A Single-Lane Freeway with an Interchange Model

Fig. 4-1 A single-lane freeway with an interchange

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In order to reduce the complexity of the traffic condition, first, we study a single-lane freeway with an interchange, as shown in Fig 4.1. We simulate a 9-km single-lane freeway with an interchange at 4 km post. There is a 200-m long

acceleration lane at the intersection of the freeway and the interchange. The speed limit on the freeway is 90 km/h, and the desired speed of each vehicle is uniformly

distributed between 85 km/h and 120 km/h. The traffic flow on the freeway before the interchange is 1000 vehicle/hour. By controlling the traffic flow input from the

interchange, we can create traffic jams on the freeway. Table 4-2 lists the traffic flow input from the interchange as the simulation goes on. Initially, there is no traffic input from the interchange. At simulation time 900 sec, we generate a heavy traffic flow input (1000 veh./h) from the interchange to cause a traffic jam on the freeway, and gradually decrease the traffic flow input from the interchange to remove the traffic jam.

The total simulation time is 1 hour, and the status of simulated vehicles recorded by VISSIM is input to a simulation program which performs the functions of both the TIC and the probes.

Table 4-2 The traffic flow input from the interchange

Simulation Time (second) Traffic Flow (veh./h)

0~900 0

900~1800 1000

1800~2400 700

2400~3000 300

Based on the status of simulated vehicles, we depict the ground truth, the traffic conditions with respect to the simulation time and the freeway location in Fig 4.2. The X-axis is the simulation time and the Y-axis is the highway location starting from 0 km post. The green areas represent that the speed of the vehicles is higher than 70 km/h (VOUT), the yellow areas represent that the speed of the vehicles is between 40 km/h (V_IN) and 70 km/h (V), and the red areas represent that the speed of the vehicles in

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Fig 4.2 The ground truth and the detected start and end positions of traffic jams

under 40 km/h (VIN). In other words, in the green areas, the traffic is a free flow, and in the red areas, the traffic is congested. We can observe that when a heavy traffic flow starts to input from the interchange at simulation time 900 sec., the interchange becomes the bottleneck of the freeway, and a traffic jam builds up before the interchange. The start position of the traffic jam travels upstream, while the end (a)

(b)

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position remains almost fixed. While the traffic flow input to the interchange decreases gracefully, the traffic jam reduces its area, separates to small traffic jams and

disappears.

Fig. 4.2(b) depicts the start and end positions of traffic jams detected by the vehicles in the road network. Each blue dot represents a start position detected by VIN

and AIN, and each black dot represents a start position detected by the space mean speed being lower than V_IN. Each purple dot represented a detected end position. From the ground truth of the simulated road, we found that the traffic jams in the road network can be bounded by the start and end position detected by the probes. The proportion of the start positions that is detected by the space mean speed alone is much less (less than 5%) than that detected by the instantaneous speed and acceleration.

Fig 4.3 depicts the messages broadcasted by the TIC. Each red dot represents a broadcast message for a start position detected by a probe. Each green dot represents a broadcast message for an end position detected by a probe. In addition, each yellow line

Fig 4.3 The messages broadcasted by the TIC

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represents a broadcast message for the start position, end position and travel time of a traffic jam. The figure shows that the report policy roughly depicts the traffic jam in the road network. While the traffic jam is starting disappearance, the number of broadcasts increases.

Table 4-3 lists the performance metrics of the system we proposed and the effects of GPS position errors. In the column of start position reports, the number to the right of the slash is the total number of start positions of the traffic jams detected by the probes.

The number to left of the slash is the number of the start position reports sent by the probes, after the probes detect that the difference between the detected start position and the start position broadcasted by the TIC exceeds the distance threshold. Equally, in the column of end position reports, the number to the right of the slash is the total number of end positions detected by the probes. The number to the left of the slash is the number of the end position reports sent by the probes, after the probes detect that the difference of the end position or the difference of the travel time exceeds the

corresponding threshold. When the GPS positioning is assumed to be no error, there are 100 broadcast messages from the TIC, i.e., 100 reports sent from the TIC. The 100 reports include 33 start position reports, 44 end position reports and 23 segment

Table 4-3 The effects of GPS position errors

GPS

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removal reports. The results indicate that these report thresholds reduce over 50% of the start position and end position reports sent by the probes, while providing a high AWC of 90%, a low location of less than 80 m, and a small travel time error of 10.4%.

In addition, when GPS positioning errors is 20 m in average, the number of broadcast messages increases by 3, the average location error increases by 20 m, the travel time error increases by 2%, and the AWC decreases by 1%. When the GPS positioning errors are 50 m, the number of broadcast messages increases by about 90%, while other performance metrics remain about the same as those when GPS positioning errors are 20 m.

We also observe the impact of different penetration rates of the probes. Fig 4.4 depicts the impact of the probe penetration rate. With the increase of the penetration rate, the number of broadcasts increases almost linearly. However, as the penetration rate increases, the location and time errors decrease only slightly.

Fig 4.4 The effects of the penetration rate of probe cars

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