Cellular Automata model for heterogeneous traffic

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

CA Models

A review of literature shows that Cremer and Ludwig (1986) were the first to propose a cellular automata (CA) model for vehicular traffic.

Their study was followed by Nagel and Schreckenberg (1992) whose model based on the concepts of CA was found to be superior in modelling the complex systems. Later, to capture the important features like hysteresis observed in real traffic, Takayasu and Takayasu (1993), Schadschneider and Schreckenberg (1997), and Barlovic et al (1998) have proposed some modifications to Nagel and Schreckenberg's model. With the help of these modifications, modelling of some of the observed traffic features such as outflow from a jam and velocity of the upstream front of the jam were made possible. Further, Brilon and Wu (1999) proposed a time oriented CA model in which the interaction horizon of a vehicle was taken to be different from the basic CA model. Also, Helbing and Schreckenberg (1999) proposed a discrete optimal velocity model in which vehicle acceleration and deceleration behaviour was modified such that a vehicle could not decelerate from a maximum velocity to zero within a single time step. To replicate the synchronized flow (Kerner and Rehborn, 1996), Knospe et al (2000) proposed a brake light model in which the behaviour of a car was dependent on the brake light status (on/off) of the vehicle leading it. Kerner et al (2002) also have proposed a parameter called synchronization distance, based on which a vehicle following another could adjust its speed accordingly.

Realizing that the single lane models are not realistic, two lane CA models were suggested by researchers (Rickert et al, 1996; Chowdhury et al, 1997; Wagner et al, 1997; Nagel et al, 1998; Knospe et al, 2000). Chowdhury et al (1997) developed a two lane CA model which could model the traffic comprising different vehicle types. In this model, the fast moving vehicles move at average free flow velocity of the slow moving vehicle even when the density of the slow vehicles is small. Similarly, Knospe et al (1999) incorporated a parameter 'anticipation' into their model to nullify the unrealistic effect of slow vehicles. According to their model, the driver is able to anticipate the speed of the vehicle moving in the front of him in the next time step.

Furthermore, implementing the CA model for the heterogeneous traffic has been suggested by some researchers (Hsu et al, 2007; Lan and Chang, 2005). Lan and Chang have modelled heterogeneous traffic comprising of cars and two wheelers with the help of a refined CA structure wherein the basic CA updating rules were applied to simulate the heterogeneous traffic. Similarly, Lan and Hsu (2006) tried to model the effect of a moving bottleneck on a homogeneous traffic stream. The modified basic structure of the CA model further helped in obtaining slightly modified traffic variables that were suitable for heterogeneous traffic (Lan and Hsu, 2006; Mallikarjuna and Ramachandra Rao, 2006). Since there are several types of vehicles that ply on the roads in developing countries, a suitable model is required to understand their behaviour in a traffic stream. On the basis of the studies conducted so far, it is evident that a CA model can be a better alternative to model heterogeneous traffic behaviour considering its ability to model complex interactions that are observed in the heterogeneous traffic.