We consider a system of two service providers each with a separate queue. Customers choose one queue to join upon arrival and can switch between queues in real time before entering service to maximize their spot utility, which is a function of price and queue length. We characterize the steady-state distribution for queue lengths, and then investigate a two-stage game in which the two service providers first simultaneously select service rates and then simultaneously charge prices. Our results indicate that neither service provider will have both a faster service and a lower price than its competitor. When price plays a less significant role in customers service selection relative to queue length or when the two service providers incur comparable costs for building capacities, they will not engage in price competition. When price plays a significant role and the capacity costs at the service providers sufficiently differ, they will adopt substitutable competition instruments: the lower cost service provider will build a faster service and the higher cost service provider will charge a lower price. Comparing our results to those in the existing literature, we find that the service providers invest in lower service rates, engage in less intense price competition, and earn higher profits, while customers wait in line longer when they are unable to infer service rates and are naive in service selection than when they can infer service rates to make sophisticated choices. The customers jockeying behavior further lowers the service providers capacity investment and lengthens the customers duration of stay.
Bibliographical noteThis research is supported in part by Niche Area Project J-BB7B and Project A-SA22 by The Hong Kong Polytechnic University.
- customer behavior
- price and service rate competition
- two-stage game