Evaluations

We use Java programming language to develop an emulation program that implements the functions of our probe cars and the TIC; we called the emulation program TIS_Emu. We input the location records generated by VISSIM to TIS_Emu, and TIS_Emu generates reports to the TIC for each probe car, and T_{max_p} and T_{min_p} based on the probe cars’ reports for the TIC.

To evaluate the performance of our system, we first check if the T_{max_p} and T_{min_p} predicted by the TIC match the change of the traffic Figs. 4-2 to 4-4 plot the travel times of all vehicles and the predicted T_{max_p} and T_{min_p} against the simulation time.

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Each blue square dot represents a general vehicles’ travel time, and each orange square dot represents of a probe cars’ travel time. A red square represents a Tmax_p and a green circle represents a Tmin_p generated by TIC. Fig. 4-2 plots the results of the light traffic flow setting (see Table 4-2), Fig. 4-3 plots the results of the moderate flow setting and Fig. 4-4 plots the results of the heavy flow setting. We can see that in every setting of flow, the predicted Tmax_p and Tmin_p generated by the TIC follow the traffic trends properly.

For the light traffic flow (see Fig. 4-2), the travel times are divided into three groups, with most of the vehicles in the middle group and very few vehicles on the upper group. The predicted T_{max_p} remains at the top of the middle group for both segments 1 and 2. , Note that at simulation time about 4200, 6600, and 7500 seconds, there are three isolated T_max of significant change, which do not affect the predicted T_{max_p}. We can see in both segment 1 and segment 2, the T_{min_p} fluctuates around the lower group. The reason is that the volume of vehicles in the lower group is too small and the limited sampling of the 10% probe cars may not fall in the lower group for every cycle, which leads to no T_min report. In this case, the TIC modified the T_{min_p} by multiplying it by (1+AdjustArg) with the constraint that the difference between T_{min_p} and Tmax_p must fall in the range of . Therefore, Tmin_p fluctuates but remains in the lower group.

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Fig. 4-2 The travel times, T_{max_p} and T_{min_p} at the light traffic flow.

For the moderate traffic flow (see Fig. 4-3), the T_{max_p} catches the change of the maximum travel time. We can observe that in the congestion worsening period (during simulation time 5000 to 7000 sec.), there is no T_min report, but T_{min_p} is properly adjusted by the T_max reports. In contrast, during the congestion relieving

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period, there is no Tmax report, but Tmax_p is properly adjusted by the Tmin reports. For the heavy traffic flow (see Fig. 4-3), the results are similar to those of the moderate traffic flow setting.

Fig. 4-3 The travel times, T_{max_p} and T_{min_p} at the moderate traffic flow

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Fig. 4-4 The travel times, T_{max_p} and T_{min_p} at the heavy traffic flow

Second, we evaluate the accuracy of the predicted T_{max_p} and T_{min_p} in our design.

A predicted T_{max_p} (T_{min_p}) is compared with the maximum (minimum) travel time of all vehicles passing the segment after the predicted T_{max_p} (T_{min_p}) is broadcasted and before the next predicted T_{max_p} (T_{min_p}) is broadcasted. The prediction error of T_{max_p}

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(Tmin_p) is defined to be the absolute error between the predicted Tmax_p (Tmin_p) and the maximum (minimum) travel time of all vehicles.

For all vehicles’ experience, we count the number of vehicles whose travel time is larger than the latest broadcasted Tmax_p and the number of vehicles whose travel time is smaller than the latest broadcasted Tmin_p. In addition, we compute the Mean Absolute Error (MAE) between each vehicle’s travel time and the mean of the latest broadcasted Tmax_p and Tmin_p. For each flow setting; we simulate with 10 different random seeds and average the 10 simulation results.

Tables 4-4 to 4-6 list the accuracy of the TIC’s predictions for each traffic flow setting. The simulation results indicate that the prediction errors of T_{max_p} and T_{min_p} are about the same for both segments and for all three traffic flow settings. The MAE in percentage of T_{max_p} fall in the range from 8.5% to 11.2%, and that of T_{min_p} from 9.3% to 11.2%. For all vehicles’ experience, 20-23% of the vehicles experience a travel time larger than T_{max_p}, and 5-12% experience a travel time smaller than T_{min_p}. Although the prediction errors of T_{max_p} and T_{min_p} are about the same, more vehicles experience a travel time larger than T_{max_p}. This does not imply we have poorer predictions for T_{max_p}. With 20 % of the vehicles whose travel time is larger than T_{max_p} and 10 % of them are probe cars, we would have 2% of all vehicles reporting T_max to the TIC. This enables the TIC to predict T_{max_p} from the reports. By contrast,

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we have fewer vehicles reporting Tmin. In particular, during the traffic congestion worsening period, we have almost no Tmin report, because Tmin_p is under-estimated.

The TIC can only adjust Tmin_p from Tmax_p. The MAE of using the mean of Tmax_p and Tmin_p to predict the average travel time is in a range of 27-39 sec. or 11-13% in percentage.

Table 4-4 Prediction accuracy for flow setting 1 (light) Prediction Error (error percentage)

Tmax_p Tmin_p

Segment 1 26.35 (9.5%) 15.73 (9.4%)

Segment 2 30.3 (10.9%) 16.11 (9.3%)

All Vehicles’ Experience

number of > Tmax_p number of < Tmin_p Travel time Error Segment 1 1210/5471 (22.0%) 387/5471 (7.0%) 29.75 (13.4%) Segment 2 1300/5934 (21.9%) 330/5934 (5.3%) 27.19 (12.3%)

Table 4-5 Prediction accuracy for flow setting 2 (moderate) Prediction Error (error percentage)

Tmax_p Tmin_p

Segment 1 29.01 (9.9%) 20.31 (10.9%)

Segment 2 32.12 (10.1%) 24.87 (11.2%)

All Vehicles’ Experience

number of > Tmax_p number of < Tmin_p Travel time Error Segment 1 1162/5728 (20.1%) 521/5728 (9.1%) 30.97 (13.0%) Segment 2 1232/6186 (20.0%) 570/6186 (9.2%) 31.77 (11.9%)

Table 4-6 Prediction accuracy for flow setting 3 (heavy) Prediction Error (error percentage)

Tmax_p Tmin_p

Segment 1 33.11 (8.5%) 31.8 (10.3%)

Segment 2 34.62 (9.5%) 30.76 (10.8%)

All Vehicles’ Experience

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number of > T_{max_p} number of < T_{min_p} Travel time Error Segment 1 1302/5692 (23.0%) 678/5692 (11.9%) 39.34 (12.1%) Segment 2 1295/6102 (21.3%) 631/6102 (10.6%) 34.42 (11.1%) We also compute the communication overhead of our system. Tables 4-7 to 4-9 list the communication overhead for each traffic flow setting. We count the numbers of Tmax reports, Tmin reports and broadcast messages (BMs). The total number of PCs passing segment 1 or 2 is about 1000 for each flow setting. About 200 PCs send T_max reports and 100 PCs send T_min reports. This indicates that we reduce the number of reports by 67% to 72%, compared with the segment-based report approach. Since the TIC broadcasts the traffic information every traffic light cycle, in three hours, TIC only broadcast 180 times for 2 segments.

Table 4-7 Communication overhead for flow setting 1 (light) Communication Overhead

Table 4-8 Communication overhead for flow setting 2 (moderate) Communication Overhead

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Table 4-9 Communication overhead for flow setting 3 (heavy) Communication Overhead

number of PCs Report Max Report Min number of BMs

Total 1021.9 213.5 125.6

Reports 180

reduced 67.0%

At last, we investigate the effects of the penetration rate of the probes. We simulate the three flow settings with various penetration rates of probes equals, 2.5%, 5%, 10%, 20% and 40%. We compare the prediction error, the travel time error, the number of reports and the percentage of reports reduced. The results are depicted in Figs. 4-5 to 4-8.

Fig. 4-5 The prediction errors for different penetration rates of probes 0%

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Prediction Error

α, β = 0 α, β = 0.04

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Fig. 4-6 The travel time errors of different penetration rates of probes

Fig. 4-7 The number of reports for different penetration rates of probes 0%

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Number of reports

α, β = 0 α, β = 0.04

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Fig. 4-8 The reports reduced for different penetration rates of probes Figs 4-5 and 4-6 show that when the penetration rate of probes increases, both the prediction error and the travel time error decrease slightly. We also simulate two settings of α and β, α = 0, β = 0 and α = 0.04, β = 0.04. The results in Fig. 4-5 and 4-6 indicate that for the two settings of α and β, the prediction error and the travel time error are about the same. Fig. 4-7 shows that as the penetration rate of probes

increases, the number of reports increases significantly. In addition, the rising slop of the red line (α = 0.04, β = 0.04) is much bigger than the blue line (α = 0, β = 0). The results in Fig. 4-8 show that as the penetration rate of probes increases, the percentage of the reduced reports increases, and the reduced reports of blue line (α = 0, β = 0) is much larger than that of the red line (α = 0.04, β = 0.04).

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