The stability of downtown parking and traffic congestion

Arnott, Richard; İnci, Eren · 2010 · OpenAlex-citations

DOI: 10.1016/j.jue.2010.05.001

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Summary

This paper addresses a longstanding debate in transport economics regarding the stability of steady-state hypercongested traffic equilibria. Classical traffic flow theory distinguishes between congested travel (higher velocity) and hypercongested travel (lower velocity, where increased flow increases speed). Since Walters (1961), scholars have debated whether steady-state hypercongested equilibria are stable. Recent work by Small and Verhoef argues that such equilibria are dynamically unstable, proposing that high demand is instead rationed through steady-state queues at entry points, effectively replacing the backward-bending portion of the user cost curve with a vertical segment at capacity. Arnott and Inci challenge this resolution by demonstrating that stable, steady-state hypercongested equilibria can exist under specific structural conditions. To investigate this, the authors employ a structural model of downtown traffic and on-street parking, analyzing its non-stationary dynamics. The model assumes an isotropic (spatially homogeneous) street network where drivers enter, travel to destinations, and either park immediately or cruise for parking if spaces are unavailable. The system is characterized by two regimes: saturated parking, where all spaces are occupied and cars cruise for vacancies, and unsaturated parking, where vacancies exist. The authors derive autonomous differential equations governing the pools of cars in transit, cars cruising for parking, and occupied parking spaces. By assuming Poisson distributions for driving distances and visit lengths, they enable a complete phase plane analysis of the system’s transient dynamics, allowing for a rigorous stability assessment that respects the physics of traffic flow. The study finds that stable, steady-state hypercongested equilibria do exist within this specific model. In the saturated regime, cars cruising for parking contribute disproportionately to congestion compared to cars in transit, reducing system throughput. The authors show that when steady-state demand is too high to be rationed through congested travel, the necessary trip price increase to ration demand can be generated through hypercongested travel rather than solely through queue formation. The specific mechanism—queues versus hypercongestion—depends on the details of the traffic system, particularly the impact of cruising behavior on throughput. The significance of these findings lies in challenging the universality of Small and Verhoef’s resolution. The authors argue that while their model is specific, the underlying mechanism—where dissipative activities like cruising for parking undermine system performance—is representative of many heavily congested traffic systems. Consequently, the conclusion that stable hypercongested equilibria never exist is not general. Instead, the paper implies that the stability of traffic equilibria and the method of demand rationing depend critically on the specific structural features of the traffic network, such as the presence of parking search behaviors that reduce effective capacity.

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• traffic density