Cellular Automata model for heterogeneous traffic

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

In homogeneous traffic while the values of the parameters like stochastic deceleration or delayed acceleration are assumed same for all vehicles, for heterogeneous traffic conditions, different vehicles have different acceleration capabilities hence it is logical to assign large probabilities to long and slow vehicles. This is also valid due to the fact that heavy vehicles maintain large gaps in front under jamming conditions in addition to their length component. On the basis of the few models developed for heterogeneous traffic so far, it has been observed that the probability attached to stochastic acceleration or deceleration for heavy vehicles is higher as compared to that for smaller vehicles (Kerner and Klenov, 2004).

Acceleration behaviour

The acceleration and deceleration values are constant for homogeneous traffic, whereas the same acceleration deceleration values could lead to unrealistic vehicle dynamics in heterogeneous traffic. As shown in Table 1, acceleration capabilities are varying with vehicle type and also with the speed. Instead of using a constant acceleration, two different values have been used for different speed ranges in the study. Also, the updating procedure adopted in the present model after incorporating the heterogeneous-traffic-specific behaviour is described as Step 0: Determination of randomization parameter

This step is crucial in modelling the fluctuation of driver behaviour and in modelling the delay in acceleration and deceleration. Depending on the speed in the previous time step and the vehicle type, suitable values are assigned to the randomization parameter, thus

If ([V.sub.n] = 0) then p = [p.sub.0]

Else p = [p.sub.dec]

Step 1: Synchronization

This step is crucial in modelling the vehicle interactions near the end of the free flow regime. If the leading vehicle is within the synchronization distance (function of leading and following vehicle's speed), the vehicle following it would accelerate/decelerate depending on the difference of speed between the two vehicles, thus

If (gap > synchronization distance) then [v.sub.n] = minimum ([v.sub.n] acceleration ([v.sub.n], [.sub.n]), [V.sub.max,n])

Else

If ([v.sub.n] < [v.sub.n]-1) then [v.sub.n] = minimum ([v.sub.n] acceleration ([v.sub.n], [l.sub.n]), [v.sub.max,n])

If ([v.sub.n] > [v.sub.n]-1) then [v.sub.n] = maximum ([v.sub.n] - deceleration ([v.sub.n], [l.sub.n]), 0)

Step 2: Deceleration

This step is to prevent unwanted vehicle collisions, thus

If ([v.sub.n] > gap) then [v.sub.n] = gap

Step 3: Randomization

Using the randomization parameter values arrived at in the [0.sup.th] step, the vehicle speed is adjusted according to

If (p = [p.sub.0])

[v.sub.n] = maximum ([v.sub.n] - deceleration ([v.sub.n], [l.sub.n]), 0)

If (p = [p.sub.dec])

[v.sub.n] = maximum ([v.sub.n ]- 1, 0)

Step 4: Repositioning

Using the final value of the speed, vehicles are updated to new positions in this step, thus

[x.sub.n](t l) = [X.sub.n](t) [v.sub.n](t)

Where [v.sub.n], [x.sub.n], [l.sub.n] and [V.sub.max, n] corresponds to the speed, longitudinal position, length and maximum speed of the subject vehicle respectively.