Mean Waiting Time Approximations for Symmetric and Asymmetric Polling Systems with Time-Limited Service

Abstract

Cyclic polling systems are frequently used as models for the performance evaluation of token passing Local Area Networks (LANs) such as Token Ring or Token Bus and High Speed Local Area Networks (HSLANs), e.g., FDDI (Fiber Distributed Data Interface). The model is characterized by Poisson arrival processes, general independent packet service and switchover times and infinite buffer lengths. Frequently, the service disciplines exhaustive service or limited service are considered, because many results for these disciplines are available in the literature [14, 15]. However, they are not always appropriate for modeling the time-limited service disciplines defined in the standards for Token Ring, Token Bus and FDDI.In this paper, we concentrate on these time-limited service disciplines to which little attention has been payed due to the complexity they impose on the mathematical model. Both the synchronous service discipline (fixed maximum service time) and the asynchronous service discipline (cycle time dependent maximum service time) are considered. Our approach is based on the use of the pseudo-conservation law, for which new approximate expressions for the mean unfinished work left behind by the server in a queue will be derived. With these expressions new pseudo-conservation laws for the weighted sum of the mean waiting times are obtained. They are used to determine the mean waiting times in symmetric systems. With additional assumptions relating the mean waiting times to the second moment of the cycle time solutions for asymmetric systems are obtained. Finally, the results of the analysis are validated by comparison to simulation results.