial in Twin Cities, Minnesota, was used as the test site for validating the measurement of TOSI and SOSI values. Figure 23a illustrates the six coordinated intersections at the test location. Figure 23b shows the detector layout of four intersections along Operation of traffic signal systems in oversaturated conditions Page 59

the arterial. Advance detectors are located on the major approaches and stop-bar detectors on the minor approaches. Stop-bar detectors are used to detect the presence of vehicles and advance detectors are located about 400 feet upstream from the stop line to detect vehicles for green extension on the coordinated phases. To verify the estimated queue length, we also installed (6’x6’) stop-bar and link entry detectors along TH55 at these six intersections (see Figure 23 for the detector configurations at the four major intersections). These additional detectors are not used for regular traffic signal operations; rather, the data collected from these detectors are used for algorithm verification. The detectors are monitored on a lane-by-lane basis. TH 55 Advanced detectors a) b) Rhode Island Ave. Glenwood Ave. TH 55 Stopbar detectors Winnetka Ave.Boone Ave. Additional detectors Phase 6 Phase 2400 ft 2635 ft 842 ft 1777 ft 375 ft Figure 23. a) TH55 data collection site; b) detector layout High-resolution event data including signal phase changes and vehicle-detector actuations are continuously collected from the six intersections and are archived by the SMART-Signal system and transmitted in real time back to the University of Minnesota’s ITS Laboratory. Figure 24 shows sample data collected at the study site including the start and end times of each vehicle-detector actuation event and every signal phase change event. The signal phase duration can be calculated from the time difference between the start and end of a signal event. The time interval between the start and end of a vehicle actuation event is the detector occupancy time. The time interval between the end of a vehicle actuation event and the start of next vehicle actuation event (from the same detector) is the time gap between two consecutive vehicles crossing the detector. Operation of traffic signal systems in oversaturated conditions Page 60

08:09:15.012, D8 on, 7.902s 08:09:15.481, D8 off, 0.468s 08:09:16.761, G3 off, 29.389s 08:09:16.761, Y3 on, 179.021s 08:09:17.620, D9 on, 2.686s 08:09:18.151, D10 on, 2.593s 08:09:18.307, D9 off, 0.687s 08:09:18.823, D10 off, 0.671s 08:09:20.244, Y3 off, 3.482s 08:09:21.649, D22 on, 80.953s 08:09:22.008, D22 off, 0.359s 08:09:23.242, G1 on, 172.806s Detector #8 on at 08:09:15.012; Vacant time is 7.902s Green Phase #3 off at 08:09:16.761; Green duration time is 29.389s Detector #9 off at 08:09:18.307; Occupy time is 0.687s Yellow Phase #3 off at 08:09:20.244; Yellow duration time is 3.482s Green Phase #1 on at 08:09:23.242; Red duration time is 172.806s Figure 24. Sample data collected at the test site Estimation Results of Overflow Queue Length Using the event-based data from the SMART-Signal system, the queue length estimation method discussed above was applied for the estimation of overflow queue lengths. We note that field evaluations of the queue length estimation method have been conducted by a Minneapolis-based transportation consulting firm and the evaluation results have been reported in Liu et al. (2009a). The average of the Mean Absolute Percentage Error (MAPE) of the queue length estimation is within 15%. Figure 25 presents an oversaturation case based on the data collected by an advance detector on the eastbound approach at the intersection of Glenwood Avenue on Feb. 28, 2008. As indicated in Figure 25, overflow queues appeared at the end of the first two cycles. In this particular case, the reason for the occurrence of oversaturation was signal preemption on the side street which created a shorter cycle length in the second cycle (the cycle length was 132 seconds during the preemption which was 48 seconds less than the normal cycle length). Due to the insufficient green time, some queued vehicles could not be discharged until the next cycle. Using the estimated overflow queue length, the oversaturation severity indices for these two cycles are estimated at 7.5% and 7.0%, meaning that at least 7.5% and 7.0% of green time in these cycles will be used for the discharge of the overflow queue. In the calculation of these severity indices, we have assumed that the space headway for the jammed condition is 25 feet and the saturation headway is two seconds. It should be noted that the estimated maximum queue lengths (500 - 600ft) during these three cycles are not long when compared with the link length (1777ft from Glenwood to Rhode Island). However, overflow queuing occurs at the end of the first two cycles indicating that the volume of traffic joining the discharging platoon after the last stopped vehicle has started to move is rather high. A portion of those newly arriving vehicles joins the discharging platoon but could not pass the intersection during the green phase, which forms the overflow queue. Operation of traffic signal systems in oversaturated conditions Page 61

Case of Oversaturation 0 100 200 300 400 500 600 700 16:48:00 16:49:26 16:50:53 16:52:19 16:53:46 16:55:12 16:56:38 16:58:05 Queue Length Profile at Eastbound Glenwood Distance (feet) Time Residual Queue Figure 25. Estimation results of overflow queue for eastbound approach at Glenwood As we discussed previously, if the entire green time is used for queue discharge, the departure shockwave cannot be identified. In this case we can only measure the minimum of the maximum queue length within a cycle. We present such cases in Figure 26 below. The data was collected from an advance detector on the eastbound approach at the Boone Avenue intersection on Feb. 28, 2008. During the first five cycles, the departure shockwaves could not be identified, so we can only estimate the minimum values of the maximum queue length. The queue lengths in this case are quite long, averaging around 1500 feet in the first five cycles. The minimum values of the overflow queue length are also estimated, as shown in Figure 26. The minimum oversaturation severity indices (TOSI) are estimated at 9.8%, 19.4%, 10.5%, 11.3%, and 10.3% for these five cycles. The oversaturated condition persists until the sixth cycle. Queue Trajectories 0 300 600 900 1200 1500 1800 7:48:00 7:50:53 7:53:46 7:56:38 7:59:31 8:02:24 8:05:17 Queue Length Profile for Eastbound Approach at Boone AveDistance (feet) Time Residual Queues G=98sec G=112sec G=98sec G=114sec G=115sec G=116sec Figure 26. Estimated overflow queue length for eastbound approach at Boone Avenue Operation of traffic signal systems in oversaturated conditions Page 62

Example Results for Detection of Spillover The spatial detrimental effect caused by oversaturation is characterized by spillover, which can be diagnosed by identifying the second type of QOD. In Figure 27, we present the detector occupancy time within an afternoon peak hour cycle on Nov. 17, 2008 for westbound TH55 at Rhode Island Avenue. As shown in the figure, QOD caused by spillover is identified. This means that vehicles cannot be discharged from the intersection although the traffic light is green. Oversaturation is therefore identified at this intersection for this cycle. Occupation Time 6800 7000 7200 7400 7600 7800 17:12:20 17:13:03 17:13:47 17:14:30 17:15:13 Detector Occupancy Time for Westbound TH 55 at Rhode Island Ave. Distance (feet) Time Occupancy Time of Advance Detector Occupancy Time of Stop-bar Detector 2v2v QOD caused by red phase QOD caused by spillover Stop-bar Detector Advance Detector Figure 27. Identification of QOD caused by downstream spillover To further verify that there is a spillover happening in the downstream link, vehicle trajectories are derived based on the vehicle events collected by the advance detector at the intersection of Rhode Island Avenue. A simplified car-following model, which is similar to the one developed by Newell (2001), is used to generate the vehicle trajectories for the purpose of illustration. Vehicles are assumed to accelerate if their speeds are less than free-flow speed (55mph on this particular arterial) and decelerate if higher than the free-flow speed, approaching a red light or the back of a queue. The distance between any two vehicles satisfies a safety distance constraint which is determined by the speeds of the two consecutive vehicles. The driver’s reaction time is set at 1.0 second and space headway between two vehicles in a stationary queue is assumed as 25 feet. The maneuver decision of a vehicle to pass the intersection or not during the yellow time is determined according to its speed, remaining yellow time, and distance from the front vehicle. Lane-changing behaviors are not taken into account in this model. The estimated vehicle trajectories starting from the advance detector line at the intersection of Rhode Island Avenue and ending at 500 feet downstream from the intersection of Winnetka Avenue are presented in Figure 28. As clearly indicated in the figure, the downstream queue spills back from Winnetka to Rhode Island and blocks the Rhode Island intersection during the green time, resulting in QOD. Operation of traffic signal systems in oversaturated conditions Page 63

Traj 7000 7500 8000 8500 9000 17:12:03 17:12:46 17:13:29 17:14:12 17:14:56 17:15:39 17:16:22 17:17:05 Distance (feet) Intersection Winnetka Intersection Rhode Island Location of Advance Detector Location of Advance Detector Time Spillover Vehicle Trajectories in the Case of Spillover from Winnetka to Rhode Island Figure 28. Vehicle trajectories in the case of spillover from Winnetka to Rhode Island Further investigation indicated that this spillover started at 17:06:31, continued for approximately 30 minutes and ended at 17:36:31. The QOD due to downstream spillover was found in nine consecutive cycles. This is also confirmed by observing the queue length profile of the downstream intersection at Winnetka Avenue during these cycles. As shown in Figure 29, the maximum queue lengths for these nine cycles are around 1200 – 1500ft, which is significantly longer than the link length (842feet). This indicates that, during these cycles, the Rhode Island intersection must be blocked for a portion of green time (S-OSI > 0). Interestingly, because of the reduction in usable green time, overflow queues were also generated at the Rhode Island intersection for some cycles (i.e. T-OSI > 0). This demonstrates that the oversaturated traffic condition at Winnetka (T-OSI > 0 and S-OSI = 0) has spread upstream, leading to insufficient green time to discharge the queue (T-OSI > 0 and S-OSI > 0) at Rhode Island. Please see Table 7and Table 8 for oversaturation severity index estimates at Winnetka and Rhode Island. Since there was no downstream blockage at Winnetka, S-OSI was always zero during that time period. Operation of traffic signal systems in oversaturated conditions Page 64

0300 600 900 1200 1500 1800 17:05:17 17:12:29 17:19:41 17:26:53 17:34:05 17:41:17 Time Queue Length Profile at the Intersection of WinnetkaDistance (feet) Figure 29. Queue length profile at the intersection of Winnetka when Rhode Island intersection is oversaturated Operation of traffic signal systems in oversaturated conditions Page 65

Table 7. Oversaturation Severity Indices (OSI) for Winnetka Avenue Intersection Winnetka Avenue Cycle Start Available Green (sec) OSI: Created by Overflow Queue OSI: Created by Spillover Overflow Queue (ft) Unusable Green (sec) T-OSI (%) Unusable Green (sec) S-OSI (%) 17:06:14 101 0.0 0.0 0.0 0.0 0.0 17:09:14 101 180.3 0.0 0.0 0.0 0.0 17:12:14 101 178.8 14.4 14.28 0.0 0.0 17:15:14 101 0.0 14.3 14.16 0.0 0.0 17:18:14 101 149.1 0.0 0.00 0.0 0.0 17:21:14 101 157.6 11.9 11.81 0.0 0.0 17:24:14 102 156.4 12.6 12.36 0.0 0.0 17:27:14 106 130.1 12.5 11.81 0.0 0.0 17:30:14 101 153.4 10.4 10.31 0.0 0.0 17:33:14 105 0.0 12.3 11.69 0.0 0.0 17:36:14 102 0.0 0.0 0.00 0.0 0.0 Table 8. OSI for Rhode Island intersection Rhode Island Cycle Start Available Green (sec) OSI: Created by Overflow Queue OSI: Created by Spillover Overflow Queue (ft) Unusable Green (sec) T-OSI (%) Unusable Green (sec) S-OSI (%) 17:06:31 136 0.0 0.0 0.0 0.0 0.0 17:09:31 136 0.0 0.0 0.0 3.0 2.2 17:12:31 136 89.6 0.0 0.0 28.0 20.6 17:15:31 136 164.3 7.2 5.3 28.8 21.2 17:18:31 136 0.0 13.1 9.7 15.0 11.1 17:21:31 136 180.4 0.0 0.0 41.7 30.6 17:24:31 135 165.3 14.4 10.7 34.1 25.2 17:27:31 139 138.2 13.2 9.5 25.2 18.1 17:30:31 120 125.3 11.1 9.2 16.3 13.6 17:33:31 141 0.0 10.0 7.1 8.6 6.1 17:36:31 135 0.0 0.0 0.0 0.0 0.0 Operation of traffic signal systems in oversaturated conditions Page 66

Summary of Diagnostics for Severity of Oversaturation In this section, we presented a methodology for measurement of oversaturation (overflow queue lengths) from conventional detectors and high-resolution phase timing data and two derived metrics for the severity of oversaturation. The temporal detrimental effect of oversaturated conditions is characterized by the occurrence of overflow queues and the spatial detrimental effect of oversaturated conditions is characterized by the effect of downstream spillover on upstream queue discharge. We developed two algorithms to identify oversaturated approaches. The first method estimates the overflow queue length using a simple traffic model based on the estimation of forward and backward traveling shockwaves as vehicles arrive and depart at the approach. The second method estimates the effects of downstream spillover by identifying long detector occupancy times during the green phase. Two OSI were defined for quantitative characterization of the two types of oversaturation. The TOSI measure indicates the percentage of green time that is spent during the next cycle clearing the queue from the previous cycle. The SOSI measure indicates the percentage of green time that is wasted because of downstream blockage. Our field-test results on the TH55 arterial in the Twin Cities area demonstrate that the developed algorithms are very effective in identifying and quantifying oversaturated conditions. The approach to collecting and processing this information was implemented using the SMART-signal hardware harness and field processors developed in other previous research, but the models are simple enough to be implemented by others with access to second-by-second signal timing and lane-by-lane detector data. The presence of TOSI > 0 indicates the need for additional green time for a phase. For an individual intersection, the values of TOSI provide a direct indicator of how much additional green time is necessary for that phase to clear the overflow queue. Similarly, SOSI > 0 indicates the need for additional green time at a downstream location, or might indicate that the upstream green time should be shortened. In simple situations with just one affected approach, mitigation strategies are relatively simple to identify. However, when presented with oversaturation on more than just a single phase at an intersection or with TOSI and SOSI >0 for many intersections on a route it is not obvious what a rational approach to solving the problem might be. In addition, TOSI and SOSI do not directly measure storage blocking and starvation symptoms that are also problematic issues in oversaturated conditions. Our approach to the remainder of the research based on this initial development of real-time diagnostics is three-fold. First, we look at the problem from a “top-down” perspective (whereas, considering diagnostic metrics would be considered a “bottom-up” approach) by developing a methodology for design and evaluation of signal timing plans for oversaturated conditions. This methodology considers design principles for cycle, splits, and offsets to minimize the occurrence of TOSI and SOSI effects before they occur at all. The methodology considers both the design of timing plans and the schedule for implementing them by time-of-day to address the three primary regimes of oversaturated conditions (loading, processing, and recovery). This methodology is Operation of traffic signal systems in oversaturated conditions Page 67

described in the next section of the report. Two simulation examples of applying the methodology on real-world test networks are described in Chapter 4. Secondly, we describe the development of a tool for online application of pre-configured strategies (that could be designed with the methodology presented in the preceding section) using real-time detector data to determine when to switch from a “normal” operation to a plan designed for “loading” or from a plan designed for “loading” to one designed for “processing” and so on. Each strategy can be triggered using detection of TOSI and SOSI above configured thresholds. One simulation example of applying the approach to a real-world network is detailed in Chapter 4. Finally, we developed a heuristic approach using measured TOSI and SOSI values to directly modify green times on an oversaturated route. The heuristic approach adjusts splits and offsets on the route to drive TOSI and SOSI as close to zero as possible in order to maximize throughput on the critical route. This methodology and its application to two real-world networks are described in Chapter 4. Operation of traffic signal systems in oversaturated conditions Page 68

A Multi-Objective Methodology for Designing and Evaluating Signal Timing Plans Under Oversaturated Conditions In the previous section we described algorithms to calculate the intensity of oversaturation on an individual approach. This detailed information is necessary from a bottom-up perspective to quantify the presence and effects of oversaturated conditions. In this section, we describe a top- down methodology which will be used to explore the performance differences between signal timing strategies in oversaturated conditions. There are four essential parts to the design of timing plans for handling oversaturated conditions: (1) The identification of the critical routes and the flows along those routes, (2) The determination of ranges of feasible timing plan parameters that meet criteria to address oversaturation on those routes, (3) The selection of the objective function to solve for optimal timings, and (4) The scheduling of a sequence of timing plans that are tailored to each regime of oversaturated operation. Based on the lack of significant research in this area, for this part of the project, we explore several questions in this area and develop a comprehensive process for implementing this analysis: 1. Assuming certain design principles for timing plan design during oversaturated conditions, does optimization for different objectives result in substantive differences in performance? 2. As of traffic demand and resulting congestion changes over time, what is a best schedule for implementation of multiple timing plans? 3. Are there sets of timing plan parameters that out-perform other timing plan parameters for more than one optimization objective? 4. What design components of a complicated mathematical process can be distilled into principles that practitioners might be able to apply? This process is then applied in several simulation test cases which illustrate typical results for real-world networks. Comparisons of one set of timing parameters and the schedule for implementing multiple timing plans is then made using the comprehensive output measures available from the simulation model. It is first necessary to understand the nature of the traffic patterns on the network before designing optimal control strategies. During oversaturated conditions, the temporal and spatial extent of the congestion is always changing and different movements and routes may become critical, causing different types of detrimental effects over time. Designing optimal control strategies in these cases becomes challenging because of the wide range of potential approaches Operation of traffic signal systems in oversaturated conditions Page 69

that might be taken to mitigate any specific scenario. The systematic mathematical optimization procedure described in this section was developed in an attempt to provide a rational approach for arriving at specific timing plan parameters that take into account both oversaturated conditions and critical route flows. This is an experimental approach that builds upon previous research but still requires additional development to arrive at a process that a practitioner can directly apply. Overview of the Methodology The proposed methodology shown in Figure 30 starts by identifying the critical routes in the network. Using traditional origin-destination (O-D) estimation methods during congested periods can be challenging because congestion causes low volume counts on links and long travel times. Nevertheless, the analysis can still be carried out with reasonable accuracy. Critical routes can be determined using judgment calls by the local staff after on-site observation of vehicle flows. In most cases, experienced local staff would have a reasonable idea of the critical routes and peak periods. They can build from this knowledge to determine critical route design scenarios. This part of the analysis is critical in the overall timing strategy framework. Once the network’s critical routes have been identified and mapped into the network configuration, the problematic traffic symptoms of oversaturation can be directly determined (i.e., spillback, starvation, storage blocking, and cross blocking). A wide array of control strategies can be considered to address the detrimental effects of these problematic traffic symptoms. We provide a systematic procedure for determining a set of cycle, splits, and offsets for a particular objective function. Phase sequence, phase reservice, and other tactical treatments such as green time extension or truncation are not directly included in the procedure. Strategic measures, such as gating, are applied in an ad-hoc manner by determining the size of the network (traffic is gated at the most upstream location(s) considered in the system). Evaluation of potential control strategies is then carried out by extracting performance measures from the simulation output. Optimal control strategies can then be determined with regard to each performance objective using multi-objective (Pareto front) analysis. The details of the design principles for control strategies that address oversaturated conditions are presented in the next sections. These timing plan design principles are based on known traffic engineering concepts from the literature. Operation of traffic signal systems in oversaturated conditions Page 70

Figure 30. Framework for determination of control strategies used in this research Framework for Determination of the Traffic Flows on Critical Routes Volumes on critical routes can be determined using detailed theoretical analysis, including synthetic O-D estimation, volume correlation analysis, and clustering of detector data. It can also be determined using relatively new technological methods, such as Bluetooth data or data from the upcoming Connected Vehicles technologies. Alternatively, it could also be reasonably estimated using field observation and local knowledge of traffic patterns on the congested system. The methodology used in this research is illustrated conceptually in Figure 31. This step is indispensable in designing appropriate signal control strategies in the next step. There are two main parts to the identification of critical route flows. The first is to use correlation analysis between detector counts at different locations to determine which detector movements change simultaneously. For example, if all eastbound through movement detector volumes are highly correlated (mostly increase and decrease together) and their volume is high, then one can consider that as an indication that the eastbound movements on a corridor constitute a critical route. The same rationale can be applied to a whole network to trace all of the critical routes. The magnitude of traffic flow on each route determines the importance of each route and its Operation of traffic signal systems in oversaturated conditions Page 71

contribution to the design of the control strategy. The second key principle is the concept of volume spillover. If the volume on the critical route cannot be accommodated in the current time period, one must consider that additional flow (spillover) is present during the next analysis time period and one must consider timing plan parameters (cycle, splits, and offsets). In order to design a set of control strategies that can account for the detrimental effects of congestion, a set of problematic scenarios should be designed to encompass the extremes of the possible traffic patterns. That is, when the same system detector counts on a network can correspond to two possible critical route scenarios, both possible scenarios should be taken in consideration when designing control strategies. This is illustrated in Figure 31 in the step where the maximum feasible volume is determined on each critical route. Figure 31. Framework for volume estimation on critical routes Figure 32 illustrates the research framework for designing timing plans for critical routes under oversaturated conditions. The framework utilizes network configuration (i.e. link lengths, storage bay lengths, etc.) and critical route volumes to produce the basic signal timing parameters of cycle time, splits, and offsets. Cycle length in oversaturated conditions is determined based on the network’s link geometry and volume levels. Cycle length cannot exceed certain values on certain links to prevent queue spillback. Splits and offsets are then determined for each intersection through an iterative procedure. This iterative procedure protects the capacity on Detector Data Volume Analysis Correlation Analysis Movement Clustering Identify network critical routes Maximize network critical routes volume Background traffic Local Practitioners Opinions Volume on Critical routes Operation of traffic signal systems in oversaturated conditions Page 72

critical routes and attempts to prevent spillback and starvation which results in several sets of timing parameters. Since we now have a range of possible timing values, simulation is then used to evaluate the performance of the generated timing plans for the three principle optimization objectives: minimize delay, maximize throughput, and manage queues. Next, multi-objective analysis is conducted to eliminate the dominated timing plans and to identify the best non- dominated sets of timing parameters (cycle, splits, and offsets). This framework is illustrated in Figure 32and described in more detail in the following section. Figure 32. Timing framework for oversaturated conditions Cycle Length Determination Determining cycle length for the network during oversaturated conditions is a critical task. Failure to determine the optimal cycle will increase the possibilities of spillback and intersection blockage. In undersaturated conditions, cycle length is directly a function of the volumes and Operation of traffic signal systems in oversaturated conditions Page 73

capacities of the approaches in the system. In oversaturated conditions, however, cycle length is a function of the storage capacity of the links, the arrival rate during red intervals along the arterial, and the green split ratio at each intersection. For example, a network including a short link with a high arrival rate during red on that link would require a shorter cycle length to prevent spillback into the upstream intersection. Networks with longer approach distances can tolerate longer cycle times before problematic symptoms arise. The Internal Metering Policy (IMP) developed by Lieberman et. al. (2000), provides an upper bound of intersection background cycle length to avoid spillback at upstream intersections. This is the maximum cycle that ensures the queue formation shockwave dissipates before reaching the upstream intersection. Figure 33 illustrates the calculation of the maximum cycle length that prevents spillback (Lieberman, et al, 2000). Figure 33. Shockwave at signalized intersection Some typical upper bounds for cycle lengths using this equation are shown in Figure 34. A family of curves is presented that illustrates the highest feasible cycle length for specific link lengths and split ratios for a specific approach demand. Each of the blue lines indicates that cycle lengths which are below the line will not create spillback to the upstream intersection and generate overflow queues. For example, assuming the 800vph approach demand, a split ratio of 0.5 for the downstream through phase, and a 700ft link length, the maximum cycle time that could be implemented before spillback would occur is 150 seconds. Where: L: link length W: upstream intersection's width Ga: Effective green downstream h: discharge headway l: loss time Lv: vehicle effective length RL: location of where the shockwave is canceled C: Cycle length SF: safety factor (vehicle clearance) u: speed of queue discharge wave v: speed of leading vehicle in incoming platoon ω : speed of stooping wave Δ : relative signal offset     −       −− ≤ C lG L LSF L W L LhC a v v )( 1 Operation of traffic signal systems in oversaturated conditions Page 74

Figure 34. Upper-bound of cycle length that prevents spillback Roess et. al., (2004) presented another formulation to calculate the maximum cycle length in oversaturated conditions. In this formulation, maximum cycle length is a function of the downstream critical lane discharge rate (v) and the link length (L). Eq. 11 Some typical upper bounds for cycle lengths using this equation are shown in Figure 35. A family of curves is presented that relate the highest feasible cycle length for a specific link length (800ft) and red split ratios for varying saturation flow rate. Each of the blue lines indicates that cycle lengths which are below the line will not create spillback to the upstream intersection and generate overflow queues. For example, assuming an 1800 vph saturation flow rate and a 0.5 red split ratio, the maximum cycle calculated with this equation is 130 seconds. ivD LC 3600×≤ Operation of traffic signal systems in oversaturated conditions Page 75

Figure 35. Upper-bound of cycle length as a function of saturation flow rate As illustrated in the figures, short link distances create the most severe limits on cycle length during high demand periods. While this theoretical cycle time calculation can be used as a guide, many other factors must be considered in the selection of the cycle including pedestrian requirements and minimum green times. In the optimization methodology presented here, we use the Lieberman equation for determination of cycle time as it results in more restrictive values. The Roess equation tends to permit or suggest higher cycles than are typically feasible. Design of the three components (cycle, splits, and offsets) together is critical to arriving at a feasible control strategy with fixed timing parameter values. For example, short links can be protected from spillback not only by shortening the cycle length, but also by reducing the arrival rates during red by adjusting the offset values for the critical routes that pass through this link (i.e., by using offsets that avoid spillback). Another approach to avoid spillback is to provide additional green time at the downstream intersection (i.e. flaring the green) creating a metering effect at the upstream intersection. The following sections describe a methodology for determining splits and offsets that mitigate oversaturated conditions. Following the description of the methods for separately determining splits and offsets for a given cycle time, we describe a methodology for combining the two computations. Determination of Splits The optimum splits of an intersection depend on the relative demand on the conflicting approaches, discharge rates, and minimum green times that satisfy pedestrian and safety policy requirements. The maximum and minimum green times are typically regulated by agencies (e.g., minimum green time that accounts for pedestrian crossing time). In our design framework, the Operation of traffic signal systems in oversaturated conditions Page 76

green splits are initially allocated based on the v/c ratios given a specific cycle time. In the case of phase failure (i.e., v/c> 1), the 95th percentile queue of the critical approach is checked against the storage capacity. If the storage capacity of an approach is violated, splits are re-allocated to avoid the spillback. Other methods can be used to protect critical movements of an intersection to minimize overflow queues. One method is to impede the flow on critical routes upstream at pre-specified gating links with considerable storage capacity. Another method is to double cycle the subject intersection creating a phase reservice effect. Double-cycling is most effective for heavy arrivals during the red phase. At this stage of timing plan design, these methods are applied based on engineering judgment. We do not yet have mathematical methods developed for a comprehensive selection of the various combinations of treatments. Design of Offsets Maintaining progression during oversaturated conditions is a difficult task. Queues that form as a result of insufficient downstream capacity and from heavy turning from upstream side streets inhibit the movement of platoons through the arterial, thereby reducing the overall system effectiveness. There are two competing objectives when it comes to designing offsets in oversaturated conditions: (1) preventing spillback at the upstream intersection and (2) maximizing the green time at the subject intersection. The first objective is achieved by an offset that prevents the stopping shockwave from reaching the upstream intersection. The stopping shockwave progresses towards the upstream intersection during the red interval of the through phase, reducing the speed of the discharge wave at the upstream intersection. This may even cause blockage as illustrated in Figure 36. The second objective is to prevent starvation at the subject intersection. This is achieved if the first vehicles released from the upstream intersection join the discharging queue before crossing the downstream intersection. Further delay in releasing vehicles from the upstream location will cause downstream starvation where some of the green time is wasted between the discharge of the overflow queue and the arrival of the next platoon. This is illustrated in Figure 37. Fundamentally, the range of offsets that satisfies both conditions of starvation and spillback avoidance is computed from the length of the link, the vehicle travel speed, the overflow queue lengths, and the queue discharge rate. The fundamentals of spillback and starvation avoidance are described in the next two sections. Offsets to Avoid Spillback Spillback-avoidance offsets prevent spillback at the upstream intersection by causing the stopping shockwave to dissipate before reaching the upstream intersection. The ideal offset can be calculated using several methods that consider (a) vehicle dynamics, (b) queue perception impact that influences the approaching vehicle’s speed, and (c) the platoon dispersion effect. The following equation is derived based on Newton’s 2nd law of motion. For a given length (L) of a link, queue-link ratio (ρ), headway (h), vehicle length (Lv), and discharge rate (Us). The Operation of traffic signal systems in oversaturated conditions Page 77

value of (p) is the design value used for computing maximum and minimum offset values, such that ( ) h L L u L vs .1 ρ−−      ≥∆ Eq. 12 where ∆ is the difference between the starting times of the upstream and downstream green phases. Note that ∆ is not the offset that one would key into a traffic controller. ρ is a constraint or assumption on the length of the average overflow queue. Figure 36. Spillback avoidance offset Offsets to Avoid Starvation Starvation occurs on the subject approach when vehicles discharging at the upstream intersection arrive later than the time that the standing (overflow) queue has been discharged. Starvation results in loss of capacity by the wasting of valuable green time. A starvation avoidance offset ensures that the first released vehicle joins the discharging queue at the downstream intersection just as the back of the queue begins to move. The maximum value of a starvation-avoidance offset can be computed as follows: Eq. 13 v L L hL v −≤∆ ..ρ Operation of traffic signal systems in oversaturated conditions Page 78

Figure 37. Starvation avoidance offset Similar to the computation of the spillback avoidance bound on offsets, a design value for ρ must be assumed. By calculating the bounds on the offset values (max and min), a feasible zone for offset values can be established. This is illustrated in Figure 38. This feasible zone determines the offset range that can meet objectives of efficiently utilizing the capacity of both the upstream and subject intersections. Figure 38. Offset values feasible region As shown in Figure 38, the feasible zone of offsets that satisfies both objectives is shown as a function of the queue ratio (ρ). This feasible zone is highlighted in green. For example, if the Operation of traffic signal systems in oversaturated conditions Page 79

queue ratio is 0.5 (half of the 800 ft link length is filled with a queue) then the relative offset is constrained in the region of offsets between (-30s, 10s). If the relative offset is less than -30s, the downstream green phase will be starved. The light will remain green after the overflow queue is discharged and before the oncoming platoon arrives. If the relative offset is greater than 10s, the oncoming platoon will arrive at the back of the queue too early and the resulting shockwave will spillback into the upstream intersection. As would be expected, the higher the queue length ratio becomes, the more negative the relative offset needs to be. If the offset value exceeds the cycle time, the modulus operation is used to determine the value. The value of (ρ) is selected based on the expected overflow queue, link length, and vehicle travel speed. However, due to the stochastic flow rates of through and side street turning movements, (ρ) can be expressed by a probabilistic function that identifies the likelihood of both spillback and starvation. As illustrated in Figure 38, there is a range where (ρ) can be contained without violating the control objectives. However, if (ρ) differs significantly from its design value, the offset performance will degrade and could result in a condition of de facto red and spillback upstream, or a waste of downstream green time. Therefore, it is essential to design the offsets to control the value of (ρ) within a range. This can be achieved by (1) reducing cross-street green time, and (2) prohibiting cross-street turnings during red to regulate the growth of the queue length on the receiving link. This procedure for determining offsets and splits is applied to the critical route. Creating queues on side streets and minor phases is sometimes unavoidable in order to address the problematic symptoms of oversaturation. Combining the Design of Splits and Offsets Figure 39 illustrates the split-offset calculation procedure for an oversaturated network. The initial splits based on calculation of v/c ratios are used as a starting point in an iterative procedure. Next, the expected queue lengths are estimated for approaches with v/c > 1. The ρ values for approaches that are part of critical routes are then constrained by pre-specified thresholds to inhibit the buildup of further queues. The resulting queue-to-link ratios are then used to determine the bounds of offsets that can avoid spillback avoidance and starvation. The following section lists the equations used in the calculation framework. Operation of traffic signal systems in oversaturated conditions Page 80

Figure 39. Split-offset calculation procedure 1-Volume per cycle (VPC): Compute the average arrival volume on an approach during a cycle length: 𝑉𝑃𝐶 = 𝑉×𝐶 3600 Eq. 14 2- Compute the 95th percentile volumes on each link based on the expected volume and the peak hour factor (PHF). 𝑉𝛼 = 𝑉 × 𝑃𝐻𝐹 × (1 + 𝜎95𝑡ℎ × √𝑉𝑃𝐶𝑉𝑃𝐶 ) Eq. 15 3- Calculate the initial splits for each intersection based on the v/c ratio for each approach j of intersection i (𝑣/𝑐)𝑖𝑗. The capacity of each approach is iteratively changed after the queue control offsets are computed in Step 6, such that Operation of traffic signal systems in oversaturated conditions Page 81

(𝑣/𝑐)𝑖𝑗 = 𝑉𝑖𝑗 𝑆×𝑔𝑖𝑗 𝐶� Eq. 16 4- Calculate the expected queue length on each approach (𝑄𝑖𝑗) for v/c greater or less than 1: v/c< 1 𝑄𝑖𝑗 = 𝑉𝑖𝑗3600 × (𝐶 − 𝑔𝑖𝑗) × (1 + 1𝑠 𝑉𝑖𝑗� ) × 𝐿𝑛𝑖𝑗 Eq. 17 v/c> 1 𝑄𝑖𝑗 = �(𝑉𝑖𝑗 − 𝑠 × 𝑔𝑖𝑗𝐶 ) × 𝐶3600 + 𝑉𝑖𝑗 × 𝐶3600� × 𝐿𝑛𝑖𝑗 Eq. 18 5- Calculate the queue-link length ratio (𝑝𝑖𝑗) based on the expected queue length (𝑄𝑖𝑗) from Step 4 and the available storage capacity for each approach (𝐿𝑖𝑗), where 𝑝𝑖𝑗 = 𝑄𝑖𝑗𝐿𝑖𝑗 Eq. 19 6- Calculate the bounds for offset values that avoid starvation and spillback according to the (𝑝𝑖𝑗) ratio from Step 5. For the main approach ∆> p𝑖𝑗 × 𝐿𝑖𝑗𝑢𝑠 − �(𝐿𝑖𝑗(1 − 𝑝𝑖𝑗)) ∆𝑚𝑖𝑛> �𝐿𝑖𝑗𝑢𝑠 � − 𝐿𝑖𝑗�1 − 𝑝𝑖𝑗�𝐿𝑣 .ℎ ∆𝑚𝑎𝑥< �𝐿𝑖𝑗×𝑝𝑖𝑗×ℎ𝐿𝑣 � − 𝐿𝑖𝑗𝑣 Eq. 20 The splits and offsets for the network are then calculated using an optimization procedure that protects critical routes from both spillback and starvation by minimizing the degree of saturation on all approaches on the critical route for the given cycle time. This procedure’s inputs and outputs is illustrated in Figure 40. Optimization Problem Formulation Minimize the degree of saturation on all approaches on the critical routes Operation of traffic signal systems in oversaturated conditions Page 82

𝑀𝑖𝑛 ∑ ∑ ∑ �𝑣𝑖𝑗𝑟 𝑐𝑖𝑗𝑟� �𝑗∈𝐽𝑖∈𝐼𝑟∈𝑅 Eq. 21 Subject to the following constraints: Cycle length constraint ∑ (𝑔𝑖𝑗 + 𝑌𝑖𝑗)𝑗 = 𝐶 Eq. 22 Queue lengths constraints (storage capacity): 𝑄𝑖𝑗 < 𝐿𝑖𝑗 Eq. 23 Degree of saturation constraints on the critical routes, such that: 𝑣𝑖𝑗 𝑟 𝑐𝑖𝑗 𝑟� ≤ 1 Eq. 24 Queue-link ratio constraints (queue management): 𝑝𝑖𝑗 𝑟 < 𝛾 Eq. 25 Minimum greens constraints: 𝑔𝑖𝑗 ≥ 𝑔𝑚𝑖𝑛 Eq. 26 Maximum greens constraints: 𝑔𝑖𝑗 ≤ 𝑔𝑚𝑎𝑥 Eq. 27 For all critical routes in the network: ∀ 𝑟 ∈ 𝑅,∀ 𝑖 ∈ 𝐼, ∀𝑗 ∈ 𝐽 Eq. 28 Where: C: cycle length (s) c: capacity (veh/hr) v: volume (veh/hr) g: effective green (s) Qb: size of initial queue (ft) u: delay parameter si : adjusted saturation flow rate per lane of approach (i), veh/s Operation of traffic signal systems in oversaturated conditions Page 83

d(k)I : mean departure rate from approach (i) during cycle k, veh/s q(k)I : length of queue on approach (i) at the beginning of cycle k, veh g(k)I : effective green time for arterial approach (i) during cycle k, s gc(k)I: effective green time for cross approach (i) during cycle k, s AV(k)j : arriving vehicles into approach (i) during cycle k, veh 𝑉𝑖𝑗: Approach (j) volume at intersection (i) (vehicle per hour) 𝑔𝑖𝑗: Approach (j) green time at intersection (i) (sec) 𝑔𝑚𝑖𝑛: Minimum green split (sec) (𝑣/𝑐)𝑖𝑗: v/c ratio of approach (j) at intersection (i) 𝑄𝑖𝑗: Queue length of approach (j) at intersection (i) (ft) 𝑝𝑖𝑗 𝑟 : Queue-link ration for approach (j) at intersection (i) for the critical route (r) 𝛾𝑖𝑗 𝑟 : Maximum value for the queue-link ratio for approach (j) at intersection (i) for the critical route (r) 𝐿𝑖𝑗: Storage capacity of approach (j) at intersection (i) (ft) ∀ 𝑟 ∈ 𝑅: For each critical route (r) in the network’s set of routes (R) ∀ 𝑖 ∈ 𝐼: For each intersection (i) in the network’s set of intersections (I) ∀𝑗 ∈ 𝐽 : For each approach (j) in the intersection’s set of approaches (J) Figure 40. Split-offset optimization framework Construction of the Pareto Front Multi-objective evolutionary algorithms are used to examine the effectiveness of alternate strategies for oversaturated intersections. A multi-objective approach allows for the optimization of several objectives simultaneously. Unlike traditional methods of assigning pre-defined weights to each objective function, multi-objective evolutionary algorithms produce Pareto Operation of traffic signal systems in oversaturated conditions Page 84

fronts. A Pareto front is the combination of compromise solutions of all of the objectives being considered in the problem. Figure 41shows two objectives (for the purpose of illustration, any number of objectives can be used): throughput and delay. In this example, each point on the Pareto front would correspond to a complete set of timing plan parameters (e.g., the cycle, splits, and offset). Consider, for example, that a particular control strategy for oversaturated conditions was successful in reducing both system-wide delay and increasing throughput. A control action “X” (e.g., increasing major phase duration) can further increase throughput, where another control action “Y” (e.g., left-turn reservice) can further reduce the total delay. Both points A and B in Figure 41 correspond to optimal solutions, but with different importance assigned to each objective. Point A for example, corresponds to a weight of 100 percent assigned to the objective of increasing throughput, and 0 percent assigned to the objective of minimizing delay. Point B corresponds to a 0 percent weight assigned to maximizing throughput and a 100 percent weight assigned to minimizing total delay. Figure 41. Conceptual illustration of Pareto front in assessing multiple objectives In addition, the shape of the Pareto front itself provides invaluable information to the analyst. One would know, looking at the shape of the Pareto front, how much an objective function would be compromised if another objective function were to be favored. For example, in Figure 42a, the engineer can choose any solution that lies in the Pareto front, where in Figure 42b, the bad solution range is labeled as such because any additional increase in throughput will result in a very large increase in delay. B A LOS Th ro ug hp ut (v eh /h ou r) Optimal solutions Pareto front Operation of traffic signal systems in oversaturated conditions Page 85

(a) (b) Figure 42. Information provided by the shape of the Pareto Front (a) Pareto front of unrestricted solution range (b) Pareto front of restricted solution range This approach differs from traditional methods used in signal timing optimization because it allows for the consideration of multiple objectives simultaneously. The assignment of weights to each individual objective can be done at the end of the analysis as opposed to assigning arbitrary weights to different objectives without knowing the consequences of that assignment beforehand. The use of multi-objective optimization is a key element of the research approach since there is no easy way to quantify when a system should be transitioned from an objective of delay minimization to one of queue management or maximizing throughput. Control Objectives There are three major management objectives considered in this research: (1) delay minimization, (2) throughput maximization, and (3) queue management. We will briefly discuss each from a qualitative perspective and then present the mathematical formulation used in the optimization methodology for each objective. Good solution range LOS Th ro ug hp ut (v eh /h ou r) LOS Th ro ug hp ut (v eh /h ou r) Good solution range Bad solution range Operation of traffic signal systems in oversaturated conditions Page 86

Delay Minimization Most offline optimization tools use some kind of formulation for minimizing delay and stops, perhaps balanced with some consideration for providing progression on an arterial route. In undersaturated conditions, this objective is handled sometimes quite loosely to perhaps include solutions that might only be considered to be effective or only acceptable and not really a true minimum total delay. This includes (a) minimizing the delay at a single intersection and (b) minimizing delay in a network or series of intersections on a travel route (progression). Intersection delay might be characterized in one of two manners. The first is what might be referred to as the classical Webster’s method which is to allocate green time to phases to minimize the total delay at the intersection given known demand for all movements. Since demand fluctuates and is not directly measurable with traditional detection systems, the second and more commonly used interpretation of the objective minimize delay is to minimize the frequency that a traffic signal does not serve all the waiting cars during the green time. In other words, minimize delay means to minimize phase failures in actuated-coordinated signal systems. The former is minimization of system delay. The latter is minimization of user delay. Minimization of user delay is the traditional basis for most actuated-coordinated signal timing in North America. Green splits are typically allocated to ensure that side streets and left-turn phases have a cushion of additional time in case they need more than they typically need on average to minimize cycle failures. In most cases this additional time is re-allocated to other phases when the phase gaps out due to lack of additional demand. Depending on the use of fixed or floating force offs, the extra time is either returned to the coordination phase or the next phase in the sequence is given additional time. Avoiding cycle failures is an equitable traffic management policy; one that over-emphasizes the importance of light traffic movements such as left turns and side streets. It does not minimize total delay; it rather minimizes each driver’s perception of being delayed at the signal. In undersaturated conditions, this policy can be improved upon by adaptive traffic control strategies, but in most low and medium flow scenarios, a cycle-failure avoidance policy is hard to beat as it meets the objective to provide a consistent user experience for drivers. However, when green times are not long enough to serve all the vehicles that were waiting at the start of the green time, policies with fixed split times have no way to react to these changes. Even if the arrival rate remains constant but is still higher than the service rate (maximum green time), the overflow queue will continue to grow for that phase. Objectives that continue to consider equity service at the intersection will over-emphasize the minor movements at the detriment to the movements and phases that are oversaturated. Progression is an objective that blurs the lines between minimizes delay and maximize throughput. Progression is achieved in signal systems by arranging for the green time windows to be consecutively opened (by way of setting offsets) in a desired direction of travel to allow Operation of traffic signal systems in oversaturated conditions Page 87

vehicles to continue through a sequence of intersections without stopping. By carefully setting the offset values, the objective of minimizing delay (equity treatment for all users) can still be satisfied at individual intersections while at the same time meeting the system objective of progression and providing the consistent user experience that drivers’ tend to expect on arterial roads. This objective is hindered when overflow queues begin to form on the movements that are designated for progression. Offsets that were designed (i.e. forward progression offsets) assuming that no queues were present will further exacerbate the situation by creating situations where the overflow queues grow faster than necessary because the upstream vehicles arrive before the overflow queue has started to move. Throughput Maximization Minimizing user delay is simply not appropriate when the situation is oversaturated and it is no longer possible to avoid cycle failures. Thus, maximizing the number of vehicles actually served by the intersection, with respect to the vehicles presented to the intersection (the load), is a more appropriate objective. This keeps as much of the system operational as possible, with the unfortunate effect of delaying movements or phases where the total traffic demand is quite low. From an equity perspective, strategies that maximize throughput might be considered to punish light movements to the benefit of the greater good. This is done by moving much heavier phases for longer amounts of time more frequently than would be expected by the typical actuated control approach. Strategies that maximize throughput have the following characteristics: • Make best use of the physical space (e.g., lag heavy left turns, run closely-spaced intersections on single controller). • Make best use of green time in the cycle (e.g., prevent actuated short greens, separate congested movements from the uncongested ones, phase re-servicing). • Reduce the negative impact of other influences (e.g., buses, pedestrian movements) on the overall ability of the signal system to process vehicle flows. Measurement and Assessment of Throughput There are several ways to measure or assess the throughput of a traffic signal network or system: • The total number of vehicles input to a system of intersections. • The total number of vehicles output by a system of intersections. • The ratio of the total vehicles output from the system to the total vehicles input to the system. Throughput is a rate such as vehicles per hour or vehicle-miles per hour. The concept of an input rate and an output rate must be considered together with the identification of the spatial extent of the system of intersections of interest. When a control strategy is operating efficiently, the Operation of traffic signal systems in oversaturated conditions Page 88

overall output processing rate of the intersections in the system closely matches the input processing rate and overflow storage of vehicles in the system does not occur. In oversaturated conditions, the output rate is less than the input rate and overflow queuing begins to build up within the system at various points. At some point in many oversaturated systems, queues will build outside of the system cordon boundaries when queues inside of the system reduce the ability for those vehicles from entering the area. When a mitigation strategy increases both the total output and the total input rates, it can truly be determined to have increased the capacity of the traffic control system. If the mitigation strategy increases total system input, but not output, then it uses more of the available spatial capacity of the system. This in itself is a valuable performance improvement and is desirable during the loading and processing regimes. Similarly, if a mitigation strategy increases total system output, but not input, it is reducing the congestion and oversaturation inside the system cordon line. This is preferable during the recovery regime. Queue Management The goal of throughput maximization strategies is increasing input, increasing output, or both. At some point, however, no further revision to the signal timing will increase maximum throughput and queues will continue to grow until demand diminishes. The reason that strategies largely have the same performance during the peak time is that the queues are so pervasive that the cause-and-effect relationships between control actions and the traffic situation are masked by hysteresis. Hysteresis is a delay between an offered input and the system output. For example, when the green time of a downstream intersection can process only one-third or one-quarter of the upstream queue, it is no longer that important if the offset is set for positive or negative progression. When the light turns green at the upstream intersection, there is limited storage for the entering traffic and spillback begins to create SOSI > 0 at the upstream location. The one-to- one dynamic of the offset relationship from one intersection to another is no longer applicable. The shorter the link distances between intersections, the faster the system can quickly degrade from stable operation to pervasive queues, thereby skipping any potential improvement that a throughput maximizing strategy could have achieved. This usually requires constraining capacity upstream from a bottleneck at locations where queue storage will not cause network gridlock, or increasing green time at downstream signals to increase output flow. As noted by Denney, 2008, if throughput maximization strategies are a curative approach, then queue management strategies can be considered a palliative approach with the objective of treating symptoms rather than seeking a cure. It is in this context that the commonly held belief that “there is nothing that can be done, there is simply too much traffic” is mostly true. Synchronizing the actions of multiple controllers in a system of intersections for the purpose of queue management is very difficult within the context Operation of traffic signal systems in oversaturated conditions Page 89

of actuated-coordinated control by commanding patterns with different parameters. The coordination of actions between intersections for queue management must closely resemble the operation of a diamond interchange with a carefully orchestrated sequence of actions, with rapid feedback between the detection of queue extent and the application of rapid-response mitigation strategies such as phase truncation and green extension. Design of timing plans according to the principles described in Step 4 and adjustment of green times according to the technique described in Appendix B can begin to address these situations. Formulation for Delay Minimization Objective To compare the performance of timing plans optimized for delay versus throughput versus queue management, we need to first formulate optimization objectives for all three goals. The delay minimization objective is represented in this process by choosing green splits throughout the network that minimize the total delay based on the HCM methodology (Akcelik, 1988). The HCM control delay formula accounts for random and platooned arrival of vehicles as well as progression quality and delay resulting from pre-existing queues. The minimization process is constrained by a feasible cycle length range, minimum green, maximum green, queue storage limits, and v/c ratios on approaches that are part of critical routes. Unlike other timing programs, the developed timing tool generates an optimal timing plan for each time period in the volume profile (e.g., 15-min). Moreover, for approaches with v/c > 1, un-served volumes are shifted to the next period volume (i.e., volume spillover) to represent the temporal effect of un-served demand. Optimization formula: Min (Delay = d1 + d2 + d3) 𝑑1 = 0.5 × 𝐶 × �1 − 𝑔𝐶�21 − �𝑚𝑖𝑛 �1, 𝑣𝑐� × 𝑔𝐶� 𝑑2 = 900 × 0.25× ��𝑣 𝑐 − 1���𝑣 𝑐 − 1�2 + 4 × �𝑣𝑐�0.25 × 𝑐� 𝑑3 = 1,800 × 𝑄𝑏 × (1 + 𝑢) × 𝑡𝐶 × 𝑇 Eq. 29 Subject to the following constraints: Cycle length 𝐶𝑚𝑖𝑛 < 𝐶 < 𝐶𝑚𝑎𝑥 Eq. 30 Operation of traffic signal systems in oversaturated conditions Page 90

Cycle length constraint ∑ (𝑔𝑖𝑗 + 𝑌𝑖𝑗)𝑗 = 𝐶 Eq. 31 Queues lengths constraints (storage capacity): 𝑄𝑖𝑗 < 𝐿𝑖𝑗 Eq. 32 Critical routes movements degree of saturation constraints: 𝑣𝑖𝑗 𝑟 𝑐𝑖𝑗 𝑟� ≤ 1 Eq. 33 Minimum greens constraints: 𝑔𝑖𝑗 ≥ 𝑔𝑚𝑖𝑛 Eq. 34 Maximum greens constraints: 𝑔𝑖𝑗 ≤ 𝑔𝑚𝑎𝑥 Eq. 35 For all critical routes in the network: ∀ 𝑟 ∈ 𝑅,∀ 𝑖 ∈ 𝐼, ∀𝑗 ∈ 𝐽 Eq. 36 Throughput Maximization The throughput maximization objective is represented in this approach by optimizing green splits throughout the network in order to maximize the objective developed by Abu-Lebdeh (2001). This objective was designed to obtain signal control so that system throughput is maximized subject to constraints on state and control variables (i.e., green times, and offsets) such that no de facto red is formed. Offsets are set to ensure continuity of movement and green times on the critical route(s) are within specified ranges and have v/c ratio less than 1. Optimization formula: Eq. 37 Subject to the following constraints: Cycle length 𝐶𝑚𝑖𝑛 < 𝐶 < 𝐶𝑚𝑎𝑥 Eq. 38                 +        −×+×+∑∑ ∑ −k i k jkjk j jk jk jk jk ikikik qAVs q g g AV qMinjdgcMax )()( )( )( 1)( )( )()()( , Operation of traffic signal systems in oversaturated conditions Page 91

Cycle length constraint ∑ (𝑔𝑖𝑗 + 𝑌𝑖𝑗)𝑗 = 𝐶 Eq. 39 Queues lengths constraints (storage capacity): 𝑄𝑖𝑗 < 𝐿𝑖𝑗 Eq. 40 Critical routes movements degree of saturation constraints: 𝑣𝑖𝑗 𝑟 𝑐𝑖𝑗 𝑟� ≤ 1 Eq. 41 Minimum greens constraints: 𝑔𝑖𝑗 ≥ 𝑔𝑚𝑖𝑛 Eq. 42 Maximum greens constraints: 𝑔𝑖𝑗 ≤ 𝑔𝑚𝑎𝑥 Eq. 43 For all critical routes in the network: ∀ 𝑟 ∈ 𝑅,∀ 𝑖 ∈ 𝐼, ∀𝑗 ∈ 𝐽 Eq. 44 Where: d1: Uniform delay d2: incremental delay d3: delay due to pre-existing queues (for under saturation d3 = 0) C: cycle length c: capacity v: volume, and g: effective green Qb: size of initial queue T: analysis period, hour t: duration of oversaturation within T, h u: delay parameter si : adjusted saturation flow rate per lane of approach (i), veh/s d(k)I: mean departure rate from approach (i) during cycle k, veh/s q(k)I: length of queue on approach (i) at the beginning of cycle k, veh g(k)I: effective green time for arterial approach (i) during cycle k, s gc(k)I: effective green time for cross approach (i) during cycle k, s AV(k)j: arriving vehicles into approach (i) during cycle k, veh 𝑉𝑖𝑗: Approach (j) volume at intersection (i) (vehicle per hour) Operation of traffic signal systems in oversaturated conditions Page 92

𝑔𝑖𝑗: Approach (j) green time at intersection (i) (sec) 𝑔𝑚𝑖𝑛: Minimum green split (sec) (𝑣/𝑐)𝑖𝑗: v/c ratio of approach (j) at intersection (i) L: Link length (ft) 𝑄𝑖𝑗: Queue length of approach (j) at intersection (i) (ft) 𝑝𝑖𝑗 𝑟 : Queue-link ration for approach (j) at intersection (i) for the critical route (r) 𝛾𝑖𝑗 𝑟 : Maximum value for the queue-link ratio for approach (j) at intersection (i) for the critical route (r) 𝐿𝑖𝑗: Storage capacity of approach (j) at intersection (i) (ft) ∀ 𝑟 ∈ 𝑅: For each critical route (r) in the network’s set of routes (R) ∀ 𝑖 ∈ 𝐼: For each intersection (i) in the network’s set of intersections (I) ∀𝑗 ∈ 𝐽 : For each approach (j) in the intersection’s set of approaches (J) Queue Management Control The queue management control objective is achieved primarily by generating green splits that minimize the degree of saturation of pre-determined critical routes in the network. Critical movement’s (v/c) ratios and links’ p-ratios (i.e., queue-to-link ratio) upper bound are set according to the control strategies that will be applied (e.g., metering, gating, green flaring). Optimization formula: Minimize the degree of saturation on approaches on the critical routes 𝑀𝑖𝑛 ∑ ∑ ∑ �𝑣𝑖𝑗𝑟 𝑐𝑖𝑗𝑟� �𝑗∈𝐽𝑖∈𝐼𝑟∈𝑅 Eq. 45 Subject to the following constraints: Cycle length constraint ∑ (𝑔𝑖𝑗 + 𝑌𝑖𝑗)𝑗 = 𝐶 Eq. 46 Queue lengths constraints (storage capacity): 𝑄𝑖𝑗 < 𝐿𝑖𝑗 Eq. 47 Critical routes movements degree of saturation cosnstraints: 𝑣𝑖𝑗 𝑟 𝑐𝑖𝑗 𝑟� ≤ 1 Eq. 48 Queue-link ratio constraints (Queue management ): 𝑝𝑖𝑗 𝑟 < 𝛾 Eq. 49 Operation of traffic signal systems in oversaturated conditions Page 93

For all critical routes in the network: ∀ 𝑟 ∈ 𝑅,∀ 𝑖 ∈ 𝐼, ∀𝑗 ∈ 𝐽 Eq. 50 Where: C : cycle length c : capacity v : volume, and g : effective green Qb: size of initial queue T : analysis period, hour t : duration of oversaturation within T, h u : delay parameter si : adjusted saturation flow rate per lane of approach (i), veh/s d(k)I : mean departure rate from approach (i) during cycle k, veh/s q(k)I : length of queue on approach (i) at the beginning of cycle k, veh g(k)I : effective green time for arterial approach (i) during cycle k, s gc(k)I: effective green time for cross approach (i) during cycle k, s AV(k)j : arriving vehicles into approach (i) during cycle k, veh 𝑉𝑖𝑗: Approach (j) volume at intersection (i) (vehicle per hour) 𝑔𝑖𝑗 : Approach (j) green time at intersection (i) (sec) 𝑔𝑚𝑖𝑛 : Minimum green split (sec) (𝑣/𝑐)𝑖𝑗 : v/c ratio of approach (j) at intersection (i) 𝑄𝑖𝑗 : Queue length of approach (j) at intersection (i) (ft) 𝑝𝑖𝑗 𝑟 : Queue-link ration for approach (j) at intersection (i) for the critical route (r) 𝛾𝑖𝑗 𝑟 : Maximum value for the queue-link ratio for approach (j) at intersection (i) for the critical route (r) 𝐿𝑖𝑗 : Storage capacity of approach (j) at intersection (i) (ft) ∀ 𝑟 ∈ 𝑅: For each critical route (r) in the network’s set of routes (R) ∀ 𝑖 ∈ 𝐼: For each intersection (i) in the network’s set of intersections (I) ∀𝑗 ∈ 𝐽 : For each approach (j) in the intersection’s set of approaches (J) Development and Analysis of Timing Plans for Managing Oversaturated Conditions The procedure described in this chapter is designed to produce a range of potential timing plans that are optimized for different objectives. Those timing plans are then compared with each other based on the performance measures for which they were or were not optimized. This allows the analyst to use Pareto analysis to determine those timing plans that are non-dominated. Operation of traffic signal systems in oversaturated conditions Page 94

In addition, the methodology considers the time-varying nature of the traffic demands. Particularly for oversaturated conditions, the process of generating the timing plans must consider that any un-served demand must be serviced in the next time period. Any un-served demand in that time period will spill over to the next time period, and so on. Similarly, since the oversaturated problem is dynamic in nature, the process explicitly considers that multiple timing plans will be needed. The methodology allows the results of the analysis to indicate where it is beneficial to switch from one timing plan to another, which also indicates in general where the objectives of the strategy may change from minimizing delay to maximizing throughput, or managing queues. These considerations are discussed further in the following sections. Using Volume Profiles on Critical Routes in the Design of Signal Timing Plans Traditionally, a signal timing plan is generated based on the highest observed volumes of the conflicting movements. It is assumed that this condition is the worst possible condition that the timing plan will experience, and thus all other combinations of traffic volumes will have at least as good, if not better, performance using the same timing parameters as designed for the limiting case. However, during oversaturated conditions, generating a timing plan using the highest volumes does not account that approach capacities are limited, and the critical route flows and demand rates will change over time. Observing a change in the volume ratios is a good indication of the need for a new signal timing plan to accommodate the new demand. Periods when a new signal timing plan may be warranted are identified by the changes in either the total traffic demand or demand for a particular phase split. As volume profiles of conflicting movements vary from one time period to another, optimal splits will change accordingly. This is well known, but is not typically considered in optimization for undersaturated conditions because the causal linkages between the two traffic conditions are relatively weak since overflow queues are not generated. Therefore, the methodology described here generates several timing plans for each time period and compares the performance of applying the different timings during time periods where the traffic demand is much different than the time period for which it was designed. This is illustrated conceptually in Figure 43. The y-axis represents traffic demand for each conflicting movement. In this example, only northbound and westbound traffic flows are shown. The x-axis represents time and is divided into 11, 15-minute time periods. The timing plan that was optimized for time period 5 results in timing parameters where green allocation to the phases serving northbound and westbound traffic are relatively equal. However, the timing plan that was optimized for time period 9 results in the westbound volume being more than double that of the northbound volume. Therefore the timing plan parameters would be very different from the timings optimized for period 5. This illustrates the necessity of designing a set of timing plans that accommodate the fact that the profile of the future traffic is changing dramatically. For example, it may be beneficial over the long run to have started running the timing plan optimized for the conditions in time period 9 Operation of traffic signal systems in oversaturated conditions Page 95

during time period 5, instead of allowing the westbound queues to grow until the timings for time period 9 are finally implemented. These kind of trade-offs are analyzed and brought to light by the multi-objective Pareto front analysis process. Figure 43. Two conflicting movement volume profiles Explicit Consideration of Volume Spillover As discussed above, the temporal qualities of the volume profile on the critical routes are essential to take into consideration. This methodology explicitly takes into consideration the fact that any un-served volume for each time period will be added to the arrival volume in the next time period. The volumes on several approaches during oversaturated conditions would be expected to exceed their capacities (green splits). This concept is illustrated in Figure 44. As the red line (demand) exceeds the green line (capacity), that latent demand is stored outside of the system and must be served at a later time period. The black line indicates how the un-served volume builds up and then dissipates over time. The application of this concept ensures that optimal timing plans are evaluated through the entire volume profile and that the new traffic state created due to using a specific plan is used in the evaluation or update of timing plans. Operation of traffic signal systems in oversaturated conditions Page 96

Figure 44. Concept of volume profiles that generate un-served demand Optimization Procedure The optimization problems for minimizing delay, maximizing throughput, and managing queues are mixed integer nonlinear problems with nonlinear constraints. The Generalized Reduced Gradient (GRG) algorithm, one of the methods provided by Excel-solver, is used to search the timing plan space and find the optimal timing plans. The GRG method is a robust nonlinear programming method that uses a hill-climbing iteration process. The GRG method has been proven to be one of the most efficient and effective methods for Nonlinear Programming problems with Nonlinear constraints. The basic concept of GRG method entails linearizing the nonlinear objective and constraint functions at a local solution with a Taylor expansion. Then, the concept of reduced gradient method is employed which first divides the variable set into two subsets of basic and non-basic variables. Next the GRG method employs the concept of implicit variable elimination to express the basic variables as functions of the non-basic variables. Finally, the constraints are eliminated and the variable space is reduced to only non-basic variables. This approximated problem is used to search for the optimal solution. The process is fairly efficient and allows reasonably responsive problem resolution using common tools (Microsoft Excel). Performance Measure Evaluation for the Generated Optimal Timing Plans The optimization tool generates several optimal timing plans. These timing plans are generated based on the control objective (either total delay or total throughput) and the assumed volume profiles on each movement. The concept of volume spillover as described earlier is used to optimize a sequence of timing plans for each objective function. Response surfaces are then created for each performance measure that shows how each timing plan would perform if that timing plan were applied to the entire volume profile. Figure 45 shows the response surface for delay and Figure 46 for throughput. Operation of traffic signal systems in oversaturated conditions Page 97

The surface for total delay uses the HCM equation to compute the performance of the timing plan for each time period. Similarly, the surface for total throughput uses the Abu-Lebdeh (2000) objective function to compute the performance. The x-axis of the surface represents the 11 time periods of the scenario. The y-axis represents the performance measure. The z-axis lists the timing plans that were generated from the optimization process for each optimization objective. Timing plans P1 through P8 represent plans obtained from optimizing total delay. Timing plans P9 through P17 represent the plans obtained from optimizing for total throughput. Figure 45. Delay surface representing the performance of each timing plan for each time period Operation of traffic signal systems in oversaturated conditions Page 98

Figure 46. Throughput surface representing the performance of each timing plan for each time period Switching Between Control Strategies The decision to switch between control strategies is based on several factors: 1. The sensing/identification that the traffic scenario has switched from one canonical state to another, and 2. The mapping of the identified scenario to the appropriate strategy based on the recommended objective for that particular degree of saturation. These decisions thus must be based on a robust mechanism to appropriately switch from one objective to another in order to identify which timing plan is more suitable. The mechanism used in this research is based on robust pattern recognition techniques such as the Bayesian pattern recognition approach or discriminant analysis (Abbas and Sharma, 2006). Thus, a second optimization procedure can be applied that will result in the optimal timing plans and the optimal time that the plans should be switched from one to another to adjust the overall objective of traffic management from one objective to the next. Based on the general concept of an oversaturated scenario having three regimes of operation (loading, processing, and recovery), we defined two canonical sets of objectives for testing and evaluating this approach. Two canonical control strategies were developed and evaluated in this research:  Delay minimization -Queue management -Throughput maximization Operation of traffic signal systems in oversaturated conditions Page 99

 Throughput maximization -Queue management -Throughput maximization A timing plan that is optimal for the first objective would be applied during the loading regime. A timing plan that is optimal for the second objective would be applied during the processing regime. A timing plan that is optimal for third regime would be applied during the recovery period. Identifying the times at which it is optimal to switch from one objective to another is the goal of applying the pattern recognition methodology. This methodology requires running many combinations of the timing plans in simulation and observing the results. In addition to the duration constraints for each regime of the peak period, a minimum duration of each strategy is considered. This is because when a new timing plan is selected, the controller must transition to the new plan. During this transition period, systematic operation in the network is interrupted while each controller adjusts to the new parameters. Because of this disruption, transitions are minimized and one must be assured that the benefits of the new plan overcome the dis-benefits of the transition period. Figure 47 illustrates the total input, total output, and resulting total vehicles in the system for a test network under the throughput-queue management-throughput strategy. The blue line roughly depicts the capacity of the plans that are applied during each regime. Similarly, Figure 48 illustrates the total input, total output, and resulting total vehicles in the system for a test network under the delay-queue management-throughput strategy. Note in Figure 47how the total output is higher using a plan that is designed for throughput maximization than the total output in Figure 48 for a plan that is designed for minimizing total delay. The resulting performance is quite different in the two cases during the processing regime as the total vehicles in the system jumps to over 2,800 vehicles when starting with delay minimization and maxes out to only 2,000 vehicles in the system using throughput maximization in the loading regime. Also, when using a minimizing delay strategy during the loading regime the throughput maximizing strategy during the recovery regime must have much higher capacity to process the additional queues that are stored in the system in a timely manner. Two examples of the application of this procedure on test networks are reported in Chapter 3 for the Reston Parkway in Northern Virginia and the Post-Oak area of Houston. Operation of traffic signal systems in oversaturated conditions Page 100

Figure 47. Example of optimal timing plans and scheduling based on the minimum delay objective Figure 48. Example of optimal timing plans and scheduling based on the throughput – maximization objective Summary There are four essential parts to the design of timing plans for handling oversaturated conditions: 1. the identification of the critical routes and the flows along those routes, 2. the determination of ranges of feasible timing plan parameters that meet criteria to address oversaturation on those routes, Operation of traffic signal systems in oversaturated conditions Page 101

3. the selection of the objective function to solve for optimal timings with respect to a particular objective, and 4. the scheduling of a sequence of timing plans that are tailored to each regime of oversaturated operation. In this part of the research project we developed a comprehensive process that addresses these four elements. The process is non-trivial and should be considered experimental at this time. Significant additional research and development will be necessary to transfer this type of approach from state-of-the-art to state-of-the-practice. The process of developing the procedures and testing the results provided a wide range of insights into the critical components of handling oversaturated conditions with fixed-value traffic signal timing plans and traditional time-of-day scheduled responses. The process begins by identifying critical oversaturated routes in a network of interest. The procedure is designed to find timing plans that will minimize problematic symptoms (spillback, starvation, and storage blocking) on the critical route(s). There are wide range of timing (cycle, split, and offset) combinations that can satisfy these goals. Thus a second step is to apply an optimization procedure that searches the range of feasible combinations of settings and addresses a particular objective. Three objectives were tested to evaluate the theory (or generally held assertion) that different objectives are needed in different regimes of operation. The third step is to identify when to switch from one regime of operation to the next. This is done with a simulation-in-the-loop, multi-objective procedure. Test cases for this approach are reported in Chapter 3 and findings from the tests are reported in Chapter 4: Conclusions. Operation of traffic signal systems in oversaturated conditions Page 102

Online Implementation of Mitigation Strategies In the previous two sections we described quantitative measures for estimating the severity of an oversaturated condition and a process for generating timing plans that are designed to mitigate oversaturated conditions. When the oversaturated scenario is recurrent, either of these methods can be used to generate mitigation timing plans and apply those timing plans on a TOD scheduled basis. However, when the scenario is non-recurrent, mitigation strategies should be implemented that use the status of field detectors to determine when to implement the mitigation. This section of the report describes an online processing tool that can be used to implement non-recurrent strategies. Once the mitigation timing plans are designed offline and loaded into field controllers, logic rules based on field detection can be employed to react to the oversaturation. To implement a mitigation strategy online, detection zones must be deployed, those detectors must be connected to field controllers, and there must be communications from the field controllers to a central system. Existing traffic responsive logic in central systems might be configured to select among mitigation strategies and normal operating timing plans. Central systems that use the UTCS/USDOT traffic responsive logic should be configured such that “K” values in V+KO calculations are sufficiently large so that the occupancy data far overshadows the volume inputs. This is critical since the volume measurement is largely unreliable and the detector data is dominated by occupancy during oversaturated conditions. Using existing traffic responsive logic components of central systems does not require high-speed communications between field controllers and central. While detector occupancy increases during oversaturation, its value is capped at 100%. As long as the queue extends across the detection point, there is no way with occupancy alone to determine the difference between a queue of 200 vehicles from a queue of 50 vehicles. As part of the research project, experimental software was developed that can assess TOSI and SOSI and measure queue lengths. These algorithms are integrated with a logic processor tool that can use these measures in selection of mitigation strategies. This software is part of the deliverables for this project. The key features of the logic processor is that it uses straight-forward “if…then” threshold rules to determine if a detector status condition is met or not. This can include TOSI, SOSI, queue length, and detector occupancy. These conditions can be combined for several detector stations in “AND” and “OR” logic to make more complicated decisions based on multiple detection inputs. Similarly, thresholds and “if…then” logic can be applied to determine when to stop applying a certain strategy. Queue measurement and TOSI/SOSI measures provide a more accurate determination of oversaturated conditions, but it is not required that these measures be used to trigger online Operation of traffic signal systems in oversaturated conditions Page 103

mitigation strategies. Traditional occupancy measurements can also be used with the logic processor application, given that the detectors are located appropriately and aggregation of the data is configured appropriately. Queue measurement and TOSI/SOSI measures requires high- resolution (i.e. second-by-second) data on phase timing and detector occupancy data to be collected and returned to the central system for processing. Determining Detector Locations Queue length estimation and identification of saturated occupancy is best applied with detectors that are significantly upstream of the stop bar and as short as possible (standard 6’x6’ loops or zones are preferable). Utilization of occupancy data from stop bar detectors is not recommended since those detectors will report 100% occupancy during the red interval of the traffic phase, as well as during the green interval if sufficient demand is present. 100% occupancy on a stop bar detector during a cycle does not immediately indicate that the phase is oversaturated since the entire standing queue may be dissipated during the green phase. It is necessary to use detectors that are upstream of the stop bar to indicate that persistent queues are present. As stated earlier, it is also important that these detection zones are reported back to the controller on a lane-by-lane basis. Considering just one zone for a multiple lane approach will result in significant over- estimation of the level of saturation. The balance between “too far upstream” and “too close to the stop bar” is a case of engineering judgment. The further upstream of the signal that a detection zone is situated, the longer it will take for the growing queue to occupy this detection zone for a significant portion during the cycle. If the detection zone is too far upstream, situations where it would be helpful to apply a mitigation strategy could be missed. The closer that the detection zone is located to the stop bar, the sooner the occupancy level will be close to 100% during the cycle time. If the detection zone is too close to the stop bar, the occupancy data used for decision making may result in “false positive” indications resulting in application of mitigation strategies to intermittent conditions. In our test cases, reasonable performance was obtained with detector locations that are approximately located where dilemma zone protection or extension detectors are typically placed; between 150-500ft upstream of the stop bar or at mid-block locations as illustrated in Figure 49. Situating detection zones at approximately mid-block locations seems to be a good compromise between false-positive, false-negative, and reaction time considerations. Operation of traffic signal systems in oversaturated conditions Page 104

Figure 49. Recommended placement of oversaturation detection zones Placement of Detectors for Online Recognition of a Scenario In simple situations involving an individual approach or an individual intersection, it is straight- forward to identify where detection zones are needed since they should be placed on the approaches where the queuing is experienced. Similarly when dealing with a route or network scenario, the detection points should be placed where the queuing will determine when one or another mitigation strategy is necessary. However, when dealing with a route or network situation, it is a more subjective process to determine where the detection zones should be and which zones should be considered in decision making. While logic conditions could be constructed that are quite complicated, in most situations, simpler logic and fewer detection points will be easier to manage and understand. Figure 50 illustrates the placement of oversaturation detectors for a common scenario. In this test case, there are three critical routes competing to access the same destination (toll booths at a border crossing). At various times of day, each route can become more critical than the others. In addition, the toll booth plaza can also become saturated to the point that no addition in flow of vehicles is possible. Thus, it is important to monitor each of the routes and select an appropriate timing plan depending on which combinations of routes are oversaturated. Approximately mid-block placement or using existing extension detectors Operation of traffic signal systems in oversaturated conditions Page 105

Figure 50. Example placement of oversaturation detection points Detector Data Aggregation Intervals and Persistence Time Aggregation of detector occupancy data is also important in balancing the occurrence of false positive and false-negative conditions. There are two important considerations here: (a) the interval over which the detector occupancy is reported and (b) the number of intervals for this condition to be true before an oversaturated condition is considered to be true. Most controller firmware allows aggregation of detector data on a minute-by-minute basis. We recommend using the lowest possible aggregation level of one minute. Persistence times of three to five minutes (larger than most typical normal cycle times) are recommended to provide responsive reaction to oversaturated conditions. Selection of an occupancy threshold (or queue length, or TOSI/SOSI measures, if used) is also an important consideration in determining reaction time and balancing false positives and false negatives. In order to minimize the number of false-negative indications, it is important that the threshold be set relatively high. However, the threshold should also not be set at 100%. Occupancy thresholds in the 80%-90% range seem effective in providing a compromise between reacting to oversaturated conditions in a timely fashion, but not resulting in false positives. Logic Configuration Example Considering the case shown in Figure 51, a number of mitigation timing plans can be applied based on the status of the oversaturation detectors. There are three components to setting up the congestion response plan in the logic tool: Common Destination for all routes Operation of traffic signal systems in oversaturated conditions Page 106

• Configuration of the detection points • Configuration of the logic clauses • Configuration of the mitigation timing plans This setup is illustrated in Figure 51. In this example, not all of the oversaturation detectors are used as inputs. Figure 51. Set up for inputs, logic, and actions The key component of the setup is the configuration of the logic engines. The logical clauses should consist of mutually exclusively true clauses that result in only one of the timing plans (“action sets”) selected for implementation. In this test case, we constructed a logic table to determine what types of actions would be appropriate under each combination of detector conditions. This is illustrated in Table 9. The top part of the table is the truth table. This should include all combinations of detection stations either detecting a queue or not. If detection of a queue at that point is not important, a (-) line is shown. For example, in the first column if queues are detected on the first three links, the westbound right-turn-on-red (RTOR) indication would be disallowed with a blank-out sign. The timing plan change includes the actions listed in the bottom part of the table. For example, the sixth column action indicates that the green time for the northbound and westbound phases will be increased. Thus, a new timing plan will be commanded to the field with the same cycle time but with green re-allocated from the eastbound left-turn phase to the westbound and northbound phases. In this example, the action set consists of a timing plan change only at the key intersection. More comprehensive actions could be constructed for timing plan modifications at the adjacent intersections as well and included in the same action sets. Table 10 provides cross-reference information for the link names in Table 9 with Figure 50. Operation of traffic signal systems in oversaturated conditions Page 107

Table 9. Example logic conditions and actions Table 10. Cross reference of link names in Table 9 with Detectors in Figure 50. Link Detectors Northbound Plaza entry link 1002,1003 Northbound Goyeau 1006,1007 Eastbound Left turn 1009 Westbound Right turn 1004,1005 One logical clause (the third column in Table 9) is illustrated in Figure 50. In this case, high occupancy (oversaturation) is detected at the entrance to the toll plaza, and on the northbound route, but the eastbound left turn route is not oversaturated. Under this condition, the eastbound left turn is omitted for a short time and the RTOR of the westbound approach is also disallowed, allowing the traffic on the northbound route to get as much preference as possible. After the northbound queue is dissipated (below 50% occupancy in the logic shown in Figure 52) a different timing plan can then be selected. Condition Queue detected on NB Plaza Entry Link Y Y Y Y N N N N N N N N Queue detected on NB Goyeau Link Y Y N N Y Y N N Y Y N N Queue detected on EB Left-Turn at Goyeau Y N Y N Y N Y N Y N Y N Queue detected on WB Right-Turn at Goyeau - - - - Y Y Y Y N N N N Action Increase EB Left Turn Phase √ √ √ Increase NB Through Phase √ √ Increase WB Through Phase √ √ √ √ Eliminate RTOR for WB Right Turn √ √ √ √ Omit NB Through Phase √ Omit EB Left Turn Phase √ √ √ Operation of traffic signal systems in oversaturated conditions Page 108

Figure 52. Logic engine example As shown in this example, thresholds for each detector input can be selected independently and AND…OR logic can be applied between the inputs for a certain logic clause. The example shows three inputs per logic clause, but this could conceptually be increased to any number. We developed this initial tool with three inputs per clause to represent a three-lane approach or segment of roadway. Thus, the congestion identification logic could look at up to three lanes (AND) or any of the three lanes (OR) to exceed the congestion thresholds to have the clause evaluate as true. After a single logic clause is evaluated as true or false, logic for up to two other locations can be combined with this clause (although this again can easily be extended to more detection stations). Each of these locations can be evaluated using AND…OR logic in combinations (A and B and C) or (A or B or C). The current design does not allow for more complex logic such as “A and (B or C)” or “(A and B) or (C and D)”, although these type of extensions would not be difficult if cases can be identified that require more complex combinations. Begin and Return Conditions Each clause has a begin and a return condition. This will reduce waffling of the logic from on and off conditions. This is an identical concept to the way that traffic responsive thresholds key the currently selected plan running for 15-30 minutes. In this example, the AND condition in the first row indicates that the occupancy of the detectors 2002, 2006, and 2007 must all be above 85%, for the clause to resolve as true. This condition will then remain true until the occupancy Operation of traffic signal systems in oversaturated conditions Page 109

of all the detectors drop below, 50%. This reduces waffling in the timing plan decision if just a single lane drops below 50% for several cycles. Certainly more experimentation and research is necessary to provide guidelines on the setting of entry and return thresholds. Regardless of their exact values, it is important to make sure that the entry and exit thresholds are not exactly the same number. If the entry threshold is 85%, the exit threshold should be at least, say, 75% or lower. If the begin and return thresholds are the same value, much more frequent switching between plans will occur resulting in significant performance degradation. Persistence Time Thresholds Begin and return conditions for each clause each have persistence time thresholds, which can be changed independently, to make sure that the entry or release condition is persistent for a minimum amount of time before the clause is evaluated as true or false. The approach is currently designed so that the entry and release conditions for all clauses in the logic use the same values for the persistence time. This could be modified, but we find no empirical evidence or theoretical justification for different persistence thresholds. However, some experimentation does reveal that it may be useful to configure the “begin” and “return” persistence times differently. In particular, it seems to be more effective to configure a very low threshold for “begin” persistence and a longer time threshold for “return”. In our testing, entry thresholds of one minute and return thresholds of three to four minutes seemed to provide reasonably responsive operation. This rule of thumb specifically refers to the use of detector occupancy as trigger inputs, as TOSI, SOSI, and queue length estimates were not tested as extensively. Online Performance Evaluation Framework For the research project, this experimental congestion management logic tool was integrated with Virtual D4 traffic control software and the Vissim simulation system as illustrated in Figure 53. This system can use detector occupancy, TOSI/SOSI, and queue length as inputs to logic clauses. Field integration of the logic tool using TOSI/SOSI and queue estimation algorithms with real- world traffic controllers would be necessary for any field implementation. The system is part of the deliverables for this project and thus can be redistributed to anyone by NCHRP. Operation of traffic signal systems in oversaturated conditions Page 110

Figure 53. Online oversaturation management research software integration The online process is implemented in a software-in-the-loop framework as illustrated below. • Vissim simulation model • Queue length and oversaturated conditions estimator module • Congestion manager module • D4 Virtual traffic controller module Vissim is used to represent the “real world” movements of drivers in the case study locations and their responses to traffic control strategies. The traffic control strategies are implemented in Vissim using the D4 virtual traffic controller. D4 is real-world software used to control intersections in San Francisco and San Jose, CA, among other locations including Windsor, ON. This software-in-the-loop approach (SILS) replaces the internal approximate control logic of the modeling software with the algorithms of the actual traffic controller, thereby allowing simulation software to be used with full controller functionality at faster-than-real-time speed. This has been shown in previous testing to improve simulation performance to better than 3:1 real-time speeds. VISSIM Congestion Manager Oversaturation Estimation Virtual D4 Second by second data Phase timing and detector actuations SQL Database Shared Memory Area Operation of traffic signal systems in oversaturated conditions Page 111

The first step of the evaluation process, as shown above in Figure 53, is to obtain access to the traffic signal phase timing information and detector actuations inside of the simulation model and use that data to estimate queue lengths and compute oversaturation estimates. The queue length and oversaturated conditions measurement module was developed by the University of Minnesota. This module then sends these estimates of queue length and oversaturation intensity on a cycle-by-cycle basis to the congestion manager as illustrated below in Figure 54. Figure 54. Research software integration – Step 2 The congestion manager uses these measurements in the generic if/then logic to determine which action plans should be enabled. If a plan change or other control action is required, the congestion manager communicates this information to the Vissim simulation by sending a control message to the D4 virtual controller(s) as illustrated below in Figure 55. D4 has a very simple shared memory interface that allows any external program to send commands by writing the desired plan information to the shared memory. VISSIM 118 Congestion Manager Oversaturation Estimation Virtual D4 Shared Memory Area Queue Length TOSI SOSI 2 Detector Occupancy 2 Operation of traffic signal systems in oversaturated conditions Page 112

Figure 55. Research software integration – Step 3 D4 then acts on the plan commands sent by the congestion manager and implements the requested change to the traffic control strategy, such as phase omits, phase reservice, split and cycle time modifications, simultaneous offsets, and other strategies, by running the newly- requested plan. This step is illustrated in Figure 56. Note that this approach is not adaptive; these alternative plan designs must be pre-loaded on the controller and set up appropriately before-hand by the engineer. VISSIM Congestion Manager Oversaturation Estimation Virtual D4 SQL Database Shared Memory Area Plan s lection Preempt 3 Operation of traffic signal systems in oversaturated conditions Page 113

Figure 56. Research software integration – Step 4 After the new plans are implemented during the oversaturated conditions, the Vissim model collects the performance data such as delays, throughput, stops, and so on for effectiveness evaluation as identified below in Figure 57. VISSIM Congestion Manager Oversaturation Estimation Virtual D4 SQL Database Shared Memory Area Change timing values4 Operation of traffic signal systems in oversaturated conditions Page 114

Figure 57. Research software integration – Step 5 A similar process is applied in the offline case, except the congestion manager module is not used to dynamically change signal timing strategies based on the congestion estimates. In the offline case, the changes to signal timing patterns are simply programmed ahead of time based on the analysis of the baseline conditions and implemented in the simulation model at the pre- defined times. In either case, multiple runs will be conducted to make sure that statistical variations in the effectiveness of a given strategy are captured. Summary In this section we described a process and a software tool for implementing mitigation strategies in an online manner for non-recurrent conditions. The first step of the process is to design the mitigation strategies based on observation of the condition and load those congestion plans into the field controllers in the network of interest. Based on measurement of TOSI, SOSI, queue length, or detector occupancy, the online tool can select the best matching timing plan or plans based on simple if…then logic. A truth table is used to map out all of the possible combinations of detector conditions that can lead to one plan or another being selected. The tool was integrated with the Vissim microscopic simulation system with the D4 SILS virtual traffic controller. The tools (minus Vissim and the D4 SILS) are part of the deliverables of the project. In Chapter 3, we provide an example application of the tool to mitigate oversaturated conditions in a real-world situation. The performance results of this test were mixed, primarily because of VISSIM Congestion Manager Oversaturation Estimation Virtual D4 SQL Database Shared Memory Area Effectiveness Measures5 Operation of traffic signal systems in oversaturated conditions Page 115

the extremely challenging nature of the chosen problem. The process and the tool, however, were proven to be a viable method to tie together the design of mitigation strategies with the measurement of oversaturation severity estimates and queue length measurement. Further in Chapter 3, we also describe an experimental methodology for direct calculation of green time adjustments from TOSI and SOSI measures on an oversaturated route. This procedure was applied and tested in an offline manner for two test cases in this project. However, the procedure may have promise for online application as well. This potential research and development effort is left for future work. Operation of traffic signal systems in oversaturated conditions Page 116