多源多汇Nash流随时间的变化
Multi-Source Multi-Sink Nash Flows Over Time
摘要：
随时间推移的纳什流描述了自私用户的行为，这些自私用户渴望尽早到达目的地，同时沿着具有容量和过境时间的网络的弧行进。在过去的十年中，他们已经在单源单汇网络的确定性排队模型，这是特别相关的和经常使用的交通和运输网络的背景下，进行了深入的研究。在这种情况下，随着时间的推移存在纳什流，可以通过具有特殊属性的静态流序列来描述，即所谓的“具有重置的瘦流”。这种洞察力也可以在算法上用于计算纳什流随时间的变化。我们提出了一个扩展这些结果的网络与多个源和汇，这是更相关的实际应用。特别是，我们提出了一个微妙的概括薄流与重置产生一个紧凑的描述，以及计算多终端纳什流随着时间的推移的算法方法。
英文摘要：
Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been thoroughly studied in single-source single-sink networks for the deterministic queuing model, which is of particular relevance and frequently used in the context of traffic and transport networks. In this setting there exist Nash flows over time that can be described by a sequence of static flows featuring special properties, so-called `thin flows with resetting'. This insight can also be used algorithmically to compute Nash flows over time. We present an extension of these result to networks with multiple sources and sinks which are much more relevant in practical applications. In particular, we come up with a subtle generalization of thin flows with resetting which yields a compact description as well as an algorithmic approach for computing multi-terminal Nash flows over time.
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