Time-headway distribution for random-sequential-update TASEP with periodic and open boundaries

The temporal-headway distribution for Totally Asymmetric Simple Exclusion Process(TASEP) with random-sequential update is investigated.Considering the stationary/steady state of the process,exact formula for the step-headway distribution is derived for conditions when the stationary measure is Bernoulli,Le.,for periodic boundaries and for open boundaries with entering boundary rate α and leaving boundary rate 0 satisfying α+β=1.The step-headway formula for general values of boundary rates is calculated numerically by means of the matrix product ansatz.The formula is applicable mainly for the model defined on finite small lattice representing short segment of complex network.In this case the dependency of the motion of individual particles is noticeable and cannot be neglected.The finite lattice results are compared to continuous time distribution obtained by mans of the large L limit It can be observed that the scaled distribution converges quite fast to continuous time distribution.However,in the case of rather small lattice the distribution significantly differs from the limiting one.Moreover,in the case of Bernoulli stationary measure,the distribution is not dependent on the position of the reference site on the lattice.Considering general values of boundary parameters,the shape of the distribution is influenced by the density profile of the process near boundaries.This influence vanishes with increasing lattice size.

Model of Traffic Speed-Flow Relationship at Signal Intersections

Speed-flow relationship is the fundamental for the traffic simulation and traffic volume forecast. Traditional quadratic polynomial model can’t reflect the saturate flow at signal intersections. In order to determine the speed-flow relationship at signal intersections, the speed and time-headway of vehicles at two signal intersections were investigated and the accuracy of software used to get the speed was tested. After vehicle starting-up from queuing, the time-headway reduces gradually with the increase of speed. The relationship of power exponential function between speed and time-headway is formulated. Traffic volume can be calculated by the vehicle time-headway. Then the speed-flow relationship was developed and an S-shaped curve model was built in this paper. In the S-shaped curve model, traffic flow approaches to the saturate when the speed doesn’t increase. Thus, S-shaped curve model is better to describe the speed-flow relationship at signal intersection. The results can provide a reference to determine the parameters in traffic simulation and for the study of level of service of intersections.