New insights and improvements of using paired alternative segments for traffic assignment

Abstract

The recent literature observes that the development of advanced algorithms for the traffic assignment problem (TAP) heavily relies on the proper use of some specific topological structures. This paper focuses on discussing a particular topological structure named paired alternative segment (PAS), which consists of two path segments sharing the same starting and ending nodes but no other common nodes. We first present two alternative conditions that establish an equivalency relationship between user equilibrium (UE) flows and PAS structures. Starting from the traffic assignment method by paired alternative segments (TAPAS), we then examine the utilization of PASs for TAP and explore some algorithmic and implementation issues, which leads to the birth of an improved TAPAS procedure (termed iTAPAS in this paper). Compared to the original TAPAS, iTAPAS enhances the algorithmic efficiency in two aspects: (1) a more effective PAS identification method is used; (2) each PAS is set as being associated with only one origin in the UE-finding process. Some analytical results based on the new PAS identification method are presented to justify the convergence and efficiency of iTAPAS. A simplified post-process procedure is also presented to achieve the proportionality for iTAPAS. Numerical results obtained from applying the new and original algorithms for several large networks reveal that iTAPAS is nearly two times faster than TAPAS in achieving highly precise link flow solutions while it is practically identical to TAPAS in finding stable path flow solutions that meet consistency and proportionality.