## BJHRule

A slow-to-start rule which simulates a possible delay before a car pulls away from being stationary. Having discussed the case of a bare highway, we then consider the presence of a junction. We study the effects of acceleration, disorder, and slow-to-start behaviour on the queue length at the entrance to the highway. Interestingly, the junction's efficiency is improved by introducing disorder along the highway, and by imposing a speed limit.

Cellular automatontraffic flow

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#### Authorship

:
Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, UK
:
Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, UK
:
Physics Department, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
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Application-focused categoriesHuman-perspectiveEconomic activities

#### Detailed Description

Chinese {{currentDetailLanguage}} Chinese

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.

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Simon C Benjamin, Neil F Johnson, P M Hui (2020). BJHRule, Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/94fede04-4dbf-48d8-b58c-eb839d4c0f9f

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XU Kai
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#### Authorship

:
Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, UK
:
Physics Department, Clarendon Laboratory, Oxford University, Oxford OX1 3PU, UK
:
Physics Department, Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
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Last modifier
XU Kai
Last modify time
2020-12-18
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