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217 A p p e n d i x C As a bystander, it is fairly easy to watch traffic flow around the location of an incident and identify the delay associated with that incident as the queue that forms at that location. As long as that queue remains in place, even if it moves up- or down- stream as a result of shock waves and other physical phenom- ena, all the delay can be associated with the observed incident. Even if that section of roadway might normally have a queue for a portion of the time the incident queue exists, all delay can be consider incident delay, which can then be compared in severity with the delay normally present for that roadway section. The difference in those conditions can be considered to have been caused by the incident. When examine at a broader corridor level, however, the queues that form as a result of incidents can create different side effects that change the travel time experienced by motor- ists in the corridor. In some cases, the incident queue reduces downstream traffic volumes, allowing traffic to flow more smoothly. In other cases, the release of a queue that has formed behind a major accident can create a traffic volume wave when that accident scene is removed, and that wave can create one or more secondary queues downstream of the accident loca- tion. This condition is illustrated in Figure C.1, which shows (in black) the downstream movement of congestion caused when a pulse of vehicles flows downstream after having been released from a major accident scene. These secondary queues also are incident caused even though they are located at points removed from the location of the actual incident. Visually, these effects can be identified on a case-by-case basis, so long as sufficient data are present. Mathematically, for very large data sets, and when only summary statistics (e.g., corridor travel time, vehicle miles traveled, or vehicle hours traveled) are available, this task becomes much more difficult. Part of the mathematical problem is that incident- caused delay can last considerably longer than the incident itself and can extend to geographic regions far removed from the incident location itself. In Figure C.1, for example, the actual incident lasted from 5:30 to 7:00 a.m. and occurred at a location just east of where traffic detection starts in the cor- ridor, essentially to the left and above the black congestion blob in the figure. Figure C.1 does not show what happened during the incident; rather it shows the lingering effects of a severe incident after it has been cleared. An additional difficulty is that the geographic and temporal extent of the incident- caused delay is a function of the background traffic condi- tions within which the incident occurs. Compounding this difficulty is how travel times, which occur over extended times and spaces, differ from incidents, which occur in narrow tem- poral and geographic spaces. The problem of associating an incident with a trip travel time is best explained with an example. Assume that the cor- ridor being studied is 10 miles long (extending from Milepost 0 to Milepost 10), and the free-flow speed is 60 mph. Under free- flow conditions a car traverses the corridor in 10 minutes. An accident occurs at Milepost 6 at 8:00 a.m. and lasts 3 minutes, until 8:03 a.m. A car traveling the length of the corridor start- ing at Milepost 0 at 8:00 will be affected by this incident, even though the incident has been cleared before the carâs arrival at the scene, because the car starting its trip at 8:00 a.m. must travel through the queue formed by the accident. But impor- tantly, a car starting on that same trip at 7:55 (5 minutes before the accident takes place) also will be affected by the incident, because even at free-flow speeds, that car is only at Milepost 5 at 8:00 a.m. when the accident occurs. However, if that same accident occurs at Milepost 1, instead of Mile- post 6 (both inside the study corridor) the 7:55 trip will not be affected, but the 8 a.m. trip will be. Computation of Influence Variables, Seattle Analysis: Mechanisms for Determining When an Incident Affects Travel Time and Travel Time Reliability
218 Figure C.1. Extra congestion caused by release of traffic delayed behind a major accident scene on westbound I-90.
219 The other difficulty with associating incidents and specific trips is understanding the duration of the congestion that forms as a result of that incident. In the above example, the queue formed (or disruption caused) by the 8:00 a.m. acci- dent may last anywhere from zero additional minutes to sev- eral hours. If the 8:00 a.m. accident occurs in the middle of the a.m. commute period, the queue associated with that accident may last a full hour before traffic volumes reduce enough to allow the queue to dissipate. But if traffic volumes are light that morning, the queue may dissipate immediately. Thus a trip starting at 8:30 a.m. on this same corridor may or may not be influenced by the 8:00 a.m. accident, depending on the background traffic conditions occurring on the corridor and the nature of the accident itself. Thus, without a detailed and complex data set and analysis algorithm for identifying time- and day-specific speeds, along with that same level of detail for when and where incidents occur within a corridor, it is impossible to directly associate any given trip with a given incident. This level of detail was not available to the study team for this analysis. Consequently, no simple algorithm was identified that could identify which travel time (or vehicle miles traveled or vehicle hours traveled) measures for a given corridor were directly influenced by a given incident. As a substitute, this project developed three methods for defining the extent to which delay or trip travel time is influenced by any given incident. Each method has strengths and weaknesses. Taken together they are reasonably explanatory for how incidents affect travel time and travel time reliability. The three measures selected are defined as follows: ⢠Active influence assumes that any trip that starts into the corridor during a time period that contains an active inci- dent is affected by that incident. Since travel time data were available on a 5-minute basis for L03, this method of asso- ciation worked as follows: if an incident occurred from 8:04 to 8:08 a.m., trips with start times of 8:00 and 8:05 a.m. were associated with this incident. No other trips were considered to be influenced by this incident. This measure is the most restrictive of the methods used to associate incidents with travel times. All trips assumed to be influenced by an incident in this method are known to be influenced by incident-caused queues (if any form), but the method will miss some of the earliest trips influenced by the incident, and it will miss later trips that are influenced by the residual queue left after the incident has been cleared. ⢠Time extended influence assumes all incidents happen in the center of the study segment; this method extends the influence period earlier in time equal to the time it takes to drive half the corridor at free-flow speed. In addition, it assumes that influence extends an additional 20 minutes after any given incident ends. Using the 8:04 to 8:08 a.m. accident from the active influence example above, this method assumes that the incidentâs influence extends from trips starting at 7:59 a.m. to those ending at 8:28; that is, the 7:55 a.m. trip is the first affected, and the 8:25 a.m. trip is the last affected. This is an extension of three 5-minute time periods after the last period in which the incident was actually active. This technique makes the 20-minute exten- sion (which is the origin of the 5+20 name in the data spread- sheet) appear to be a 5+15 time-period extension. Although the time extended methodology will miss a few incident-influenced trips when incidents occur at the far-upstream portion of the study corridor segment, it will capture the majority of the trips that are influenced by the formation of the incident-caused queue. It also will capture a significant portion of trips that are affected by residual queues. If those queues are nonexistent or short lived, it will overestimate the influence of a given incident. However, since the intent of this analysis is to capture the effect of incidents on trip reliability, overestimating the number of fast trips that have incident influence is less important than making sure that all very slow trips are associated with their causes. Thus this bias is assumed to be acceptable. ⢠Queuing extended influence assumes that once an incident occurs, any travel time increase on the corridor is at least partly associated with the (potential) queue that forms as a result of that incident. This method assumes that any increase in travel time that occurs while an incident is active is associated with that incident. The queue extended influence approach selects the fastest corridor travel time experienced before and during the inci- dent. All subsequent travel times are assumed to be influ- enced by that incident until corridor travel times return to that fastest time. Once a measured travel time faster than the reference travel time is observed after the time extension has ended, the influence of that disruption has ended. The time extended influence definition is used to define the time periods from which the reference (fastest) travel time is selected. Note that the queue extension approach was originally tested using the 5+20âminute version of the time extension approach. It was then recomputed with new variables, including a more simple time extension defini- tion of a one-time period before the disruption and a one- time period after the disruption has been cleared. These queue extension variables use the term 5+5 in their variable definition to reflect the 5 minutes before and the 5 minutes after the recorded incident time. In off-peak (low-volume and/or low-capacity) condi- tions, the queue extension approach is an excellent measure of incident effects. If the incident occurs at the beginning of peak period conditions, the queue extension approach is likely to associate all of the peak period congestion with the incident. Although this may overstate the extent of any given
220 incidentâs congestion-causing influence, it is difficult to separate out the lasting influence of the incident on bottle- neck formation, even when detailed statistics are available. Queuing extended influence is thus assumed to be a reason- able liberal measure of the effects of incidents on the travel times experienced by motorists. None of these measures is perfect. Taken together, however, they are descriptive of the degree to which congestion and delay are related to incident occurrences. By tracking all travel times influenced by a disruption, it is possible to identify the wide range of impacts a single dis- ruption causes. The extra delay a trip experiences as a result of any given disruption changes depending on the time (relative to the formation of the queue) that a given trip arrives at the queue caused by the disruption. That queue grows from nothing to its largest extent, and then shrinks back to nothing. If the trip being monitored arrives at the beginning or end of the queue formation, the added delay experienced is modest. If it arrives at the height of the queue, its delay is the maximum experienced. The methodologies described above associate each 5-minute average travel time with an incident or nonincident condition. The result is that some of these measured travel times experi- ence the shoulders of the incident queues, and some experience the maximum queue. The result is an ability to monitor the entire spectrum of delays associated with each incident. It is therefore possible to explore the different travel times associated with any given incident, and if desired, select the maximum travel time associated with that incident. The trip with the larg- est travel time is assumed to be the trip made most unreliable as a result of that particular incident. In general, the findings presented in the body of this report concentrate on using the queue extended (5+5) measure of influence. The Washington State Transportation Center proj- ect team at the University of Washington considers the queue extended measure as the best measure of incident influence; it also is the measure of maximum influence.
