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Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers

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Abstract

This paper considers a single-server queueing model with finite and infinite buffers in which customers arrive according to a discrete-time renewal process. The customers are served one at a time under discrete-time Markovian service process (D-MSP). This service process is similar to the discrete-time Markovian arrival process (D-MAP), where arrivals are replaced with service completions. Using the imbedded Markov chain technique and the matrix-geometric method, we obtain the system-length distribution at a prearrival epoch. We also provide the steady-state system-length distribution at an arbitrary epoch by using the supplementary variable technique and the classical argument based on renewal-theory. The analysis of actual-waiting-time (in the queue) distribution (measured in slots) has also been investigated. Further, we derive the coefficient of correlation of the lagged interdeparture intervals. Moreover, computational experiences with a variety of numerical results in the form of tables and graphs are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India

    S. K. Samanta & U. C. Gupta

  2. Department of Mathematics and Computer Science, Royal Military College of Canada, STN Forces, P.O. Box 17000, Kingston, ON, K7K 7B4, Canada

    M. L. Chaudhry

Authors
  1. S. K. Samanta
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  2. U. C. Gupta
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  3. M. L. Chaudhry
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Correspondence to U. C. Gupta.

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Samanta, S.K., Gupta, U.C. & Chaudhry, M.L. Analysis of stationary discrete-time GI/D-MSP/1 queue with finite and infinite buffers. 4OR-Q J Oper Res 7, 337–361 (2009). https://doi.org/10.1007/s10288-008-0088-2

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  • DOI: https://doi.org/10.1007/s10288-008-0088-2

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