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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1997 / Article

Open Access

Volume 10 |Article ID 394369 | https://doi.org/10.1155/S1048953397000439

S. R. Chakravarthy, S. Thiagarajan, "Two parallel finite queues with simultaneous services and Markovian arrivals", International Journal of Stochastic Analysis, vol. 10, Article ID 394369, 23 pages, 1997. https://doi.org/10.1155/S1048953397000439

Two parallel finite queues with simultaneous services and Markovian arrivals

S. R. Chakravarthy1 and S. Thiagarajan1

1GMI Engineering & Management Institute, Department of Science and Mathematics, Flint, MI 48504-4898, USA

Received01 May 1996
Revised01 Jan 1997

Abstract

In this paper, we consider a finite capacity single server queueing model with two buffers, A and B, of sizes K and N respectively. Messages arrive one at a time according to a Markovian arrival process. Messages that arrive at buffer A are of a different type from the messages that arrive at buffer B. Messages are processed according to the following rules: 1. When buffer A(B) has a message and buffer B(A) is empty, then one message from A(B) is processed by the server. 2. When both buffers, A and B, have messages, then two messages, one from A and one from B, are processed simultaneously by the server. The service times are assumed to be exponentially distributed with parameters that may depend on the type of service. This queueing model is studied as a Markov process with a large state space and efficient algorithmic procedures for computing various system performance measures are given. Some numerical examples are discussed.

Copyright © 1997 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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