两段串联道路交通系统的M/G/c/c状态相关排队模型
M/G/c/c state dependent queuing model for a road traffic system of two sections in tandem
摘要：
本文提出了一种基于状态相关的道路交通流排队模型--M/G/c/c模型。该模型是基于有限容量排队理论，捕捉固定的密度流的关系。它也是从确定性Goddom计划的道路交通模拟的启发。我们首先提出了一个现有的线性情况下的M/G/c/c状态相关模型的重新制定，为了使用流量，而不是速度变量。然后，我们扩展了这个模型，以考虑上游的交通需求和下游的交通供应。在此之后，我们提出了两个路段串联的模型，这两个部分相互影响。为了处理这种相互依赖性，我们求解一个由代数方程给出的隐式系统。最后，我们得出一些性能指标（吞吐量和预期的旅行时间）。与M/G/c/c状态相关排队网络预测结果的比较表明，我们提出的模型真正捕捉到了道路交通的动态。
英文摘要：
We propose in this article a M/G/c/c state dependent queuing model for road traffic flow. The model is based on finite capacity queuing theory which captures the stationary density-flow relationships. It is also inspired from the deterministic Godunov scheme for the road traffic simulation. We first present a reformulation of the existing linear case of M/G/c/c state dependent model, in order to use flow rather than speed variables. We then extend this model in order to consider upstream traffic demand and downstream traffic supply. After that, we propose the model for two road sections in tandem where both sections influence each other. In order to deal with this mutual dependence, we solve an implicit system given by an algebraic equation. Finally, we derive some performance measures (throughput and expected travel time). A comparison with results predicted by the M/G/c/c state dependent queuing networks shows that the model we propose here captures really the dynamics of the road traffic.
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