**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

**Suggested Citation:**"2 FINDINGS." Transportation Research Board. 1996.

*Capacity Analysis of Traffic-Actuated Intersections: Final Report*. Washington, DC: The National Academies Press. doi: 10.17226/6347.

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 FINDINGS This chapter presents the most significant findings of the study and identifies the appendices in which more detail may be found. The findings relate primarily to the development and evaluation of models for estimating the signal timing plan and the delay at traffic-actuated intersections. The signal timing plan estimation and delay estimation results wait be addressed separately. SIGNAL TIMING PLAN ESTIMATION The signal timing estimation procedure included In Appendix II to HCM Chapter 9 is the logical place to begin this discussion, because it represents the status quo. Appendix 9-H recognizes that indivi- dual phase times are variable under traffic-actuated control and suggests that the average cycle length and phase times may be approximated by assuming that the controller is effective in its objective of keeping the critical approaches nearly saturated. Mathematically, this relationship may be stated as: CaV L/( ~ Y/XT) Where: (1) Cav = The average cycle length Lo = The total lost time per cycle, i.e., the sum of the lost times associated with the starting and stopping of each critical movement in the phase sequence. Y = The critical flow ratio, determined as the sum of the flow ratios for the individual movements that are critical in each phase. The flow ratio for each movement is defined as the ratio of the traffic volume to the saturation flow rate. The value of Y indicates the proportion ofthe total time that is required to accommodate all of the cntical movements, exclusive of the lost time. XT = The target degree of saturation (volume/capacity ratio). A value of 0.95 is suggested in Appendix 9-~l for traffic-actuated control. After the average cycle length has been computed, the average green times may be determined by dividing the total cycle time among the critical movements in proportion to their individual flow ratios. This is a common traffic engineering concept, and it will not be belabored here. There are four major problems with the Appendix 9-~l methodology that have drawn intense criti- cism: NCHRP Project 3-48 Final Report: Page 13

l. The fixed threshold of 95 percent saturation has not been well accepted. Several studies have indicated that a somewhat lower degree of saturation open results t3,43. 2. The method is not sensitive to the design parameters oftraffic-actuated control. The effects of detector configuration and controller settings are not reflected in Equation I. 3. The simplistic nature of this mode} does not provide for real-worId complications such as minimum and maximum green times, shared-lane permitted leg turns, left turns that are allowed to proceed on both permitted and protected phases, phase skipping due to lack of demand, constraints imposed by coordination, etc. 4. There is no basis in the mode} to distinguish between pretimed and tra~c-actuated control. A procedure that addresses all of these problems has been developed as a major product of this research. The analytical aspects of the procedure are described in detail in Appendix C. A step-by- step computational process using worksheets is presented in Appendix E. The software that imple- ments the computational procedure is described in Appendix G. Green Time Determination for Traff-lc-Actuated Controllers The detenn~nation of required Been time is a relatively straightforward process when the cycle length is given; however, traffic-actuated controllers do not recognize specified cycle lengths. Instead, they determine, by a mechanical analogy, the required green time given the length of the previous red interval and the arrival rate. They do this by holding the r~ght-of-way until the accumulated queue has been serviced. The basic principle underlying all signal timing analysis is the queue accumulation polygon (QAP), which plots the number of vehicles queued at the stop line over the cycle. The QAP for a simple protected movement is illustrated in Figure 2. The queue accumulation and discharge is represented in this very simple case as a triangle. The accumulation takes place on the leD side of the triangle (i.e., effective red) and the discharge takes place on the right side of the triangle (i.e. effective green). More complex polygons are generated when permitted movements occur and when a movement proceeds on more than one phase. Chapter 9 of the HCM includes an extensive discussion on this subject. Two methods of determining the required green time, given the length of the previous red, are illustrated in Figure 2. The first employs the "Target v/c" approach, which is the basis for the current Appendix ~ method, and for the planning method described in HCM Chapter 9. Under this approach, the green time requirement is determined by the slope of the line representing the specific target v/c ratio. If the phase ends when the queue has dissipated under these conditions then the target v/c will be achieved. NCHRP Project 3-48 Final Report: Page 14

! 8 :D ~6 - ._ an _ a) ._ ~4 > o Proposed Analytical Model Green time based on phase extension time l As HCM Appendix II Green time based on target v/c ratio _ / Red Time At\ Time (seconds) Queue Senriec T,mc Phase Extension Talc Figure 2. Queue accumulation polygon illustrating two methods of green time computation The second method recognizes the way a traffic-actuated controller really works. It does not deal explicitly with v/c ratios; in fact it has no way of determining the v/c ratio. Instead, it terminates each phase when a gap of a particular length is encountered at the detector. Good practice dictates that the gap threshold must be longer than the gap that would be encountered while the queue is being serviced. Gaps large enough to terminate the phase cannot occur until the queue service time (based on v/c = 1.0) has elapsed. Therefore, the average green time may be estimated as the sum of the queue service time and the phase extension time as shown on Figure 2. Each of these components is derived separately in Appendix C. Cycle Length Determination This green time estimation procedure is easy to implement, but it does not lead directly to the determination of an average cycle length or green times, because the green time required for each phase is dependent on the green time required by the other phases. Thus, a circular dependency is established requiring an iterative solution. with each iteration, the green time required by each phase, given the green times required by all the other phases, may be determined. NCHRP Project 3-48 Final Report: Page 15

The logical starting point for the iterative process is the minimum times specified for each phase. If these times turn out to be adequate for all phases, the cycle length will simply be the sum of the minimum phase times for the critical phases. If a particular phase demands more than its minimum time, then more time must be given to that phase. Thus, a longer red time must be imposed on all the other phases. This, in turn, increases the green time required for the subject phase. This circular dependency converges quite reliably through a series of repeated iterations. Minimum Phase Times The whole question of minimum phase time requires more attention. The specified minimum green time constraints are valid only for pretimed phases and phases that are set to recall to the minimum time regardless of demand. The real significance of the minimum phase time for an actuated phase is that the phase must be displayed for its specified minimum time unless it is skipped due to lack of demand. This situation may be addressed analytically by determining the probability of zero arrivals on the previous cycle, PoV Assuming that the phase will be displayed for the minimum time except when no vehicles have arrived the adjusted minimum phase time may be computed by multiplying the specified phase time by the quantity (! - PO`,). This relationship also has circular dependencies because, as the acljusted minimums become shorter, the probability of zero arrivals also becomes higher, which further reduces the adjusted minimums. Fortunately, the solution fits well into the iterative scheme that was just described. The use of adjusted ~r~iimum green times offers a practical method for dealing with phases that are not displayed on each cycle. The concept applies equally to pedestrian minimum times. Multi-Phase Operation Two extensions to the methodology presented to this point are required to deal with more complex situations. The first is the extension of the QAP from its simple triangular shape to a more complex shape that represents different arrival and departure times at different points in the cycle. The second is a procedure to synthesize a complete single ring equivalent sequence by combining cntical phases in the dual ring operation. The details of both procedures are described finely in Appendix C. Coordinated Semi-actuated Operation The non-actuated phases under se~-actuated control may be coordinated with similar phases at neighboring intersections to promote progression oftraflic on an arterial street. In the most common coordination scheme, a background cycle length is imposed. The actuated phases receive their allotment of green time in the usual manner, except that their maximum green times are controlled externally to ensure conformance to the specified cycle length. If the actuated phases require all of their nominal green time allotment, the interaction operates In a more or less pretimed manner. If not, the unused time is reassigned to the coordinated phase. NCHRP Project 3-48 Final Report: Page 16

The computational structure developed under this project is able to approximate this operation quite effectively. The analysis of coordinated operation requires another iterative loop which executes the procedure described in Appendix C, adding more green time incrementally to the coordinated phases until the background cycle length has been reached. The result is a timing plan that approximates the operation of the controller in the field. Volume-Density Operation The main differences between volume-density control and conventional actuated control are the rn~n~mum green settings (variable irutial), the detector configuration, the gap reduction feature and the passage time setting for the last vehicle actuation. The refinement of the proposed analytical mode! for volume-density operation focused on these areas. The "Free Queue" Parameter The free queue parameter indicates the number of led turning vehicles that may be stored in a shared lane awaiting gaps in the opposing traffic without blocking the passage of through vehicles. The current HCM procedure assumes that the first waiting left turn will block all of the following vehicles In the shared lane. This assumption produces pessimistic results in some cases. Both the through vehicle equivalence of a led turn (EL] ~ and the lane group saturation flow rate are affected. At this point, only the SIDRA [5] model considers the free queue explicitly. Because of its impor- tance to tra~c-actuated control, it is essential that the proposed analytical model recognize this phenomenon. The analytical basis for the model is described In Appendix C. A set of curves is devel- oped to illustrate the effect of the free queue on the estimated phase time as a Unction of the approach volume. The phase time analysis with a free queue is best illustrated with a simple example. Consider a trivial intersection with four single-lane approaches. All approaches are configured identically and carry the same traffic volume. On each approach, the proportions of left sums, through vehicles and right turns are 0.2, 0.7 and 0. i, respectively. This is an example of a simple two-phase hilly actuated operation. The rniriimum phase time for each approach is 15 seconds and the maximum phase time is 80 seconds. The detector is 30 feet long and placed at the stop line. The allowable gap is 3 seconds. Each phase is assigned 4 seconds yellow plus all-red and 3 seconds of lost time. Each approach volume varies from 100 vph to 800 vph, while the range of free queue is set from 0 to 2. The value ofthe free queue is not necessarily an integer. Based on the proposed method, the phase time estimation with free queues is shown in Figure 3. In this figure, the x axis represents the approach volume, y axis shows free queue values, and the vertical axis is the estimated phase times by the proposed method. The effect of the Bee queue value may be easily observed from this three dimensional surface plot. Note that the curve shown at a free queue value of zero represents the status quo. NCHRP Project 3-48 Final Report: Page 17

- to · I to ~ en ~om Figure 3. Effect of the free queue on phase times for the example problem The computational structure of the proposed analytical mode! described in Appendix E has been designed to incorporate the Dee queue concept. While it would be difficult to verify the mode! satis- factorily, either by simulation, or in the field, it is suggested that the analysis is robust and the HCM Chapter 9 procedure wall be enhanced if the free queue is included. EVALUATION OF THE SIGNAL TIMING ESTIMATION MODEL Phase Time Comparison between NETSIM and the Proposed AnalYtical Model The proposed signal timing estimation mode} was evaluated using simulation data Tom nine inter- sections and field data Tom one intersection. The sample data sets used in the simulation study are summarized in Appendm F. These data sets represent a wide variety of conditions. The results are summarized graphically in Figure 4. Each point on this figure represents a single comparison between simulated phase length obtained from NET SIM and corresponding estimates produced by the pro- posed analytical model. Note that the two methods compare very favorably. The correlation (R squared) for this comparison was 0.90, and the slope of the regression line was close to Ill. This suggests that the proposed analytical mode! was able to achieve substantially the same results as NETSIM. NCHRP Project 3-48 Final Report: Page 18

80- - 70 ~ ~- c, ~ ~- ._ ca 40 ._ ~ 20 lo 10 ~ -/ ,,,,,,, ,,,,,,, ,,,,,, ,,,,,,, ,,,,,, ,,,,,,, ,,,,,, ,,,,,,, ,,,,,, ,,,,,,, ,,,,,, ,,,,w,,,,,, ,,,,,7 c..... R2 =o.go / ............................................................................... ....... ,' a-7~. . ~. ad. . . , . it & - ,,~_ .,¢ ......... 0 10 20 ~ 40 = ~70 80 Simulated Phase Tirne (~c) Figure 4. Comparison of phase time estimates by NETSIM and the proposed analytical mode! Phase Time Comparison between the Analvtical Model and Field Data Figure 5 shows a phase time comparison between the estimates from the analytical model and field data from a multi-phase intersection in Gainesville, Florida. All led turns had protected plus per- mitted phasing. This comparison is based on 256 observations. Two groups of data points are shown in the figure because the through traffic phases tended to be substantially longer than the left terra phases. Pedestrian recall was set on each approach. Therefore, the pedestrian phase time of 22 + 5 = 27 seconds becomes the lower bound for the through phase shown in Figure 5. The maximum green time of ~ 5 seconds for lest turns set the upper bound for the left turn phases. Although the phase time estimates from the model are slightly higher chart the measured field data for left turn phases (low volume), the regression line is close to I: ~ slope. The dispersion of the data poirts is small, indicating that the phase time estimates from the analytical model are close to the field data. This is confirmed by a very high R squared value of 0.95. NCHRP Project 3-48 Final Report: Page 19

60 ~ 50 m _ oo 40 30 o - ~ 20 ._ in ~ 10 R 2 = o.g 5 (2 5 6 observations) ,, ~ Through Phases Left-turn Phases ELF O . 20 30 40 Phase Time from field Data (see) 7:00 AM - 8:00 PM 0 10 50 60 Figure 5. Phase time comparison between the proposed analytical mode! and field data ESTIMATION OF DELAY AT TRA~IC-ACTUATED INTERSECTIONS The traditional delay formulation used by virtually all analytical models is based on two terms which are added together to produce the total delay (D) in seconds per vehicle. For non-platooned arrivals, D is the sum of the first delay term (D1) and the second delay-term (I)2). The total delay per vehicle for a given lane group can be expressed as: D =D1 +D2 (2) 1. The first (uniform) delay term, D1, which is mainly based on the uniform delay (Du) as- sumes that ad vehicles arrive In a completely uniform manner. The uniform delay is com- puted as the area contained within the queue accumulation polygon (QAP). 2. The second (incremental) delay term, D2, adds a correction factor to compensate for randomness in the arrival patterns and occasional oversaturation. Three delay models will be discussed in this chapter. The first is the existing HCM delay model as it appears in the current version of Chapter 9. The other two were developed by members of the NCHRP 3-48 project team. These will be referred to as Mode! ~ and Model II, respectively. NCHRP Project 3-48 Final Report: Page 20

The BCM DelaY Model In the current HCM delay model, a delay adjustment factor, DF, is applied to Do to account for the impact of control type and signal progression on delay. These two effects are mutually exclusive. Table 9-13 In the HCM indicates the appropriate values of DF for all of the possible control modes. For isolated traffic-actuated operation (no progression effect), the DF factor is fixed at 0.85 for all lane groups. Therefore, the HCM delay mode! for isolated traff~c-actuated operation becomes D = 0.85 D~+D2 (3) Since the QAPs must be developed in detail by the proposed analytical mode! to determine the phase times, the value ofthe uniform delay, Du (i.e., the area contained within the QAP), may be computed by a simple extension to the existing phase time prediction model. The detailed development of the unifonn delay equations for computing the QAP areas of possible phasing alternatives is descnbed in Appendix D. For simple protected movements with triangular QAPs, the HCM expresses the uniform delay as: D, The incremental delay is expressed as: D2 = 225 x2 where g = C = 0.5 C jl ~ ( C)| 1 _ ( g ) [Min (x, 1.0)] u (x - 1) + ~ (x-1)2+ 16X c (5) Effective green time of the lane group; Cycle length; x = Volume/capacity ratio ofthe lane group. For the led turn movement in com pound led turn protection, x is the ratio of total leD turn volume to total led turn capacity; Hourly capacity (vehicles/hour) of the lane group. It is the maximum arrival flow that can be served under prevailing flow conditions: c = S */C where S is the adjusted saturation flow (vehicles/hour). Note that for the left turn movement in the compound led turn protection, c is the total capacity for the led turn movement. NCHRP Project 3-48 Final Report: Page 21

Note that the HCM signalized intersection analysis method deals in stopped delay as opposed to total delay. Therefore, the values shown in the HCM Chapter 9 delay equations are divided by I.3. Delay Model I Delay model I refers to the delay model developed by Ak~elik and Chung [6]. The total delay (D) is equal to the sum of the uniform delay IDS) and the incremental delay (D:) as shown in Equation 1: D=D1 +D2 The D, valueis the product ofthe uniform delay (Du) based on the QAP and a uniform delay adjust- ment parameter (fat). The uniform delay adjustment parameter proposed by Ak~elik and Chung [4] IS: D1 = fdlDu forx< 1.0 (6) D1 = fd~(X=l) Du for x > 1.0 where fd1 = Uniform term parameter' which can be computed by the following formula. Note that fdl(X=l) is the value of the uniform term parameter at the degree of saturation (x) equal to 1.0. fat = [1 + 0.40 (S g / 3600) (v / S) ~ (7) where g = Effective green time (seconds) of the lane group; S = Adjusted saturation flow (vehicles/hour) of the lane group; and v = Traffic volume (vehicles/hour) of the lane group. For compound left turn protection, fat is computed individually for the protected phase and permitted phase. Thus, in the computation of the first-temn parameter for each phase, it is necessary to use the (S go and (v / S) ~ values for the relevant green periods (l = I, 2 denotes the green periods) to com- pute (fat) ~ individually. The computation of the incremental delay term also adopts the delay model proposed by Ak~elik and Chung [61. The incremental delay, D2, can be computed by the following formula: NCHRP Project 3-48 Final Report: Page 22

D2 = 90O Tp (X- 1)+ D2 = 0 otherwise where kd = ~y2 ~ kit (x - xO) p for x > xO (8) Tp = Peak flow period (analysis periods in hours. The default value is 0.25; c = Hourly capacity (vehicles/hour) of the lane group. It is the maximum arrival flow that can be served under prevailing flow conditions: Q = S (g / C); Incremental term parameter, computed as kd = 0.40 (g S /3600~° Is (v / S)i ~ (9) For compound led turn protection, use the total (g S) for the led turn move- ment, (g S) = ~ (g Ski, use total left turn volume per hour, v = £ vi, and use the average saturation flow for the two green periods, S = £ (g Ski / £gi = (g _ S) / £ gi; x0 = Critical degree of saturation ofthe lane group. Note that with compound left turn protection, the value of xO for the left turn movement is the same as that for the protected left turn movement. If the degree of saturation, x, is below xO' the average incremental queue is zero (D2 = 0~- Xo iS expressed as follows: X = 0 42 h -a! ~Go.2 where (10) ho = Allowable gap setting as a headway value (seconds). Note that with compound left turn protection, the value of ho for the left turn movement is the same as the value of ho for the protected left turn movement; and MxG = Maximum green time setting as a controller (displayed) value (seconds). Note that with compound led turn pro- tection, MxG for the left turn movement uses the value of MxG for the protected led turn movement. Note that the delay model proposed by Akcelik and Chung was derived by calibration of the general model using simulation data. NCHRP Project 3-48 Final Report: Page 23

Delav Model ~ The structure of Delay Mode} IT has been developed more recently to achieve consistent modeling of delay for different intersection types, and for different performance statistics for the same intersection type. Model IT is based on the same general mode} structure as Model ~ but uses fat, = I.0, x0 = o.o and kd as a Unction of the gap setting (given in Table I). It was developed by IN [7], discussed in Li, Rouphai! and Ak~elik ~] and adopted by Fambro, Rouphail, Messer and Li [93. Mode! I! uses the uniform delay mode} for the first term and assigns all additional delays due to randomness (overflows) to the second term. · . · . Table I. Values of the delay mode! parameter kit in Delay Mode! ~ Gap setting headway,hO(seconds) ~ 2.5 | 3.5 | 4.0 | 5.0 || Delay parameter, kd (Li model) | 0.084 | 0.1 19 | 0.125 | 0.23 1 | Comparison of Delav Estimates between Delav Models and NETSIM Simulation For traff~c-actuated operation, the accuracy of the delay model depends on the accuracy of the estimated signal timing plan. The different analytical models were incorporated as options into the computational structure described in Appendix E. In this study, NETSIM was used as an evaluation too! for delay estimation. The data sets included four HCM Chapter 9 sample calculations, five hypothetical intersections and one field data set. Some of the traffic volumes, phase sequences and operational data were modified slightly to increase the range of conditions included in this analysis. A complete description of the data sets is given in Appendix F. Since the delay is not meaningful for movements with volume/ capacity ratio greater than one, only the delay estimates for movements with v/c ratio less than I.0 were used for comparison. Four specific comparisons were performed. In each case, the delay estimate from NET SIM was plotted against the corresponding estimate Tom an analytical procedure. The four analytical proce- dures that were compared included: The existing HCM Chapter 9 method; i.e., timing computation by the Appendix IT method and delay estimates by the current HCM Chapter 9 model; I. Delay estimates from the current HCM Chapter 9 model, based on timing computa tions by the proposed analytical model; NCHRP Project 3-48 Final Report: Page 24

Delay estimates from Mode} I, based on timing computations by the proposed analytical model; and Delay estimates Dom Mode! IT, based on timing computations by the proposed analytical model. Each of these comparisons wait be discussed separately. Delay Estimates Based on the Existing BCM Chapter 9 Method This comparison was carried out to indicate the performance of the existing HEM Chapter 9 method as a basis for evaluating the effectiveness of the proposed improvements to the methodology. Figure 6 shows the NET SIM delay estimates plotted against the corresponding estimates from the HCM delay mode! based on the phase times predicted by the Appendix IT technique. The sample size included 433 observations. When the value of the delay estimate increases, the dispersion ofthe data points increases. A large dispersion occurs at delay values over 50 seconds per vehicle. The correlation is very low (R square = 0.45~. The slope of the regression line is about 0.75. This indicates that, when compared to NET SIM, the HCM Chapter 9 technique predicted smaller delay values. 90 ID 8 0 A, 70 In _' _ 6 0 HE 50 40 a 30 20 1 0 R2= 0.45 (433 observations) ~ '-% ~_ ' ~ it_ 1 _ ~ _ ~_~ _ a ~-_ _ 0 10 20 30 40 50 60 70 80 90 Total Delay from TRAF-NETSIM (sec/veh) Figure 6. Delay comparison between the current OCM Chapter 9 procedure and NETSIM NCHRP Project 3-48 Final Report: Page 25

DCM Delay Model Estimates Based on Timing Estimated by the Proposed Analytical Model Figure 7 plots the NET SIM delay est~ates against the corresponding estimates Dom the HCM delay mode! associated with the phase times predicted by the proposed analytical model. A total of 433 observations were used in this analysis. The value of R square is equal to 0.~. The regression line is slightly less shall I: ~ slope, indicating slightly smaller delay values predicted by the HCM. Results Tom Figure 7 are much better than results Tom Figure 6, indicating that, based on the same HCM delay model, a much better delay estimation can be achieved if the phase times predicted by the developed analytical mode! are used instead of the phase times predicted by the Appendix 9-~l method. 90 so 7 0 60 - 50- _ 6~ 40 ~ 30- _ o <, 20 a 10 O- , . . . . . . 0 1 0 20 30 40 50 60 70 Total Delay from TRAF-NETSIM (sec/veh) R 2 = 0.88 (433 observations) ~ .~ : ~F :~ 80 90 Figure 7. Delay comparison between the lICM Delay Model and NETSIM Model ~ Delay Estimates Based on Timing Estimated by the Proposed Analytical Mode! Figure ~ plots the NETSIM total delay estimates against the corresponding estimates Dom Delay Mode} ~ associated with the phase times predicted by the proposed analytical model. A total of 433 observations was used in the analysis. A small dispersion of the data points is shown in this figure, as confirmed by a high R square value of 0.92. The regression line is close to I:! slope. This indicates that when Mode} ~ uses phase times predicted by the proposed analytical model, delay estimates are very close to those estimated by NETSIM. A comparison of Figures 7 and ~ suggests that, based on the same phase times, a better delay estimate can be achieved by Delay Mode} ~ over the HCM delay model. NCHRP Project 3-48 Final Report: Page 26

So - ~ 80 -, a' 70 - 60 50 40 c, 30 c, ~ 20 o 1 0 _ / I R2= 0.92 (433 observations) a._-',~'%_ ~ 'a - l it' _aer 0 1 0 20 30 40 50 60 70 80 90 Total Delay from TRAF-NETSIM (secJveh) Figure S. Delay comparison between Mode! ~ and NETSIM Mode! ~ Delay Estimates Based on Timing Estimated by the Proposed Analytical Mode! Figure 9 plots the NET SIM total delay estimates against the corresponding estimates Dom Delay Model II associated with the phase times predicted by the proposed analytical model. A small disper- sion of the data points is shown in this figure, as confirmed by a high R square value of 0.90. The regression line is close to 1:1 slope. This indicates that when Delay Model ~ uses the phase times predicted by the proposed analytical model, delay estimates are also close to those estimated by NET SIM. A comparison of Figures 8 and 9 suggests that Model I shows a slightly better correlation with NETSIM results. Model I appears to produce slightly lower delay estimates than NETS~, and Model II produces slightly higher estimates. It is clear Dom the above discussion that the analytical model proposed for signal timing estimation offers superior performance to the existing HEM Chapter 9 Appendix II method. Implementing the timing model alone' with no changes in the delay estimation model may be expected to improve the credibility of the HCM procedure. Further improvements may be made by adopting either one of the delay estimation models described in this chapter. The differences between Mode} ~ and Model II are very small. Model ~ produces delay values that are higher that NETSIM's estimates, and Model II produces values that are lower. No clear superiority can be established Tom the simulation compansons. This observation was con- firrned in the limited field studies that are reported in Appendix H. NCHRP Project 3-48! Final Report: Page 27

90 T ~80 :70 -6 0 - 50 is, 40 I_ <' 3 0 a' =~' 20- ~ ~ ~ 1 0 - _ Jew R2= o.go (433 observations) . : - ' e ' It i.' O- _ . . . . 0 1 0 20 30 40 50 60 70 80 90 Total Delay from TRAP-NETSIM (sec/veh) Figure 9. Delay comparison between Mode! ~ and NETSIM There is no performance basis to recommend one mode} over the other at this time. Under these circumstances, the most rational choice would be the one that requires the least conceptual modification to the current HEM model. This rationale favors Delay Mode} IT. NCHRP Project 3-48 Final Report: Page 28