Analysis of infinite servers polling systems with correlated input process and state dependent vacations

Abstract

This paper is concerned mainly with the stochastic modeling and performance evaluation of a generic infinite servers polling system. We assume that the infinite number of servers are coupled together and that they visit the queues as one processing unit. That is, we are considering a system where all the servers go on vacation and arrive at any queue simultaneously as a synchronized unit. The order in which the servers visit the queues is cyclic; that is, the server makes a tour of the queues during each cycle. However, we allow the possibility that the order of visit from one cycle to the next could be different. We present a simple approach for analyzing the infinite coupled servers polling system with correlated input process and state dependent vacations. Furthermore, our approach allows us to perform both transient and steady-state analyses. The approach also allows us to analyze several service disciplines. These service disciplines include the well known globally gated service discipline. In order to compute several performance measures of the system our analysis requires the solution of a system of linear equations. These performance measures include the mean and second moment of the cycle time, and the expected delay observed by a customer.