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57 Chapter Seven DELAY MODELS The purpose of this chapter is to detenn~ne the quality of the forecasts of the proposed delay model. Determining the quality of a forecast is difficult, and requires the establishment of criteria by which the forecasts can be evaluated. The criteria used here include: the amount of error present in the forecasts, that is, some measurement of the difference between the measured value and the forecasted value, the likely causes of the error, and how much of the error is attributable to measurement, the mode} structure, and to randomness, comparison of the forecasts with those produced by previous procedures, and comparison of the forecasts to some other metric. FIELD MEASUREMENTS Three events were recorded for each vehicle on the subject stop-con~oDed approach: the time that the vehicle entered the end of the queue, the time Hat it arrived at the stop line in lbe first queue position (these times are equal if there is no queue present when the vehicle arrives at the intersection), and the time Mat it departed from the stop line. The time difference between these first two events is the bme In queue. The time difference between the second and~ird events is the service time. The sum of these two times is the total delay. The total delay for each vehicle was aggregated into five minute intervals, with the delay for a given vehicle attributed to He time central in which it departed from the stop line. The average delay for a given time Interval is the sum of the total delay divided by the number of vehicles departing Dom the stop line doling that interval. MODEL TESTING Three combination capacity and delay models were tested. Mode! ~ used the service time forecasts (Capacity Mode} 2, extended) end relay Model I. Mode} 2 used service bme forecasts (Capacity Mode! 2, extended) and He TRC 373/1994 HCM Update delay mode} (Delay Mode! 2~. Mode! 3 used the capacity and delay procedures of He 1994 HEM Update models. Forecasts were prepared for each ofthe~ee groups: Group I, Groups 2~, and Group 5. Mode! 3 forecasts were prepared only for the Group sites. Figures 24 through29 show plots of He forecasted delay vs the measured delay values. The plots show that the points are sea - Ed along a line connecting equal values of forecasted delay and field data. 100 , : : go-, a 2 Model 1 Forecasts Group 1 Sites 1 10 100 Field Data Figure 24. Delay Forecast,Model 1, Group 1 Sites 100 ~ ~ 10 Model 2 Forecasts Group 1 Sites 1 10 100 Field Dam Figure 25. Delay Forecast, Model 2, Group 1 Sites

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58 100 ~ 10 If 1 1 Model 1 Forecast Groups 2,3, 4 Sees Field Dam 100 I9~ 26. Delay Forecast, Model 1, Groups 24 Sites 100 - .o ~ 10 2 1 Model 2 Forecast Groups 2,3, 4 Sites 1 10 Field Data .. Figure 27. Delay Forecast, Model 2, Groups 2~ Sites 100 10 nil IL 1 100 8 ~ 10 a' .8 a IL Model 2 Forecast Group 5 Sites 1 Field Data Figure 29. Delay Forecast, Model 2, Group 5 Sites 100 Table 73 presents a summary of the CHAFE, the MAPE, and the SE for the three groups. The MAFE is under ten seconds for all of the mode} forecasts. The MAPE varies Tom 36.9 percent to 73.S percent for all but one case, but since the mean measured delay is 10. } sec/veh, this level of variation is tolerable. The SE vanes from S.2 to 30.7. Table 73. Delay Forecast Errors Model 1 Forecast Group 5 Sees Field Data 100 Figure 28. Delay Forecast,Model 1, Group 5 Sites Group 1 Model 1 Model 2 Model 3 Group 2 Model 1 Model 2 Model 3 Group 3 Model 1 Model 2 Model 3 VALIDATION 3.9 4.8 4.0 6.7 7.3 6.6 8.2 36.9% S2.6% 69.6% S1.0% 69.S% 73.8% 264.3% The field data collected as part of the Phase I pilot study were used to validate the two proposed delay models. The date collected et the three AWSC intersections with single lanes on each approach make up this validation data set with 125 5-minute data points. Delay Forecasts The delay forecas s were plowed against the measured field delay for Me 5-minute data for Tree single lane sites. These plots are shown in Figures 30 and 31. Table 74 lists the delay forecast errors.

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s9 100 10 1 Model 1 Forecast Validation Sew (Singe Lane Sites) Table 7S. Level of Service Ranges for Stop Controlled tcrsechons Fluid Dam 100 Figure 30. Delay Forecast, Model 1, Validation Sims 100 -, al 4S ,l Comparisons wan my betw~n~e level of senice based on field measurements of delay and forecasts Tom He three models. The results are shown in Table 76. ~ all cases, He produced models perform wed, forecasting within one LOS of the measured values more than 90 percent of He time in most cases. For He Group ~ sites, He proposed mode} produces forecasts Hat are significandybetter~ant}le 1994 HCM Update procedure. Table 76. Level of Senricc Forecasts Group 1 Model 1 Model 2 Model 3 63.8% 63.1% 48.1% 96.0% 96.1% 93 I/~ Group 2 Model 1 Model 2 Model 3 S4.8% 42.1% 87.9% 86.8% Group 2 Modal 1 Model 2 Model 3 43.7% 42.0% 93.3/O 93.0H Tables 77 through 83 show the details of the level of service forecasts for each model. Table 77. M6del 1. LOS Formasts~oup 1

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60 Table 78. M6dd 2. LOS Forecast Group 1 Table 82. Model 2. LOS Forecast, Group 5 Table 79. Model 1. LOS Forecasts, Groups 2~ ............ A B C D Table 83. LOS Forecast, Validation Sites Table 84. LOS Foists, Validabon Sites Table 80. Model 2. LOS Forecasts, Groups 24 o 8 6 1 O . O Table 81. Model 1. LOS Forecast, Group 5 ............ .. I.... . 134 168 22 1 l ................. O 1 c . =3 l .............. ~- O O 2 O O O _ BINDINGS AND RECOMMENDATIONS The analysis presented In this working paper support several important findings pith respect to a decision on the appropriate capacity and delay models for AWSC intersections. These findings support a conclusion to recommend Capacity Mode} 2 (as extended) as the basis for capacity analysis of end relay Model ~ for computing delay for AWSC intersections. Findings Five findings can be made based on He results presented in this section. Variation of Forecasts. When the degree of saturation exceeds 0.8, the second term of Me delay equation

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61 dominates' and the standard deviation is of similar magnitude to the mean This means that the wide scatter Hat is evident ~ He delay plots for higher values of delay is expect This vanabon is also expected since the its ofthe sanction headway measurements for Melee of conflict cases 3 Trough 5 show a higher standard deviation than the headway values for cases ~ and 2. Potential models for delay. Both the proposed delay mode} and the 1994 HEM Update mode! provide good forecasting results. Model testing. All models produce reasonably good forecasts with similar degrees of forecast errors. Mode! validation. The forecast quakier is approximately the same as for the models tested using the study data. [eve! of Service Forecasts. All models produce LOS forecasts either equal to or within one LOS grade of the measured LOS value, more than 90 percent of the time. Models 1 and 2 produce somewhat better forecasts than the 1994 HEM update. The forecasts generally lie on or above the diagonal connecting equal values of LOS. This is conservative in one sense: poorer LOS values are predicted than are filly observed, particularly for LOS E and F. However, this may In some cases lead to signal warrants being prematurely met Recommendations The analysis presented in this report shows that bow Delay Models 1 and 2 produce good quality forecasts. While the mode} testing results weighed slightly in favor of Delay Mode} 2, the validation study showed that Delay Mode} ~ may beige more appropriate tool. Butane choice between the two modelsis difficult. Since Delay Modellis based on traffic Dow theory considerations, while Delay Mode! 2 is not, it Is recommended Hat Delay Mode} 1 be included in the proposed computational procedure to forecast delay and level of senice.

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