Technical Report CS0083

Title: A Generating-function Analysis of Multiprogramming Queues
Authors: Micha Hofri
Abstract: A simple system which consists of an input-output facility and a central processor is modeled as a two-parameter Markov chain. The conditions for stability are demonstrated and the steady-state joint probabilities are calculated explicitly. Various priority and capacity assignments result iradically different analytical situations, some of which have been considered in the literature. The present work treats a version that was considered for a time intractable. The emphasis of the work is on the analytical properties of the probability generating functions and a method to solve a resultant functional equation. The numerical results display the importance of dependence between variables in the model.

Key words: Queues, Queues in a loop, Networks, Multiprogramming, Two-Server queueing systems, probability generating functions, Steady state behavior, Too-dimensional random walk.

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