On Two-Level State-Dependent Routing Polling Systems with Mixed Service

Abstract

Based on priority differentiation and efficiency of the system, we consider an + 1 queues' single-server two-level polling system which consists of one key queue and normal queues. The novel contribution of the present paper is that we consider that the server just polls active queues with customers waiting in the queue. Furthermore, key queue is served with exhaustive service and normal queues are served with 1-limited service in a parallel scheduling. For this model, we derive an expression for the probability generating function of the joint queue length distribution at polling epochs. Based on these results, we derive the explicit closedform expressions for the mean waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system is efficient both at key queue and normal queues.