Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy

We study strategic customer behavior in a multiserver stochastic service system with a congestion-based staffing (CBS) policy. With the CBS policy, the number of working servers is dynamically adjusted according to the queue length. Besides lining up for free service, customers have the option of paying a fee and getting faster service. Customers' equilibrium behavior is studied under two information scenarios: In the no information scenario, customers only know the long-term statistics, such as the expected waiting time; in the partial information scenario, customers observe the number of working servers and understand the staffing policy upon their arrival. Unlike a queueing system with a constant staffing level, a positive externality is associated with customers' joining the CBS system. Both avoid-the-crowd and follow-the-crowd customer behaviors are possible, and multiple equilibria could exist. We develop the stationary performance measures of the system by considering the customers' strategic behavior. Numerical analysis shows that information can either hurt or improve the performance of the system, depending on the staffing and pricing policy. Another important conclusion is that the system performance is more robust to setting a relatively high than a relatively low price.