Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 4, Pages 383-405
doi:10.1155/S1048953397000439
Two parallel finite queues with simultaneous services and Markovian arrivals
GMI Engineering & Management Institute, Department of Science and Mathematics, Flint, MI 48504-4898, USA
Received 1 May 1996; Revised 1 January 1997
Copyright © 1997 S. R. Chakravarthy and S. Thiagarajan. 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.
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.