Chapter 5 Simulation
5.2 Simulation Results
In the preliminary experiment, we fine the appropriate value of each weight (1:0.5,
2:0.5, 3:0.75) to reduce the headway deviation and schedule delay of buses and don’t produce huge impact on the passengers’ waiting time. And we use these value in the below simulation.
We first evaluate the waiting time of buses in ATCB and other control strategies, which is the sum of waiting time at intersection of all buses. Figure 11 is the result of total waiting of all buses, and it shows that our scheme ATCB has the best performance at reducing bus waiting time, and it is better than other methods at least 40 percent. Both TDTSP and ADT consider bus priority which extends its current phase, the former one considers headway deviation, and the later one considers both the ordinary vehicles and buses. They have better performance than the actuated scheme which doesn’t consider bus priority. The non-fixed phase scheme doesn’t consider bus priority, but the non-fixed scheme is better than actual due to it is better for all vehicles include buses and ordinary vehicles.
Figure 11. Total waiting time of buses
0 20 40 60 80 100 120
0 1 2 3 4 5 6 7 8 9 10x 104
Time (min) Total waiting time (sec) ATCBTDTSP
Actuated AFLC Non-fixed
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Table 2. Total waiting time of buses and average waiting time of each bus in one intersection
Scheme Total waiting time in two hours
Average waiting time of each bus in one intersection
ATCB 3.79 × 104 sec 12.31 sec
TDTSP 7.04 × 104 sec 22.57 sec
Actuated 8.79 × 104 sec 28.04 sec
AFLC 6.71 × 104 sec 21.72 sec
Non-fixed 6.38 × 104 sec 20.66 sec
We could see that the best performance is non-fixed scheme, since that the non-fixed scheme don’t concern bus priority. And our ATCB concern bus priority from bus schedule delay, headway deviation, number of passengers so our total waiting time of all vehicles is more than the non-fixed scheme. But the difference is just 3.8 percent, and it is acceptable because we can save 40 percent waiting time of buses as shown in Figure 11. And TDTSP has the poor performance due to that it doesn’t concern the real-time information except bus information. Actuated scheme extends the current phase to permit vehicles pass through intersections is more better than TDTSP due to that it can avoid vehicles wasting a lot of time waiting for signals just because it misses few seconds to pass through the intersection.
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Figure 12. Total waiting time of vehicles
Table 3. Total Waiting time of buses and average waiting time of each vehicle in one intersection
Scheme Total waiting time in two hours
Average waiting time of each vehicle in one intersection
ATCB 1.47 × 107 sec 25.95 sec
TDTSP 2.23 × 107 sec 38.11 sec
Actuated 1.55 × 107 sec 26.78 sec
AFLC 1.61 × 107 sec 27.26 sec
Non-fixed 1.42 × 107 sec 24.67 sec
The passenger’s total waiting time is shown in Figure 13. And we could find that the result shown in Figure 13 is similar to Figure 12, but the performance of our ATCB is better than the non-fixed phase scheme, because we consider the number of passenger of each vehicle in our equation (5). If we don’t consider number of passengers of each vehicles like non-fixed phase scheme, the bus will be treated as ordinary vehicle without
0 20 40 60 80 100 120
0 0.5 1 1.5 2 2.5x 107
Time (min) Total waiting time (sec) ATCBTDTSP
Actuated AFLC Non-fixed
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bus priority. And we could see it has better performance of ordinary vehicles as shown in Figure 12, but it has poor performance in the result of passengers’ waiting time.
Figure 13. Total waiting time of passengers
Table 4. Total waiting time of passengers and Average waiting time of each vehicle in one intersection
Scheme Total waiting time in two hours
Average waiting time of each passenger in one intersection
ATCB 1.50 × 107 sec 24.32 sec
TDTSP 2.28 × 107 sec 36.96 sec
Actuated 1.61 × 107 sec 26.10 sec
AFLC 1.66 × 107 sec 26.91 sec
Non-fixed 1.46 × 107 sec 23.67 sec
Then we evaluate the schedule delay of buses. We need buses travel a distance to produce bus schedule delay, so we collect the information from pivot intersection, and this intersection is a congested intersection because it is passed through by buses of all bus routes. As shown in Figure 14 and Table 5, we record 30 records of the schedule
0 20 40 60 80 100 120
0 0.5 1 1.5 2 2.5x 107
Time (min) Total waiting time (sec) ATCBTDTSP
Actuated AFLC Non-fixed
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delay of buses on RouteA when it arrives at this intersection. We could find that our ATCB has a lowest average schedule delay, which is better at least 25 percent than other schemes. The variance of bus schedule delay of ATCB is 337.79, and it is better than other schemes at least 63.7 percent.
Figure 14. Bus schedule delay in a bus stop at a pivot intersection
Table 5. Average schedule delay time and Variances of buses at a pivot intersection
Scheme Average schedule delay time Variances of bus schedule delay
ATCB 30.87 sec 337.79 sec
TDTSP 46.88 sec 930.52 sec
Actuated 47.77 sec 1360.84 sec
AFLC 57.22 sec 1971.85 sec
Non-fixed 55.80 sec 985.0 sec
5 10 15 20 25 30
0 20 40 60 80 100 120 140 160 180
Bus (veh)
Bus delay (sec)
ATCB TDTSP Actuated AFLC Non-fixed
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As shown in Figure 15 and Table 5, we evaluate headway deviation of buses. We still collect records of bus headway deviation ratio at the pivot intersection. As shown in Figure 14 and Table 5, in ATCB, the average bus headway deviation ratio is 22.19 percent, and the range of bus headway deviation ratio is from -44 percent to 39 percent and variance is 601.54 percent. The second best performance is TDTSP, and its average bus headway deviation ratio is 22.19 percent, and the range of bus headway deviation ratio is from -68 percent to 70 percent and variance is 601.54 percent.
We also evaluate the total schedule delay time and bus headway deviation ratio which is shown in Table 7, and the result is similar to the result shown in Table5 and Table6.
Our ATCB still have the best performance.
Figure 15. Bus headway deviation ratio in a bus stop at a pivot intersection
5 10 15 20 25 30
-80 -60 -40 -20 0 20 40 60 80 100 120
Bus (veh)
Bus deviation ratio (%)
ATCB TDTSP Actuated AFLC Non-fixed
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Table 6. Average headway deviation ratio and variances of buses at a pivot intersection
Scheme Average headway deviation ratio
Variances of bus headway deviation ratio Scheme Total waiting
time of
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