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75 Chapter Seven DELAY This chapter documents Me delay model testing results against the field data. Model 2.5 was given the first priority among other models based on the model selection criteria discussed In chapter three. Testing of available simulation models is also documented in this chapter. BASIC DELAY MODEL TESTING The recommended time-dependent delay model (Model 2.5) is given here again: D ~ 3600~900T TV _ 1 ~ 4t V _ 1) ~ (3~CX~C)] (114) where D is the average vehicle delay, sec/veh, c is the cap acid for the movement, vehA~r, Vis the traffic volume for the movement, veb/hr, and T is the analysis time period, hr. It is important to note Cat the quality of the delay estimate is limited by the accuracy of the capacity model. This is clear in Equation 114 by the number of terms containing the parameters c and v/c. The recommended delay model was tested against the field-collected data. Figures 41 and 42 show the delay estimation results for all of the sites with standard geometry and traffic flow charactenstics. Each data powt represents an average result for a 15-minute central. Figure 41 shows the result when generally recommended critical gap and follow-up time were used (Table 28 and 29), and Figure 42 shows the result when site-specific critical gap and follow-up time were used. The analysis bme period (T) of 0.25 hour (15 minutes) was used. The regression and statistical results are shown in Table 40. It is clear that using the site-specific critical gap and follow-up time give better results than using the recommended ones based on general conditions. It should be noted that there are some data points for which the model significantly overestimates the delay. These data points were observed in the high delay range, which means Cat Me intersections are most likely close to capacity. As mentioned before, the delay model becomes more sensitive when Me volume/capacity ratio approaches over saturation. In this case, slightly underestimating the capacity will result in significantly overestimating delay. Table 42 shows the delay model results In terms of the level of service (LOS). The number of sites with the same LOS predichon and with one level difference are shown in the table. The delay model predicts the same LOS as the field observations in about 50 percent of Me cases and is within one level difference in about 90 percent of the cases. In the F level of service range, there is a slight bias towards the model producing a worse LOS Can in the field This may be due to the field sites having higher capacities than modeled due to effects such as upstream signals, two-stage gap acceptance, and flared minor approaches. These ejects are considered in chapter eight. 1 000 s ~ 100 In 8 10 1 1 aOO Al / O ,,, O O 0: O I I ~ Oat 0 0 _0' . . . . ..... . . . . .... ~T T i T ~r r ~ r T T ~ JET 10 100 1000 Field Delay, sec/veh Figure 41. Delay Model Result for Standard Sites; Generally Recommended Critical Gaps and Follow-Up Times
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76 1000 100 10 / O O \: 0 0 .p - to o ~5 Limo 0 O . . . . r ., ....l 1 10 100 1000 Field Delay, sec/veh Figure 42. Delay Model Results for Standard Sites; Site Specific Critical Gaps and Follow-Up Times Table 40. Summary of l relay Model Results Using Capacity Model 1.1 and Different Critical Gap and Follow-Up Time Values ~-- --- - . . : b ............... ......................... ''''' ' ' ....... . ,.,. . Constant 4.72 -5.S3 Std Err Y 11.82 23.62 R: 0.67 0.6S No. Obs. 218 218 Deg of Freedom 216 216 X CoeŁ 0.96 1.81 Std Err. Coef. 0.0S 0.09 MAE 7.6 13.1 MAPE 4S.8% S7.2% Because an intersection may not be congested for the entire analysis period, a smaller value for T. the time of oversaturation, may be appropriate. To test this effect, a value of T = 5 minutes was also tested in the delay equation. The results are shown in Figure 43. The difference is negligible at low delay ranges. However, for those data points in the high delay range where delays were significantly overestimated, modeled delays are closer to the field data than with T=0.25. In other words, using a larger value for T tends to result in higher `1el~v predictions than using a smaller value for T. _ ~_ in, The delay mode! was also validate with the site data collected awing Phase ~ of the project. Fig,ure 44 shows the reset. Again, each data point represents 15-n~inute interval data The MAE for the standard sites is 9.0 sec/veh and the MAPE is 36.2 percent. The regression and statistical results are shown In Table 41. Table 41. Regression Results, Phase I Validation Sites ..~.~- ''. ~',,. Constant 4.08 -22.53 Std KIT of Y Est 13.38 10S.31 R Squared 0.37 0.19 No. of Obs 77 113 Deg of Freedom 7S 111 X Coefficient 0.92 3.39 Std KIT of Coef. 0.14 0.65 MAE 9.0 49.1 MAPE 36.2% 149.% The mode! results in terms of LOS are given in Table 43 for the Phase ~ data. The results indicate that the recommended delay model is valid and provides good estimates of vehicle delays for intersections with normal traffic and geometric characteristics.
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77 Table 42. Summary of Delay Model Result in Terms of LOS as Defined in 1994 HCM 1 000 1~ 10 1 10 100 1000 Field Delay, sec/veh 1 1 Figure 43. Delay Model Result for T=S min (Recommended Critical Gap and Follow-Up Time) 1000 100 In ~ 10 a a ~ O -~ 0~.. . .~:. ;/ · a 1 10 100 1000 Field Delay, sec/veh 0 Non Standard · Standard Figure 44. Delay Model Validation for Phase I Sites (Recommended Critical Gap and Follow-Up Time)
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78 Table 43. Summary of Delay Model Results for Phase I Validation Sites in Terms of LOS I Car ~ ~ Cat ~ it ~mp.T. . . ~- . . #Predicted l :~OS ~ #shield ~ A ~ B C ~D ~E ~F A O B 2 ...................................... ............... ........... C 33 . ~.: ....... D 25 1 ! ; ;!; ; ;~ ~ 2 E 11 ...... ; ;; ; ;;; ; ;; F 6 . 3 . . . Total 77 . F 2 .................................. . ........ #Same #One LOS Level Dig 1 2 27 29 11 22 3 11 2 3 44 67 %Same LOS 50.0% 81.8% 44.0% 27.3% 33.3% S7.1% %One Level Did. 100.0% 87.9% 88.0% 100.0% SO.0% 87.0%
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These models were tested against field data. Only those sites that conformed with the limitations of each mode} were selected for the test. The number of sites tested for each mode! are as follows: . . KNOSIMO, 30 sites PICADY, ~ ~ sites TEXAS, 64 sites, TRAF-NETSIM, 9 sites Figures 45 through 48 show the results of each simulation model. Each point in these figures represents data for an entire time period, usually ~ to 2 hours. The statistical and regression results are shown In Table 45. 79 ASSESSMENT OF SIMULATION MODELS Simulation techniques have been widely used In transportation studies. A large variety of simulation models have been develops for analyzing arterials, signalized ~ntersechons, and freeways; however, few simulation models are currency available for studying unsignalized intersections. Simulation models that are Table 44. Summary of Charact~ishcs of Simulation Models being used for analyzing TWSC intersections include KNOSIMO, PICADY, TEXAS, and TRAF-NETSIM. Among these models, only the TEXAS and TRAF- NETSIM models are able to simulate AWSC intersections. Each of the simulation models mentioned above has its own features and limitations. Table 44 summarizes Me characteristics for each model. ~ .................................. KNOSIMO Microscopic · 3 or 4 leg Event Scan · single lane major street · no consideration of pedestrians and cyclists · no consideration of curve radii · consideration of grade by adjusted I,, to values · no consideration of upstream signals | ?ICADY ~ Macroscopic |.b' ;edonlefr-handedtrafEic · not based on gap acceptance · only for British capacity experience · maximum 6S feet width for major street · no consideration of pedestrians and cyclists · no consideration oftemporary blocking to major street through vehicles by major street left tums · no consideration of upstream signals ~. TEXAS | Microscopic |.o'~tisnein~valofmaximurn60rninutes Time Scan · no consideration of pedestrians and cyclists · no consideration of upshcarn signals rRAF-NETSIM I Microscopic ~ · nt consideration of pedestrians and cyclists Time Scan · no consideration of grade, or curve radii 1000 100 - o Its 10 co 1 1 O ~ O ~ 0: 0~ 00 ~ ° ,0 O' O ~ ,'0 0,^ ~. . . . . . . . . . ..... ..... , . . . · ~. . . ... ~ . 10 100 1000 Field Delay, sec/veh Figure 45. Sumulation Results Dom KNOS~O
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80 two ~ 1~ ~10 10 Fh d Delay, Ah 100 1000 Figure 46. Simulation Results from PICADY ~wv ~ 1= ~10 o ~° 1 1 10 held Dekly, "c~h r ~ .... 100 1000 Figure 47. Simuladon Results fLom TEXAS 1000 ~ 1~- 10 . . . . . . . . ., r~ ~r 10 100 Hed Dday, ~hh Figure 48. Simuladon Results from TRAF-NETSIM Table 45. Regression and Stabshcal Results for Different Simulation Models Constant l.S9 -0.14 ~-47.74 Std E'r of Y 6.8S 6.18 72.37 R Squamd 0.72 0.80 0.44 No. Obs 30 11 68 Deg Freedom 28 9 66 X Coef. 0.96 O.S4 7.76 Std Err CoeŁ 0.11 0.09 7.08 MAE 4.S 11.2 36.4 MAPE 30.2% 41.4% 126.S% S.63 2.30 0.12 9 7 0.03 0.03 19.8300.1 Eleven intersections were tested with PICADY, and average delay values for the complete observation and simulation p~iods were compared. The simulation results show~atPICADYundereshmates the measured delays ~n each case. It is likely ~at ~e emp~ncaBy based capacity formulas used by ~e program, and developed in the Un~ted Kingdom, are not calibrated to U.S. conditions. Nine intersections were s~mulated w~th the program TRAF-NETSIM. In all cases NETSIM underestimated the measured delays when using the default values for the "acceptable gap in near-side cross traff~c". The simulated delays did not exceed Il seconds even though the measured delays were much hither. Even w~th ~ncreased default values the results could not be ~mproved. In some cases ~e s~mula~ delays rema~ned low, in o~er cases ~e delays became unrealistically high. TEXAS can only consider one time intenal wi~ a max~mum duration of one hour. Altogether s~xtr-four intersections were ~nvestigated. The simulation results show that the qualit,,r of the s~mulation results varies widely. A veIy important factor is the trailic volume on the minor approach. For medium to high traffic volumes on the minor approaches (above 280 vehicles per hour) TEXAS produces an unrealistic overestimation of the measured delays. This behavior was only observed for intersections wi~ single-lane minor approaches. For intersechons with lower trafflc volumes on the minor approaches, TEXAS generally underestimates the measured delays when using the default values of 8 seconds for parameters TLEAD and TLAG. The quality of the results can be improved by va~ying the values of TLEAD/TLAG; never~eless it is not possible to assign correct consistent TLEAD/TLAG values to specif~c traff~c situations.
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81 KNOSIMO can only consider Intersections with one lane In each direction. Because of this limitation, only 30 intersections could be investigated. For Me simulation studies, the site-specific gap data were used. The results show that In most cases KNOSIMO simulated realistic delays. No systematic over- or underestimation could be observed. When companog the delays for the whole simulation and observation penods, the standard deviation between the delays generated by KNOSIMO and the measured delays is about 6.S seconds. The average deviation is about 30.1 percent. In Sumner, Me best correlation between field conditions and simulation results is g~venbyKNOSIMO. The general gap acceptance concept of KNOSIMO is recomb ended for further application. Nevertheless, the KNOSIMO program in its present version does not Fife all needs of U.S. practice. Therefore, an expansion of this or over gap acceptance based simulation programs may be desirable. The following features should be considered: more variations of intersection geometry, e.g., multi-lane major streets, central refuge areas, flared approaches.. modified major street headway distribution to account for signal control at adjacent intersections. SUMMARY AND CONCLUSIONS Some of the major conclusions of the delay mode! testing results are given below: The acc~acyofdela`,reshmabon is closely related to the accuracy of capacity estimation. Delay . . . . cannot be correctly estimated unless the correct capacity is determined. Similar to the capacity mode} testing results, using site-specific critical gap and follow-up time always yields the best delay forecast results. If site-specif~c critical gap and follow-up time information are not available, the recommended critical gap and follow-up time discussed in chapter five can also provide good capacity and delay estimates. Using Harders' basic capacity mode} and the 1994 HEM procedure, the delay mode} can predict He same LOS as observed In He field for more Can 50 percent of the cases, and predict LOS within one level difference for about 90 percent of the cases. The recommended capacity mode! and delay mode} cannot be directly used for analyzing intersections with unusual geometry and traffic flow conditions. Special considerations are necessary for analyzing these special conditions. Simulation may be the best solution when these special conditions exist. However, existing simulation programs need further improvements to adequately mode] conditions commonly encountered. Testing of the KNOSIMO, PICADY, TEXAS, and TRAF-NETSIM simulation models showed that only the KNOSIMO mode! provided good correlation with field data. However, some of its limitations need to be resolved before the mode! can be used over a wide range of conditions. The mode} should tee modified to address intersections with conditions such as a multi-lane major street, and two-stage gap acceptance.
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82 . . ,...
Representative terms from entire chapter: