Equivalent Optimization Problem for Finding Equilibrium in the Bottleneck Model with Departure Time Choices

Abstract

This study shows an equivalent optimization problem for finding equilibrium in departure time choice problem. The departure time choice problem, which deals with dynamic traffic assignment problems while considering travelers’ schedule constraints, is one of famous schemes for analyzing the time-dependent traffic flow. There are many existing studies related to departure time choice problem but it is not common for them to replace the equilibrium assignment problem by an optimization problem. The study shows an optimization problem which is equivalent to the equilibrium assignment problem. This study shows an optimization problem which is equivalent to the equilibrium assignment problem. This problem is the linear program whose primal problem shows how travelers choose their departure times in equilibrium and dual problems calculate delay at bottlenecks and travel cost in equilibrium. Because this optimization problem minimizes the sum of travel costs excluding the cost due to delay at bottlenecks over travelers, it can be said that policies eliminating the queue without changing departure times from the bottlenecks will minimize the total travel cost. This study also shows that the external cost of the congestion made by the additional demand only appears in the delay at bottlenecks.

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