Traffic Assignment Problem with Strict Capacity Constraints

Azimi, Ghazaleh · 2020 · Crossref

DOI: 10.31224/osf.io/ywkfr

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Summary

This thesis addresses the Traffic Assignment Problem (TAP), specifically focusing on improving the accuracy of transportation network modeling by incorporating strict link capacity constraints. The research is motivated by the limitations of the widely used Frank-Wolfe (FW) algorithm, which determines move directions via an "all-or-nothing" assignment that ignores capacity limits, often resulting in inaccurate outputs where link flows exceed physical capacities. To resolve this, the study proposes a modified algorithm that integrates the Out of Kilter (OFK) algorithm to determine move directions within the FW framework, ensuring that link flows remain within or equal to their capacities in every iteration. The methodology involves modifying the standard FW algorithm by replacing the unconstrained minimum cost flow subproblem with the OFK algorithm, which solves for minimum cost flow in networks with capacity constraints. The study assumes the network is in circulation form, with pure origins and destinations. The proposed method is tested on two benchmark transportation networks: the Hearn network and the Sioux Falls network. The experiments compare the performance of the proposed FW-OFK algorithm against the standard FW algorithm and a variant assuming infinite link capacities. The analysis evaluates results based on link flows, travel costs, and the ratio of flow to capacity, utilizing the Bureau of Public Roads (BPR) function for travel time modeling. The findings demonstrate that the proposed FW-OFK algorithm successfully maintains link flows within their specified capacity limits, unlike the standard FW algorithm which allows flows to exceed capacities. Comparative analysis on the Hearn and Sioux Falls networks reveals significant differences in flow distribution and travel costs between the capacitated and infinite-capacity scenarios. The results indicate that considering capacity constraints leads to more realistic traffic assignments, with the OFK-based approach providing a feasible solution that respects physical network limitations. The study presents detailed comparisons of total costs and consumer costs across iterations, showing that the capacitated model yields distinct equilibrium states compared to unconstrained models. The significance of this work lies in its contribution to more reliable traffic assignment models for transportation network operations. By integrating capacity constraints directly into the solution process via the OFK algorithm, the study offers a method to generate accurate, physically feasible traffic patterns. This approach enhances the precision of traffic prediction and control strategies, addressing a critical gap in traditional algorithms that often overlook capacity limits. The thesis concludes that incorporating strict capacity constraints is essential for realistic network evaluation and provides a viable computational method for doing so within the established FW framework.

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