Module 4 : Macroscopic And Mesoscopic Traffic Flow Modeling

Lecture 18 : Cell Transmission Models

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Numerical example

Consider a 1.25 km homogeneous road with speed $v$ = 50 kmph, jam density $k_j$ = 180 veh/km and $q_{max}$ = 3000 veh/hr. Initially traffic is flowing undisturbed at 80% of capacity: q = 2400 VPH. Then, a partial lane blockage lasting 2 min occurs l/3 of the distance from the end of the road. The blockage effectively restricts flow to 20% of the maximum. Clearly, a queue is going to build and dissipate behind the restriction. Predict the evolution of the traffic. Take one clock tick as 6 seconds.

Solution

This problem is same as the earlier problem, only change being the clock tick. This problem has been solved in Excel.

Table 1: Illustration of traffic simulation in CTM

clock tick	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	4	4	4	4	4	4	4	4	4	6	4	4	4	4	4
2	4	4	4	4	4	4	4	4	4	7	1	4	4	4	4
3	4	4	4	4	4	4	4	4	4	10	1	1	4	4	4
4	4	4	4	4	4	4	4	4	5	13	1	1	1	4	4
5	4	4	4	4	4	4	4	4	6	14	1	1	1	1	4
6	4	4	4	4	4	4	4	4	9	14	1	1	1	1	1
7	4	4	4	4	4	4	4	4	12	14	1	1	1	1	1
8	4	4	4	4	4	4	4	4	14	14	1	1	1	1	1
9	4	4	4	4	4	4	4	5	14	14	1	1	1	1	1
10	4	4	4	4	4	4	4	8	14	14	1	1	1	1	1
11	4	4	4	4	4	4	6	11	14	14	1	1	1	1	1
12	4	4	4	4	4	4	7	14	14	14	1	1	1	1	1
13	4	4	4	4	4	4	10	14	14	14	1	1	1	1	1
14	4	4	4	4	4	5	13	14	14	14	1	1	1	1	1
15	4	4	4	4	4	6	14	14	14	14	1	1	1	1	1
16	4	4	4	4	4	9	14	14	14	14	1	1	1	1	1
17	4	4	4	4	4	12	14	14	14	14	1	1	1	1	1
18	4	4	4	4	5	14	14	14	14	14	1	1	1	1	1
19	4	4	4	4	8	14	14	14	14	14	1	1	1	1	1
20	4	4	4	4	11	14	14	14	14	14	1	1	1	1	1
21	4	4	4	6	14	14	14	14	14	14	1	1	1	1	1
22	4	4	4	7	14	14	14	14	14	10	5	1	1	1	1
23	4	4	4	10	14	14	14	14	10	10	5	5	1	1	1
24	4	4	4	13	14	14	14	10	10	10	5	5	5	1	1
25	4	4	8	14	14	14	10	10	10	10	5	5	5	5	1
26	4	4	9	14	14	10	10	10	10	10	5	5	5	5	5
27	4	4	12	14	10	10	10	10	10	10	5	5	5	5	5
28	4	8	14	10	10	10	10	10	10	10	5	5	5	5	5
29	4	7	10	4	10	10	10	10	10	10	5	5	5	5	5
30	4	4	10	4	10	10	10	10	10	10	5	5	5	5	5
31	4	4	10	4	10	10	10	10	10	10	5	5	5	5	5
32	4	4	10	4	10	10	10	10	10	10	5	5	5	5	5
33	4	4	10	4	10	10	10	10	10	10	5	5	5	5	5
34	4	4	9	4	10	10	10	10	10	10	5	5	5	5	5

The simulation is done for this smaller clock tick; the results are shown in Fig. 1 One can clearly observe the pattern in which the cells are getting updated. After the decrease in capacity on last one-third segment queuing is slowly building up and the backward wave can be appreciated through the first arrow. The second arrow shows the dissipation of queue and one can see that queue builds up at a faster than it dissipates. This simple illustration shows how CTM mimics the traffic conditions.