Analysis of random polling system with an infinite number of coupled servers and correlated input process

We introduce a simple approach for modeling and analyzing a random polling system with infinite servers. We assume that the infinite number of servers is coupled together and they visit the queues as one processing unit. It is assumed that the customer arrival processes at all queues are correlated. Two classes of service disciplines, exhaustive and gated, are considered. We will derive several performance measures of the system. These performance measures include the mean cycle time and the expected delay observed by a customer. For the special case of M/D/∞ vacation queue, we also provide a new proof of a known result. The numerical results indicate that when the expected number of busy servers is high gated service produces mean waiting times less than those given by exhaustive service discipline. This result differs significantly from the known result for single server polling system and it is due to the assumption of coupled servers.