The Analysis of Random Polling Systems

In this paper, we analyze the behavior of random polling systems. The polling systems we consider consist of N stations, each equipped with an infinite buffer and a single server who serves them in some order. In contrast to previously studied polling systems, where the order of service used by the server is periodic (and usually cyclic), in the systems we consider the next station to be served after station i is determined by probabilistic means. More specifically, according to the model we consider in this paper, after serving station i, the server will poll (i.e., serve) station j (j = 1, 2, …, N) with probability pj. The main results of this paper are expressions for the expected response time in a random polling system operated under a variety of service disciplines. The results are compared to the response time in the equivalent cyclic polling systems. Also in this paper, we analyze the cycle time and the number of customers found in the system.