Analysis of Queueing Network Models with population size constraints and delayed blocked customers

Abstract

Queueing Network Models - QNM's with population size constraints and delayed blocked customers occur due to MultiProgramming Level - MPL constraints in computer systems and window flow-control mechanisms in Computer Communication Networks - CCN's. The computational cost of existing algorithms is unacceptable for large numbers of chains and high population sizes. A fast approximate solution technique based on load concealment is presented to solve such QNM's. The solution procedure is non-iterative in the case of fixed rate Poisson arrivals, while iteration is required in the case of quasi-random arrivals. Each iteration requires the solution of a single chain network of queues comprised of stations visited by each chain. We then present an algorithm to detect saturated chains and determine their maximum throughput. A fast solution algorithm due to Reiser for closed chains is also extended to the case of quasi-random arrivals. The accuracy of the proposed solution techniques is compared to previous techniques by applying it to a test case, reported in the literature, and a set of randomly generated examples.