Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network
Investigating Factors for Existence of Multiple Equilibria in Dynamic Traffic Network
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DOI：
10.1007/s11067-013-9206-6
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发表时间：
2013-09
影响因子：
2.4
通讯作者：
T. Iryo
中科院分区：
文献类型：
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作者：
T. Iryo
均匀性是网络用户均衡的一个重要特征。动态用户均衡（DUE）在一定条件下存在唯一性，而在具有两个瓶颈的双重对称网络中存在多个Wardrop均衡.这种设置非常特殊，因此，值得研究在这种情况下获得非唯一解所必需的因素，以便讨论这个特殊示例对真实的网络问题的影响。利用网络的非对称结构、随机用户均衡（SUE）和全链路模型来检验这些因素是否影响多重均衡的存在性。结果表明，放置具有等效容量的瓶颈会导致线性方程系统的奇异性，该线性方程系统描述了Wardrop的第一原理，在一个特定的网络结构中称为循环网络。然后，它被证明，这种奇异性的原因存在的多重平衡。另一方面，在SUE或全链路情况下没有发现这种奇异性，因此，在它们中没有发现非唯一解。它还表明，奇异性似乎并不是唯一的来源，提出另一个例子，其中至少有三个平衡解存在时，无论是瓶颈模型或全链路模型。
Uniqueness is an important characteristic of network user equilibrium. Uniqueness in dynamic user equilibrium (DUE) has been shown to exist under certain conditions, whereas a case with multiple Wardrop equilibria has been found in a twofold symmetric network with two bottlenecks. This setting is very special, and therefore, it is worthwhile to investigate the factors that are essential to obtain non-unique solutions in this case in order to discuss the implication of this special example for real network problems. The asymmetric structure of the network, stochastic user equilibrium (SUE), and whole-link model were employed to check whether these factors affect the existence of multiple equilibria. It was shown that placing bottlenecks with equivalent capacities causes the singularity of the linear equation system that describes Wardrop’s first principle in a particular network structure called as a loopy network. Then, it was shown that this singularity causes the existence of multiple equilibria. On the other hand, this singularity was not found in SUE or the whole-link cases, and therefore, non-unique solutions were not found in them. It was also shown that the singularity does not appear to be the only source of non-uniqueness by presenting another example in which at least three equilibrium solutions exists when either the bottleneck model or the whole-link model is employed.