Highlights A morning commute problem with queue-length-dependent bottleneck capacity has been proposed. Multiple user equilibrium states have been observed. Their stability has been preliminarily studied via day-to-day dynamics. There exists a parameter range, in which there is on solution.
Abstract When traffic control is demand-responsive, a bottleneck can have a queue-length-dependent capacity. Motivated by this fact, we studied the morning commute problem in which the bottleneck capacity increases from s 1 to s 2 as the queue length exceeds a threshold D 1 and decreases back to s1 as the queue length reduces and becomes smaller than another threshold D 2 (D 2 ≤ D 1). It has been found that multiple equilibria exist when D 2 < D 1. Their stability has been preliminarily studied via the day-to-day dynamics, and we found it is likely that only the equilibrium state with the lowest cost is stable against large disturbances. In the case where D 2 = D 1, there is no multiple user equilibrium state, and the capacity does not change more than twice. Moreover, there exists a parameter range in which there is no solution unless the bottleneck capacity can switch back and forth instantaneously. The policy of opening the shoulder lane on a 2-lane highway is discussed as an application example.
Morning commute problem with queue-length-dependent bottleneck capacity
Transportation Research Part B: Methodological ; 121 ; 184-215
2019-01-26
32 pages
Article (Journal)
Electronic Resource
English
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