A two-level mixed service polling model with batch arrival

摘要

We present a single-server and two-level mixed service polling systems with two queue types, one center queue and N normal queue. Customers arrive at the system according to a batch process. The center queue will be successively served with exhaustive discipline after each normal queue being served with parallel 1-limited discipline. In the first level, server visits between the center queue and the normal queue. In the second level, normal queues are polled by a cyclic order. We propose an imbedded Markov chain framework to drive the closed-form expressions for the mean queue length and average waiting time. Numerical examples demonstrate that theoretical and simulation results are identical and the new system efficiently differentiates priorities.