Quoted from: https://www.researchgate.net/profile/Najem_Moussa/publication/253321373_Numerical_Simulations_of_a_Three-Lane_Traffic_Model_Using_Cellular_Automata/links/5440f2f50cf228087b69bb88.pdf Daoudia A K, Moussa N. Numerical simulations of a three-lane traffic model using cellular automata[J]. Chinese journal of physics, 2003, 41(6): 671-681.

The NaSch model is a CA model which is described as follows: On a ring with L sites every site can either be empty or occupied by one vehicle with velocity v = 0, 1, ..., vmax. Let gap be the number of empty sites in front of the car, and v its velocity at time t. At each discrete time step the arrangement of N cars is updated in parallel, according to the following rules:

• Acceleration: with regard to the vehicle ahead: v'← min (v + 1, gap, vmax)
• Noise: with a probability p : v''← max(v'− 1, 0)
• Movement: the car moves v'' sites ahead. 

It is clarified that this extension can be made without changing the basic properties of the single-lane model. Moreover, lane changes lead to strong correlations between neighboring lanes. We choose the Knospe et al. exchange rules elaborated for the two-lane case which are extended here to the three-lane system. Let gapother ij (resp. gapback ij ) be the number of free cells between the vehicle on lane i and its forward (resp. back) neighboring vehicle on lane j. Note that a vehicle in lane (1) or (3) can change only to the center lane whereas a vehicle in the center lane can change to lane (1) or (3). In this case, several situations arise: if the lane-change conditions of are fulfilled only for one of the two adjacent lanes (lanes (1) and (3)), the driver will change to the latter. On the other hand, if the conditions of lane-changing are fulfilled for the two adjacent lanes, the driver will choose between these lanes according to its speed optimization criteria, e.g., the lane where the parameters gapother and gapback are most significant, or the lane where the predecessor is fastest, etc... The corresponding exchange rules are defined by the following two criteria: first, a vehicle needs an incentive to change a lane. Second, a lane change is only possible if some safety constraints are fulfilled (see Figure 1) :