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51 Chapter Six SERVICE TIME The purpose of this chapter is to determine the quality of the forecasts of Me proposed headway 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, Be 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 win those produced by previous procedures, and comparison of the forecasts to some other metric. The chapter opens with a brief discussion of the field measurements of service time and related parameters. The mode} is tested with theoretical values to determine if it correctly forecasts headways over a wide range of conditions. Next, He model forecasts are compared to the field measurements of service time. Here, consideration is given to three measurement errors: the mean absolute forecast error (MAFE), the mean absolute percent error (MAPE3, and the standard error (SE3 of the forecast. Four data sets are included in these compansons: the Group ~ sites,the sites from Groups 2, 3, and 4, He Group 5 sites, and He pilot study sites from Phase ~ of this study. Finally, a summary of the evaluation of the mode} forecasts is presented. FIELD MEASUREMENTS The senice time, or the time that a vehicle occupies He first position in queue, was measured for every vehicle at each of the approaches that were videotaped during this study. During periods of continuous queueing (that is, at least one vehicle was already present when the next vehicle arrived), He move-up time and saturation headway were a so measles The move-up time is the bme between the departure of one vehicle Tom the stop line and the time for the next vehicle in line to move up to the first position. The saturation headway is the bme between the departure of one vehicle Tom the stop line to the departure of the next vehicle. These three parameters are computed from the following three events that were recorded for each vehicle: . . . the bme that a vehicle enters the queue, the lime that a vehicle arrives at He first position (at the stop line), and the bme that a vehicle departs from He stop line. One part of the forecast error that must be considered is that resulting from measurement error. As part of He Phase ~ pilot study conducted as part of this project, an estimate of this measurement error was made. It was found that the bme recorded for the same event on a videotape by the same observer had a mean absolute difference of 0.3 seconds, With a standard deviation of 0.26 when multiple nuns were made using the same videotape. This measurement error must be considered when assessing the quality of the forecasts described in subsequent sections of He chapter. THEORETICAL MODEL TESTING Theoretical input values, over a wide range of traffic conditions, were used to determine if the computational procedure yielded logical results. For example, if there is no traffic on any of the approaches except for the subject approach, the mode} should forecast headways of 3.9 seconds. Three tests were conducted using a flow rate of 300 vph on the subject approach The results are shown In Figures 17 through 19. . When the opposing volumes were varied from 0 to 1000 vph, the forecasted headways ranged from 3.9 seconds to 4.7 seconds. This is the expected range for case ~ to case 2 conditions. When the conflicting from the left volumes were varied from 0 to 1000 vph, He forecasted heads rs ranged Tom 3.9 seconds to 5.9 seconds. This is the expected range for case ~ to case 3 conditions. When the flows on He opposing and conflicting approaches were varied from 0 to 1000 vph, the
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52 forecasted headways ranged Tom 3.9 seconds to 9.6 seconds. This is He expected range Tom case ~ to case 5 conditions. The results show Hat the theoretical mode! formulation is consistent and correct. Boo , Opposing Volume Figure 17. Effect of Oppesing Volume on Departure Headway 1 000 0 500 1000 , Opposing Volume Figure 18. Effect of Conflicting Volume on Departure Headway Case 5 Headway Analysis IN US I 0 500 1000 Opposing Volume Fig'~ 19. Effect of Opposing and Conflicting Volumes on Departure Headway MODEL TESTING WITH FIELD DATA Forecasts of ache service time (the forecast value of the departure headway minus the move-up dme) were compared to the measured values of He service time using 5-minute average data points for three site groups: Group I, Groups 2 through 4, and Group 5. Figures 20 Trough 22 show plots of the forecasted service time vs the measured values of the service time for the three site groups. ~ ad cases, there is significant scatter around the line connecting equal values of mode} forecast and field measurement. The data pouts that are most divergent in the lower right portion of the plots are probabb,r camp by blockages (usually by pedestnans) that result In higher Han expected service times. Service Time Forecast Group 1 Sites 10 O _ ~ ~c ;~;~e~ ;-;_;--_ 5-=~ ~ ~ ~-.. ~ O ==~ ~:~ =-== = 0 5 10 Field Measurement Figure 20. Senrice Time Forecast, Group 1 Sites Service Time Forecast Groups 2,3,4 Sites 10 1 1 1 1 1 1 1 1 1 1 1 I T 1 T T 1 1 ~ = = = ._ .- -. A< ,, ~ s .~a F;.- ~ , If ~, :~. - ~';~' , . . -` .q .__ -- O r 11 1 1 1 1 1 1 1 ~ 0 5 10 Field Figure 21. Service Time Forecast, Groups 2~ Sites
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53 Service Time Forecasts (Group 5) 30+ dda pools per hl~l 10 ~ 5 o o 5 Field Service Time 10 Figure 22. Service Time Forecast, Group 5 Sites Table 68 presents a summary of the mean absolute forecast error (MAFE), the mean absolute percent error (MAPE), and tibe standard forecast error (SE) for the three groups. The MAFE is the mean of the absolute values of the forecast errors for each of the 5-m~nute data points. The MAPE is the mean of the absolute values of these forecast percent error'. The SE is given in Equation 35. SE = Table 68. Model Forecast Errors ~ (Sf - sm2) i (35) 1 . . . - ; .................................................... . . . . . . . . . . . . ..... ............ ............................ ............................. ................................. ........... ........ .. ..... I .:.:.:.:.:.:.:~n :.:.:.:.:.:.:.:. .:.:.:.:.:.:.::~:.:~:~.:~.::.:~: :::.:.:.:.:.~....:.. :: · :: ::: it: :: :: . 1 0.8 3.3% 1.1 2~ 0.8 19.2% 1.3 S 1.3 29.3% 1.9 Note:~4FE = mean absolute forecast error,AL4PE = mean absolute percent error, ~ = standard forecast error The MAFE ranges from 0.S seconds to I.3 seconds. If the measurement error is approximately 0.3 seconds, Me remaining 0.5 to I.0 seconds must be attributed to either mode! error or Me result of random error. By comparison for Me Group ~ sites, Me values that are forecasted from the mode} range from I.9 seconds (degree of conflict case ~ with 3.9 seconds for the departure headway minus 2.0 seconds for Me move-up timed to 7.6 seconds (degree of conflict case 5 of 9.6 seconds minus 2.0 seconds for the move-up timed. The mean measured field value for the Group ~ sites was 4.} seconds. Thus the MAFE ranges from ~ ~ percent to 42 percent of Me extreme values, and is 20 percent of the mean measured value. These are not intended to be comparisons m~ an absolute standard but simply to provide a perspective of the quality of the forecasts for this model. Table 68 also shows that the forecast error increases with Me complexity inherent In multi-lane operations present at Group 5 sites. Some of the error is also attributable to the measurement uncertainty In the move-up time. When Me proportion of time that a continuous queue is present is low, the number Of measurements of the move-up time is also low. This increases the uncertainty in Me estimation of this value. Tables 69 Trough 71 show Me MAFE, the MAPE, and Me SE for Me individual sites within these groups. Table 69. Model Forecast Errors Group 1 Sites ................................... .............................................................. ..................................................................... ................................................................... .................................... ........ %. - d. ~ ........... - d. - ~ .; :-:-:-:-:: :-:--1~=':-:-:-:-:-::: ·:~:~:~:~:~:~ly~.~:: :~:~:~:~: ............ ........................................ AU Data CEA303 CEA304 NEA201 NEA204 NEA20S NEA206 NEA208 NWA401 NWA403 NwA40 swAnnh 0.77 0.60 0.64 0.81 0.82 0.77 1.07 0.87 0.7S 0.79 0.61 ncs 3.3% -S.1% -4.6% 9.1% 14.1% 11.4% 19.1% 12.S% -11.0% -13.3% 2.8% _1 5°/n 1.07 0.79 0.72 1.10 1.02 1.01 1.49 1.29 1.09 1.08 0.84 ~._ _ . 0.91 Note: MANE = mean absolute forecast enor,MAPE = mean absolute percent error, ~ = standard forecast error. Table 70. Model Forecast Errors Groups 2, 3, and 4 Sites AU Data 0.77 NWA402 0.81 NWA406 0.60 NWA407 0.99 SEA101 0.94 SEA1OS 0.3S SWA002 1.39 SWA004 1.77 SWA008 1.34 SWAOO9 0.60 19.2% 12.6% 10.6% 27.1% 20.3% 10.1% SS.7% 39.S% 2S.1% 21.7% 1.29 0.99 1.81 1.05 1.12 0.46 1.74 1.77 1.43 0.70 Note: My= mean absolute fores error,lL4PE= mean absolute percent error, SE= standard forecast error.
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54 Table 71. Model Forecast Errors Group 5 sires , · · ~ ~ 5$ All Data 1.33 29.3% 1.87 CEA307/308 0.75 26.4% 1.03 NEA202/203 0.92 26.7% 1.51 SEA104/107 2.01 33.0% 2.47 1 l Note: M:4FE = mean absolute forecast e'ror,lL4PE = mean absolute percent error, ~ = standard error ofthe forecast VALIDATION Mode} validation is the testing of a calibrated mode] using empirical data Mat were not used to initially calibrate the model. The data collected as part of Phase ~ of this project were used to validate the proposed senice time based capacity model. Drying this pilot study, data were collected at five AWS`; sites, four single lane sites and one site with both single and multi-lanes on its approaches. Figures 23 shows He plot office forecasted senice time vs the measured service time for single lane sites. As before, the data are scattered along Me line connecting equal values of He mode! forecasts and field measurements. The MAFE, MAPE, and He SE are shown In Table 72. The mean forecast error is I.4 seconds, slightly higher than He forecast error for the three other data sets presented In the previous section. Service Time Forecast Validation Sites (Single lane Sites) 10 l . 5 o o 5 Held Measurement 10 Figure 23. Service Time Forecast, Validation Sites Table 72. Model Forecast Errors, Validation Sites All Data 1.4 Is 3O/~ ~ s Note: ~ = mean absolute forecast e'ror, M 4PE = mean absolute percent e'ror, By= standard error ofthe forecast FINDINGS AND RECOMMENDATIONS The analysis presented here supports a number of significant findings with respect to a decision on an appropriate capacity mode} for AWSC intersections. These findings support a conclusion to recommend the service time mode] as the basis for capacity analysis of AWSC intersections. Findings Four findings based on the analysis of the proposed service time mode! are presented here. Capaci~Mode! 2. Richardson proposed a service time based mode! using the values of saturation headway measured by Hebert. While it is a substantial improvement over any previous method for computing capacity, Here are four problems with this model. First, the limitation of only two cases is severe. Drivers face much more complex conditions based on the Interaction of two or more vehicles simultaneously trying to enter the intersection. Second, vehicle type affects the saturation headway. Third, the driver~on-the-right rule of Len does not correctly describe intersection operations. Fourth, a Ianfication is needed on what He mode} actually forecasts. Proposed service time model. An extension of Capacity Mode! 2 is presented The mode! is based on five cases, each reflecting a different level or degree of conflict faced by the subject approach driver. The probability of occurrence of each case is based on He traffic intensity on He opposing and conflicting approaches. The interdependence or interaction between the traffic streams shows the need for iterative calculations to obtain stable estimates of service time. Mode] testing Forecasts of service time were made for each of the three site groups. The MAFE range from 0.S to I.3 seconds, while the MAPE ranged from 3.3 percent to 29.3 percent.
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55 Validation. The service time mode} was validated using the data collected at five sites during the Phase ~ pilot study. The mode! performed well producing a MAFE of I.4 seconds and a MAPE of 25.3%. Recommendations The service time mode], an ex ensign of Capacity Mode} 2, is recommended as the basis for the new capacity estimation procedure to be included In the next edition of the HCM. This recommendation is based on testing and analysis of this mode} using data collected during this study.
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Representative terms from entire chapter: