Optimal Allocation of Operating Toll Booths at Highway Toll Station

Optimal design and management of highway toll station system is of great benefit in avoiding highways clog, shortening queuing time of car owners and reducing its operational cost. Based on the M/D/1 queuing model, this paper considers the sum of operating cost of a toll booth per unit time and waiting cost of a customer waiting for service per unit time as an objective function, and the optimal economic cost model in single direction of inbound or outbound and that in both directions for the highway toll station are respectively established. Then, the optimal allocation of operating toll booths for both directions of highway toll station is obtained. Finally, numerical examples are given to further illustrate the influences of the parameters related to the arrival rate of the traffic flow on the optimal allocation of operating toll booths at highway toll station.