串并联网络动态平衡的计算
Computation of Dynamic Equilibria in Series-Parallel Networks
摘要：
我们考虑流体排队模型下的流动随时间的动态平衡。在这个模型中，网络链路上的队列负责流的传播。流从一个源进入网络，从一个汇离开。在动态平衡中，每一个无穷小的流动粒子都尽可能早地到达汇，给定其余流动的模式。虽然这一模式已经研究了几十年，但进展相对较近。特别是，衍生物的动态平衡的特点是薄流与复位，这使得更多的结构性的结果。我们的两个主要结果是基于薄流与重置为线性互补问题及其分析的提法。我们提出了一个建设性的证明存在的动态平衡，如果流入率是右单调的。在该方法中，作为子问题出现的带重置的细流计算的复杂性仍然是开放的。对于二端串并联网络，我们给出了一个递归算法，在多项式时间内同时求解所有流值。
英文摘要：
We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. While this model has been examined for many decades, progress has been relatively recent. In particular, the derivatives of dynamic equilibria have been characterized as thin flows with resetting, which allowed for more structural results. Our two main results are based on the formulation of thin flows with resetting as linear complementarity problem and its analysis. We present a constructive proof of existence for dynamic equilibria if the inflow rate is right-monotone. The complexity of computing thin flows with resetting, which occurs as a subproblem in this method, is still open. We settle it for the class of two-terminal series-parallel networks by giving a recursive algorithm that solves the problem for all flow values simultaneously in polynomial time.
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