Strategic Behavior of Customers and Optimal Control for Batch Service Polling Systems with Priorities

During the past few years, batch service systems have attracted considerable attention due to their wide area of applications. In this present paper, we study a special batch service polling system (the so-called Israeli queue) with priorities. Different from the previous papers which focus on the performance analysis, we aim to investigate the strategic behavior of customers and optimal design for the underlying queueing model. By considering two levels of information (observable and unobservable) provided upon customers' arrival, we, respectively, derive the equilibrium strategies of high-priority and low-priority customers, regarding the joining or balking dilemma. We also present some numerical examples to reveal the impacts of several parameters on the equilibrium strategies, together with some intuitive explanations. Finally, we formulate the revenue function of the service provider and present the Particle Swarm Optimization algorithm to seek the optimal service prices for the high-priority and low-priority customers to maximize the service provider's revenue under the two levels of information.