A Closed Form Solution for the Asymmetric Random Polling System with Correlated Levy Input Process

Abstract

We introduce a simple approach for modeling and analyzing the random polling system with asymmetric arrival rates, service times, and switchover times. It is assumed that the customer arrival processes at all queues are correlated Levy input processes. Two classes of service disciplines, random gated and 1-limited, are considered. The random gated service discipline generalizes several known service disciplines. We obtain explicit expressions for several performance measures of the system. These performance measures include the mean and second moment of the cycle time, the queue length at the beginning of a cycle of service and the expected delay observed by a customer. For the special case of independent Poisson input processes at all queues, we also provide new proof of several well-known pseudo-conservation laws.

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