Capacity allocation in a two-channel service system from a social planner’s perspective

This paper considers a capacity allocation problem in a two-channel service system. Customers can receive service from either a single-server queueing system, which serves the customers waiting in line one by one, or a clearing service system, which serves a fixed number of customers simultaneously according to its capacity. Customers who join the queueing system should wait till they receive service. In contrast, customers who join the clearing system face the risk of service denial when there are more customers than the clearing system’s capacity. The social planner aims to minimize the total expected cost of all customers by determining the capacities and the arrival rates for the two channels. There are two settings: an unobservable setting where only the expected waiting time information is available and an observable setting where real-time information about the exact workload of the queueing system is known. We also consider the same system under the same settings with strategic customers who choose one of the two channels strategically to minimize their costs. The planner still has the same objective but can now decide only on the capacity allocation. Comparing the performance of the resulting systems allows us to understand the value of coordination and information. Extensions of these systems that serve two customer types are also explored.