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ANALYTICALLY EXPLICIT RESULTS FOR THE GI/C-MSP/1/∞ QUEUEING SYSTEM USING ROOTS

Published online by Cambridge University Press:  27 April 2012

M. L. Chaudhry ,
S. K. Samanta  and
A. Pacheco
M. L. Chaudhry
Affiliation:
Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston, Ont., CanadaK7K 7B4 E-mail: chaudhry-ml@rmc.ca
S. K. Samanta
Affiliation:
Department of Mathematics and CEMAT, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal E-mail: sujit.samanta@ist.utl.pt; apacheco@math.ist.utl.pt
A. Pacheco
Affiliation:
Department of Mathematics and CEMAT, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal E-mail: sujit.samanta@ist.utl.pt; apacheco@math.ist.utl.pt
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Abstract

In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at prearrival epochs of the GI/C-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution. We also provide the steady-state system-length distribution at an arbitrary epoch by using the classical argument based on Markov renewal theory. The sojourn-time distribution has also been investigated. The prearrival epoch probabilities have been obtained using the method of roots which is an alternative approach to the matrix-geometric method and the spectral method. Numerical aspects have been tested for a variety of arrival- and service-time distributions and a sample of numerical outputs is presented. The proposed method not only gives an alternative solution to the existing methods, but it is also analytically simple, easy to implement, and computationally efficient. It is hoped that the results obtained will prove beneficial to both theoreticians and practitioners.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 2 , April 2012 , pp. 221 - 244
Copyright
Copyright © Cambridge University Press 2012

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