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Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process

Author

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  • Yung-Chung Wang
  • Dong-Liang Cai
  • Li-Hsin Chiang
  • Cheng-Wei Hu

Abstract

This paper applies a matrix-analytical approach to analyze the temporal behavior of Markovian-modulated batch-service queue with discrete-time batch Markovian arrival process (DBMAP). The service process is correlated and its structure is presented through discrete-time batch Markovian service process (DBMSP). We examine the temporal behavior of packet loss by means of conditional statistics with respect to congested and noncongested periods that occur in an alternating manner. The congested period corresponds to having more than a certain number of packets in the buffer; noncongested period corresponds to the opposite. All of the four related performance measures are derived, including probability distributions of a congested and noncongested periods, the probability that the system stays in a congested period, the packet loss probability during congested period, and the long term packet loss probability. Queueing systems of this type arise in the domain of wireless communications.

Suggested Citation

  • Yung-Chung Wang & Dong-Liang Cai & Li-Hsin Chiang & Cheng-Wei Hu, 2014. "Elucidating the Short Term Loss Behavior of Markovian-Modulated Batch-Service Queueing Model with Discrete-Time Batch Markovian Arrival Process," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:814810
    DOI: 10.1155/2014/814810
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    Cited by:

    1. Kousik Das & Sujit Kumar Samanta, 2023. "Computational analysis of $$GI^{[X]}/D$$ G I [ X ] / D - $$MSP^{(a,b)}/1$$ M S P ( a , b ) / 1 queueing system via RG-factorization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(1), pages 1-39, August.
    2. Sujit Kumar Samanta & Kousik Das, 2023. "Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-37, March.

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