Polling systems have been used to model a large variety of applications and much research has been devoted to the derivation of efficient algorithms for computing the delay measures in these systems. Recent research efforts in this area, which have focused on the optimization of these systems, have raised the need for very efficient such algorithms.This work develops the descendant set approach as a general efficient algorithm for deriving all moments of customer delay (in particular, mean delay) in these systems. The method is applied to a very large variety of model variations, including:1) The exhaustive and gated service policies, 2) Fractional service policies, 3) The cyclic visit order, 4) Arbitrary periodic visit orders (polling tables), and 5) Customer routing. For mast of these variations the method significantly outperforms the algorithms commonly used today.
Abstract-Modeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in today's computer communications demand our intensive effort to enhance the modeling capability. The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems. First we review basic properties of exponential queueing systems, and then give an overview of recent progress made in the areas of queueing network models and discrete-time queueing systems. A unified treatment of buffer storage overflow problems will be discussed as an application example, in which-we call attention to the analogy between buffer behavior and waiting time in the GI/G/l queue. Another application deals with the analysis of various multiplexing techniques and network configuration. An extensive reference list of the subject fields is also provided.
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