An Optimal Road Network Design Model with Traffic Congestion and its Application

ASAKURA, Yasuo · 1985 · Crossref

DOI: 10.2208/journalip.2.157

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Summary

This paper addresses the problem of optimal road network design by formulating it as a two-level planning problem that explicitly accounts for traffic congestion. The research is motivated by the need to integrate user behavior into system optimization, moving beyond traditional approaches that treat traffic assignment and network design as separate or simplified processes. The model is interpreted as a non-cooperative, non-zero-sum game between a planner and road users. The planner’s master problem aims to minimize the sum of total transportation costs (travel time) and total link construction costs by determining continuous link capacities. The user’s subproblem is a user equilibrium traffic assignment, where travelers choose routes to minimize their individual travel times, resulting in congestion effects. The study proposes a heuristic solution procedure effective for convex performance and cost functions. Specifically, it assumes a Bureau of Public Roads (BPR) type performance function for travel time and a linear cost function for construction. The solution method involves iteratively solving the user equilibrium subproblem to determine link flows, which are then used to update the optimal link capacities in the master problem. This approach allows for the handling of large-scale networks by decomposing the problem, avoiding the computational difficulties associated with large-scale non-linear programming methods. To validate the model, the authors applied it to the central region of Kyoto Prefecture, Japan. The test network consisted of 98 links (196 directional) and 62 nodes, with 15 links designated for potential expansion. Input data included future Origin-Destination (OD) traffic volumes derived from the 1980 Road Traffic Census, converted to passenger car equivalents. Existing link capacities were calibrated using observed traffic counts and equilibrium assignment results, achieving a correlation coefficient of 0.8982 between observed and calculated flows. Sensitivity analysis was conducted by varying the weight parameter ($\xi$) representing the trade-off between construction costs and travel time savings. The results demonstrated that the model effectively identifies optimal expansion strategies. As the weight on construction costs decreased, the model recommended greater capacity expansions, leading to reduced total travel times but higher construction expenditures. The analysis identified a specific cost threshold (approximately 30 billion yen) beyond which additional investment yielded diminishing returns in time savings. The model also highlighted that major arterial routes should be prioritized for expansion. The study concludes that the proposed two-level framework is a practical tool for road network planning, though it notes limitations regarding fixed OD matrices and simplified cost functions, suggesting future work on endogenous demand modeling and more complex cost structures.

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• traffic density