Quoted from: https://iopscience.iop.org/article/10.1088/0305-4470/29/12/018/pdf Benjamin S C, Johnson N F, Hui P M. Cellular automata models of traffic flow along a highway containing a junction[J]. Journal of Physics A: Mathematical and General, 1996, 29(12): 3119.

The NS model involves two additional rules that produce a closer simulation of real traffic. (a) Cars may move with a range of integer speeds, s = 0,...,smax. A car with speed v = s − 1 on the previous step will move in the next step with a speed given by the lowest of the following quantities: (i) v = s, (ii) v = smax, or (iii) v equal to the number of vacant sites to its immediate right. This will be referred to as the acceleration rule. (b) The cars are subject to a random disordering effect as follows. For each car whose scheduled speed for the next update is v > 0, there is a probability Pfault that it will in fact move with speed v − 1. This will be referred to as the disorder rule.

The second rule is intended to reflect the flawed behaviour of real (human) drivers. In this spirit, we will now introduce a further rule, referred to as the slow-to-start rule. The rule will model the small, but finite delay before a car pulls away from being ‘static’, i.e. when it has reached the head of a queue. This can arise from a driver’s loss of attention as a result of having been stuck in the queue, or from the slow pick-up of his vehicle’s engine. This rather subtle feature of real traffic is likely to become important at high car densities, particularly since no such delay is likely to occur as cars decelerate, i.e. as they brake. The resulting asymmetry is liable to cause queues to lengthen. We define the slow-to-start rule as follows: a given static car moves either on its first opportunity with probability 1 − Pslow or second opportunity with probability Pslow. We note that the disorder rule can also cause cars to be slow in moving off from the heads of queues. However, the disorder rule affects vehicles of all velocities with equal probability; it introduces a general ‘noise’ into the system. By contrast, the slow-to-start rule affects only static cars on the first occasion that they are free to move; it reflects a distinct physical phenomenon of driver behaviour as described above.