Computing system-time and system-length distributions for MAP/D/1 queue using distributional Little's law

Authors:
Gagandeep Singh;M. L. Chaudhry;U. C. Gupta
Affiliations:
Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India;Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston Ont., Canada K7K 7B4;Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India
Venue:
Performance Evaluation
Year:
2012

Citing 7
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Abstract

In this paper, we first present (in terms of roots) a simple closed-form analysis for evaluating virtual queueing-time and actual system-time distributions for the MAP/D/1 queue. Then we obtain the system-length distribution, using the distributional Little's law. The analysis proposed here is based on the roots of the characteristic equation of the Laplace-Stieltjes transform of the virtual queueing-time distribution. Numerical aspects have been tested for a variety of arrival and service-time parameters and a sample of numerical outputs along with detailed discussion on accuracy and computation-time is presented.