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 with considering travellers' schedule constraints, is one of the famous schenes for analyzing the time-dependent traffic flow. There are many existing studies related to the departure time choice problem but it is not common for them to replace the equilibrium assignment problem with an optimization problem. This study shows an optimization problem which is equivalent to the equilibrium assignment problem. This problem is the linear programme whose primal problem shows how travellers choose their departure times in equilibrium and dual problem calculates 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 travellers, 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.(A) Reprinted with permission from Elsevier. For the covering abstract see ITRD E134766.
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