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Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N

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  • M.L. Chaudhry
  • U.C. Gupta

Abstract

Discrete‐time queues with D‐MAP arrival process are more useful in modeling and performance analysis of telecommunication networks based on the ATM environment. This paper analyzes a finite‐buffer discrete‐time queue with general bulk‐service rule, wherein the arrival process is D‐MAP and service times are arbitrarily and independently distributed. The distributions of buffer contents at various epochs (departure, random, and prearrival) have been obtained using imbedded Markov chain and supplementary variable methods. Finally, some performance measures such as loss probability and average delay are discussed. Numerical results are also presented in some cases. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 345–363, 2003.

Suggested Citation

  • M.L. Chaudhry & U.C. Gupta, 2003. "Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(4), pages 345-363, June.
    • Handle: RePEc:wly:navres:v:50:y:2003:i:4:p:345-363
    DOI: 10.1002/nav.10047
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    References listed on IDEAS

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    1. David Heimann & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis IV," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(4), pages 753-766, December.
    2. Marcel F. Neuts & Eugene Klimko, 1973. "The single server queue in discrete time‐numerical analysis III," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(3), pages 557-567, September.
    3. Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis I," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 297-304, June.
    4. Eugene M. Klimko & Marcel F. Neuts, 1973. "The single server queue in discrete time‐numerical analysis II," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 305-319, June.
    5. Attahiru Sule Alfa & Marcel F. Neuts, 1995. "Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process," Transportation Science, INFORMS, vol. 29(2), pages 109-117, May.
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