Road traffic microsimulations based on the individual motion of all the involved vehicles are now recognized as an important tool to describe, understand, and manage road traffic. Cellular automata (CA) are very efficient way to implement vehicle motion. CA is a methodology that uses a discrete space to represent the state of each element of a domain, and this state can be changed according to a transition rule. The well-known cellular automaton Nasch model with modified cell size and variable acceleration rate is extended to two-lane cellular automaton model for traffic flow. A set of state rules is applied to provide lane-changing maneuvers. S-t-s rule given in the BJH model which describes the behavior of jammed vehicle is implemented in the present model and effect of variability in traffic flow on lane-changing behavior is studied. Flow rate between the single-lane road and two-lane road where vehicles change the lane in order to avoid the collision is also compared under the influence of s-t-s rule and braking rule. Using results of numerical simulations, we analyzed the fundamental diagram of traffic flow and show that s-t-s probability has more effect than braking probability on lane-changing maneuver.

Cellular automata (CA) is a mathematical machine that arises from very basic mathematical principles. Though they are remarkably simple at the start, CA has variety of applications. It has been used extensively for modeling of single-lane traffic. Some modifications are required to extend these models to two-lane traffic as these generally fail to explain the lane-changing behavior. First traffic flow model using the concept of one-dimensional CA was given by Nagel-Schrekenberg popularly known as Nasch model [

In the present study the cell size is reduced and variable acceleration rate (rather than 1) is taken into account [

The Nagel-Schrekenberg model is a probabilistic CA model for the description of single-lane highway traffic. Mathematically it is expressed by four rules given as follows.

Acceleration:

Deceleration:

Randomization:

Movement:

Where

Acceleration:

Where acceleration

Most of the major roads are two-lane one-way roads. We consider a two-lane model with periodic boundary conditions, where additional rules defining the exchange of vehicles between the lanes are applied. For our model we adapt the Nasch model to provide vehicle movements. Any vehicle may perform lane-changing maneuver based on three criteria: incentive criterion, improvement criteria, and safety criteria [

Incentive criteria:

Improvement criteria:

Safety criteria:

where

We now implement a further rule to two-lane model, which is referred to as slow-to-start rule [

CA model developed so far with modified cell size and variable acceleration rate and with implementation of slow-to-start rule for two-lane traffic is given as

Together with lane-changing rules:

The numerical simulation is carried out with randomly generated initial configurations on a closed track containing 10,000 cells which represents a simulated road section of 5 km. The periodic boundary condition is that

The computational formulas used in numerical simulation are given as follows:

where (

The behavior of lane-changing criteria can be explained if two criteria are fulfilled to initiate lane change. First, the situation on the other lane must be more convenient and second the safety rules must be followed. A probability

(a) Relationship between lane changing rate and density at braking probability

Relationship between lane-changing rate and density obtained from the Nasch model at various values of

A detailed comparison of the single-lane model with the corresponding two-lane model with effects of parameters

Relationship between density and flow with lane change and without lane change at various values of parameters

Figure

Relationship between density and average velocity with lane changing and without lane changing at various values of braking probability

Relationship between density and lane-changing rate at various values of maximum velocity

We have extended the BJH model to two-lane model with a reduced cell size and a variable acceleration rate. The reduced-cell-size CA model is more appropriate to describe the finer variability in traffic flow rather than the Nasch model with cell size

We also investigated the speed variance near the maximum flow and observed that density of maximum flow is in the region of density of maximum speed variance in case of nonzero values of braking probability. Thus presence of any amount of variability is sufficient to result in high speed variance. High speed variance means that different vehicles in the system have widely varying speeds. It means that a vehicle would experience frequent speed change per trip through the system. Since s-t-s rule in traffic flow enhances the lane-changing tendency among vehicles, combined effect of braking rule and s-t-s rule is significant in high-density region. Actually s-t-s rule reflects the feature of real driving and is distinct from general disorder rule. Therefore combined study of disorder rule with s-t-s rule is necessary for a safety point of view. Present model reveals all the features of two-lane traffic flow.

This work is partially supported by a grant-in-aid from the Council of Scientific and Industrial Research, India.