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Transient analysis of a Markovian queue with chain sequence rates and total catastrophes

Author

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  • B. Krishna Kumar
  • A. Vijayakumar
  • S. Sophia

Abstract

Queueing systems with state-dependent arrival and service rates along with catastrophes are investigated. Explicit expressions for the transient probabilities of system size are obtained. The corresponding steady-state probabilities are deduced. Busy period distribution is also found. Some performance measures are obtained for the system. Extensive numerical illustrations are provided. It is observed that the limiting distributions do not exist in the absence of catastrophes.

Suggested Citation

  • B. Krishna Kumar & A. Vijayakumar & S. Sophia, 2009. "Transient analysis of a Markovian queue with chain sequence rates and total catastrophes," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 5(4), pages 375-391.
    • Handle: RePEc:ids:ijores:v:5:y:2009:i:4:p:375-391
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    Cited by:

    1. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.
    2. B. Krishna Kumar & S. Pavai Madheswari & S. Anantha Lakshmi, 2011. "Queuing system with state-dependent controlled batch arrivals and server under maintenance," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 351-379, December.

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