Inducing Optimal Service Capacities via Performance-Based Allocation of Demand in a Queueing System with Multiple Servers

Abstract—In this paper, we study the use of performance-based allocation of demand in a multiple-server queueing system. The same problem with two servers have been studied in the literature. Specifically, it has been proposed and proved that the linear allocation and mixed threshold allocation policies are, respectively, the optimal state-independent and state-dependent allocation policy in the two-server case. The multiple-server linear allocation has also been shown to be the optimal state-independent policy with multiple servers. In our study, we focus on the use of a multiple-server mixed threshold allocation policy to replicate the demand allocation of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. Our results indicate that, for any given multiple-server state-independent policy that prohibits server overloading, there exists a multiple-server mixed threshold policy that gives the same demand allocation and thus have the same Nash equilibrium (if any). Moreover, such a policy can be designed so that the expected sojourn time at a symmetric equilibrium is minimized. Therefore, our results concur with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers. Index Terms—queueing system, threshold allocation, game theory I