Cellular Automata model for heterogeneous traffic

Journal of Advanced Transportation, Fall, 2009 by Ch. Mallikarjuna, K. Ramachandra Rao

Where d(s) and t(s) are the total distance travelled and the total time spent by all the cells over the considered general measurement region respectively whereas Is] denotes the volume of the general measurement region. The units for flow, density and speed are cells/sec, cells/unit cell length, cell length/sec respectively for one cell width of the road. Since the density represents the cell occupancy, it is expressed as the percentage occupancy in this study. By multiplying these values with the number of lateral divisions of the road, one gets the values for the entire road width. The results presented in this section are obtained using this methodology.

The path of a car over time and space in the general measurement region is shown in Figure 3. The size of the car is taken as 2 X 9 cells and it is assumed that the car is travelling with constant speed of 2 m/sec such that it takes 5 sec to traverse a stretch of 10 m (20 cells) road length. It is also assumed that all the 18 cells (vehicle area) enter as well as leave the measurement region within the stipulated period. About 18 cells of the car in the region are considered as separate vehicles and the time taken by these 18 cells to traverse the measurement region is 180 sec such that the distance traversed by these 18 cells is 360 cells. The volume of the measurement region would then be 10 sec X 20 cells X 5 cells. If cars are the only vehicles that traverse through the measurement region, from equations (2) and (3), the flow value becomes 0.36 cells/sec per unit road width (cell width), whereas the density value becomes 0.09 cells per unit road length (cell length) per unit road width (cell width).

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Results

Main emphasis in this study is given to understand the heterogeneous traffic behaviour in the free flow regime. As discussed earlier, all the measurements are taken over a general measurement region. A homogeneous traffic stream is simulated and the results are used to validate the new CA structure and the new data collection methodology. The flow-occupancy relationships obtained for different homogeneous vehicle groups over a two-lane road are shown in Figure 4(a), and it can be seen that the results obtained conform with the established ones. Since the cell width is taken as a constant, which is crucial under the congested traffic conditions, the results related to congested flow may not represent the true traffic behaviour. The slope of the free flow branch is equal to the free flow velocity of the respective vehicle group. In this figure, the flow value represents the number of cells per second per sub-lane that pass the considered road section. Maximum flows achieved in case of only cars and only buses are 3000 vehicles/hr and 1800 vehicles/hr, respectively.

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In another simulation run, about 95% cars and 5 % buses (89.1% car cells and 10.9% bus cells) are simulated and the resulting maximum flow achieved over the two-lane road is 12 cells/sec (Figure 4(b)). In an absolute number of vehicles, the maximum flow consists of 111 buses and 2140 cars. Finally, to simulate the real heterogeneous traffic behaviour, different types of vehicles are incorporated into the model and the resulting flow-occupancy relationship is shown in Figure 5. The traffic stream simulated consists of 50% cars, 5% buses, 20% three-wheelers and 25% two-wheelers which represent a typical urban traffic stream observed in India. In this case also the maximum flow equals 12 cells/sec and under maximum flow conditions, about, 1482 cars, 150 buses, 594 three-wheelers and 1500 two-wheelers are found to flow in a one hour period.