Cellular Automata model for heterogeneous traffic

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

The randomization parameter is calculated based on the speed of the vehicle in the previous time step and vehicle type as a first step in this study. This step is similar to the velocity dependent randomization used in Knospe's model (2000). In the acceleration step, unlike in other CA based models, the acceleration value is a function of vehicle type and vehicle speed. This is more relevant in case of heterogeneous traffic where different vehicles have different acceleration capabilities. To incorporate enhanced interactions, the vehicle would accelerate only when the gap available in front of it is greater than the synchronization distance which is a function of the vehicle speed. The vehicle's speed is updated in the randomization step depending on the probability assigned in the [0.sup.th] step. The vehicle's position is updated using the velocity value obtained after the third step. Different parameter values used in this study are also listed in Table 2.

The important features of the proposed CA model for heterogeneous traffic summarized as:

1. The cell length in the present model is decided based on the acceleration and deceleration capability of heavy vehicles observed on the Indian highways and on the vehicle length.

2. Cell widths are based on the vehicle width and average lateral spacing maintained between vehicles.

3. The driver behaviour is modelled as stochastic and the model incorporates vehicle type also.

4. As opposed to the lane changing procedure used in the conventional CA model, various types of lateral movements have been considered which are more meaningful under heterogeneous traffic conditions.

5. Five types of vehicles with different maximum speeds are simulated in this model.

Results and Analysis

Data collection

The macroscopic traffic variables such as flow, speed and density are defined differently in this study to incorporate heterogeneous nature of the traffic (Lan and Hsu, 2006; Mallikarjuna and Ramachandra Rao, 2006). The basis for these modifications follow conventional traffic measurements for a general measurement region and since lane discipline is absent under heterogeneous traffic conditions, measurements taken over a single lane have no relevance under these conditions. Even after taking measurements considering the lane markings, validity of the fundamental relationships between traffic

variables are not known since various types of vehicles are present in the traffic stream. To overcome these problems, each cell is considered as one vehicle and each sub-lane is considered as one lane while taking measurements over the general measurement region. On account of the above assumptions, the cells (unit vehicle size) inevitably follow the lane discipline. A measurement region of width W, length L and at time T is considered while taking the measurements. The traffic variables such as flow, speed and density are defined over this measurement region by:

q(s) = d(s) / |s| (2)

k(s) = t(s) / |s| (3)

v(s) = q(s) / k(s) = d(s) / t(s) (4)