基于TASEP模型的两道交叉情形下车辆运动研究

输送现象广泛存在于社会中,对分析车辆运动规律、解决道路拥堵现象具有重要的现实应用价值。完全非对称排它过程(Totally Asymmetric Simple Exclusion Process,TASEP)模型是一种描述一维晶格上粒子运输的经典模型,已被广泛应用于交通领域。本文基于排他过程对双道交叉情境下车辆运动进行仿真研究,通过在模型中输入粒子(车辆)进入以及移出该模型(十字路口)的概率α和β,并多次改变α和β的大小,得到不同取值范围下的车辆运动规律密度图,发现在车辆运动过程中,系统始终存在3个稳定相位:高密度-高密度相(HH),低密度-低密度相(LL),高密度-低密度相(HL)。并且最终得到α、β与车辆在交叉道中密度的数学关系,且较为符合真实的交通状况,同时为研究城市交通流模型提供了借鉴。

基于交通路网的TASEP模型的扩展研究

完全非对称的简单排它过程(Totally Asymmetric Simple Exclusion Process,TASEP)模型是一种描述一维晶格上粒子运输的一种经典模型,其主要考虑了粒子之间的体积排斥效应,已被广泛应用到生物、交通等领域。文中主要对传统的TASEP模型进行了扩展研究,结合实际交通网络的结构和特性对TASEP模型进行了如下改进:1)粒子在各条边上的跳跃率是异质的,即设置各条边上的跳跃率不同且符合泊松分布;2)在交叉路口的粒子在选择下一个路段时是非随机的。具体地,设计了一种实时路径策略,结合各个时刻各条边上的流量值与粒子数得到对应边上粒子的平均移动“速度”;在此基础上引入“理性”参数α来控制粒子的路径选择:α的值越大,粒子越倾向于运动到平均速度越快的连边上。结果显示,随着参数α值的增大,网络中粒子的整体运动得到了优化,使得系统的流量有较大的提升,从而可以缓解网络拥塞。文中通过结合复杂网络的概念和方法,对传统TASEP模型做出了两点改进:1)设计出粒子在交叉口处的路径策略优化其行驶路径;2)为研究城市交通流模型提供了新的思路和方向。

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.

元胞自动机交通流模型中的车辆更新方式研究

基于TASEP(Totally Asymmetric Simple Exclusion Process)模型,使用蒙特卡洛方法模拟开放边界条件下不同车辆更新方式对稳态时车辆特性及相变行为的影响,得到不同注入概率α和输出概率β条件下的交通流基本图。结果表明,不同更新方式对系统的稳态特性及相变行为有较大影响,流量和密度随α和β的不同而变化,模拟结果与解析解吻合。随机更新方式下道路车流量的大小由输出概率决定,当输出概率达到一定值时,它的增大无法提高道路上的车流量;顺序更新方式的优点是仅当输入和输出概率都相等时,系统保持畅行相;而局部并行更新方式下得出的相图则与顺序和全局并行更新这两种方式下得到的相图类似且可以更好地反映交通流现实。

基于并行更新规则的粒子ASEP模型及其仿真研究

交通拥堵问题困扰人们由来已久。为了探究道路行驶中突发状况限制车辆行动速度会对道路行车状态造成的影响,建立边界处粒子的跳跃率不同的ASEP模型,探究跳跃率的改变对系统内粒子流量与粒子密度造成的影响。模型分为入口、出口两种情况,在特定取值下系统稳态MC相将会消失。此外由于跳跃率p增加分别会使两种情况下模型内粒子密度减少或者增加,利用计算机模拟粒子运行过程、蒙特卡洛算法进行数据统计,获得结果与理论值一致。

Theoretical investigation of synchronous totally asymmetric simple exclusion process on lattices with two consecutive junctions in multiple-input-multiple-output traffic system

In this paper, we study the dynamics of the synchronous totally asymmetric simple exclusion process （TASEP） on lattices with two consecutive junctions in a multiple-input-multiple-output （MIMO） traffic system, which consists of m sub-chains for the input and the output, respectively. In the middle of the system, there are n （n 〈 m） sub-chains via two consecutive junctions linking m sub-chains of input and m sub-chains of output, respectively. This configuration is a type of complex geometry that is relevant to many biological processes as well as to vehicular traffic flow. We use a mean-field approach to calculate this typical geometry and obtain the theoretical results for stationary particle currents, density profiles, and a phase diagram. With the values of m and n synchronously increasing, the vertical phase boundary moves toward the right and the horizontal phase boundary moves toward the upside in the phase diagram. The boundary conditions of the system as well as the numbers of input and output determine the no-equilibrium stationary states, stationary-states phases, and phase boundaries. We use the results to compare with computer simulations and find that they are in very good agreement with each other.

Existence of spontaneous symmetry breaking in two-lane totally asymmetric simple exclusion processes with an intersection

We study two-lane totally asymmetric simple exclusion processes(TASEPs)with an intersection.Monte Carlo simulations show that only symmetric phases exist in the system.To verify the existence of asymmetric phases,we carry out a cluster mean-field analysis.Analytical results show that the densities of the two upstream segments of the intersection site are always equal,which indicates that the system is not in asymmetric phases.It demonstrates that the spontaneous symmetry breaking does not exist in the system.The density profiles and the boundaries of the symmetric phases are also investigated.We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.

理论研究Y型通道同步完全非对称简单排它过程(英文)

主要研究Y型通道同步完全非对称简单排它过程.该模型是我们生活中最简单的几何图形,存在于交通系统、管网系统及电网系统等.过去利用完全非对称简单排它过程研究Y型通道时,考虑的主要是进入分支的流量(粒子在分离点进入两条分支)相同,而实际上流量经常是不同的.参数p和q(p<q和p+q=1)分别用来描述进入两条分支的流量比例.不同p和q条件下的稳态粒子流量、密度及相图的理论结果可以获得,理论计算的粒子密度与计算机仿真结果十分吻合.可以发现,当(q-p)增加时,高密度相的面积增加.所获的结果可以帮助我们如何更好地选择管网直径和如何减少交通系统的堵塞.

Totally Asymmetric Simple Exclusion Process under Exit Control Feedback Policy

The effect of the exit control feedback policy on traffic flow was investigated in this paper.Here,the exit rate(β)can be defined as a function of the hopping rate(p),the current(J)and the bulk density(ρ_(bulk)),which can be rewritten as β=p-J/ρ_(bulk).A model based on normal totally asymmetric simple exclusion process(TASEP)has been analyzed by mean field approach.It is found that a phase transformation point exists in the phase diagram,which is determined by p.In addition,the traffic flow of the system achieves maximum current when the exit rate maintains itself atβ=p/2 for all other phases except the low density(LD)phase.The result implies that we can use the control feedback policy to make the traffic flow reach the maximum value when the traffic system is in the traffic jam status.