User-equilibrium Route Set Analysis of a Large Road Network

Bar-Gera, Hillel; Boyce, David · 2005 · Crossref

DOI: 10.1016/b978-008044680-6/50036-2

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Summary

This paper addresses a significant gap in transportation research regarding the characteristics of route sets in large-scale user-equilibrium (UE) models. While the static, deterministic UE model has been studied for decades, little was known about the specific properties of the route sets that comprise its solutions for large networks. The authors aim to answer two primary questions: what are the number, range, and frequency of routes per origin-destination (OD) pair in a UE solution, and how does this number vary with OD generalized travel cost, flow, and direction? Understanding these properties is crucial for assessing the validity of the UE model for travel forecasting and for guiding empirical validation efforts. To investigate these questions, the authors applied the Origin-Based Assignment (OBA) algorithm to a detailed model of the Chicago Region. The network consists of 1,790 zones, 12,982 nodes, and 39,018 links, representing morning peak period travel in 1990. The model incorporates both auto and transit modes, with auto flows derived from person-trips and truck flows. The UE solution was computed with high precision, achieving a maximum excess cost of 1E-13 minutes and total misplaced flow of 1E-10 person-trips. The authors defined the UE route set by including all routes with an excess cost below a threshold of 2E-12, ensuring the set closely approximates the true equilibrium routes. The analysis relied on exploratory methods, using spreadsheets and graphical representations to examine the distribution of routes across the network. The results reveal that the solution contains 8,602,026 routes connecting 3,202,310 zone pairs, averaging 2.686 routes per OD pair. Approximately 56% of OD pairs are connected by only one route, while the maximum number of routes for a single pair is 1,920. About 90% of all OD pairs have five or fewer routes, whereas 90% of all routes connect OD pairs with 40 or fewer routes. The analysis further demonstrates that the number of routes per OD pair is strongly correlated with generalized travel cost and flow. OD pairs with lower costs and higher flows tend to have more alternative routes. Specifically, single-route OD pairs dominate at very low costs (98% at 1 minute) but decline to 32% at higher costs (150 minutes), where multi-route options become more prevalent. The distribution of routes is also sensitive to congestion levels; reducing the deterrence parameter increased the total number of routes significantly. The significance of this work lies in providing the first detailed empirical characterization of UE route sets for a large road network. By establishing the baseline properties of route multiplicity in equilibrium solutions, the study offers a foundation for validating route choice models against observed data. The findings highlight that while most OD pairs have few routes, a substantial portion of total traffic volume is distributed across OD pairs with moderate route options. This insight aids practitioners in understanding the complexity of route choice in large networks and underscores the importance of precise solution algorithms like OBA for accurate travel forecasting.

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• traffic density