Deterministic state-based information disclosure policies and social welfare maximization in strategic queueing systems

Abstract

Understanding the impact of the queue length information on the behavior of customers is nowadays a hot topic for strategic queueing problems. Particularly, it is important to understand how this information impacts the equilibrium behavior and therefore global performance metrics in order to give some recommendations to service providers for optimizing their objective. Recent works are focused on information policies in order to optimize the provider’s profit. In this work, the aim is to maximize the expected social welfare. It is intuitive that the expected social welfare is higher when more information is available to new customers. In some circumstances, and particularly when the queue is overloaded, providing the information up to a particular level of occupancy yields a better expected social welfare compared to always providing queue length information to new customers. This counterintuitive result comes mainly from the strategic behavior of customers at equilibrium when queue length information is not available. After proving that there exists such an optimal information disclosure policy (IDP) for arbitrary arrival and service rates, we go further and study the expected social welfare for the overloaded context in which the arrival rate equals the service rate. Finally, numerical illustrations corroborate our contributions, and moreover, they show that an admission control policy can be also proposed, combined with an IDP, in order to optimize the expected social welfare of the system.