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GI/G/1/∞ batch arrival queueing system with a single exponential vacation

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Abstract

In the article the queueing system of GI/G/1 type with batch arrival of customers and a single exponentially distributed vacation period at the end of every busy period is considered. Basic characteristics of transient state of the system are investigated: the first busy period, the first vacation period and the number of customers served during the first busy period. New results for the Laplace transform of the joint distribution of these three variables are obtained in dependence on the initial conditions of the system.

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References

  • Borovkov AA (1972) Probabilistic processes in the queueing theory. Nauka, Moscow

    Google Scholar 

  • Bratiychuk MS, Kempa W (2003) Application of the superposition of renewal processes to the study of batch arrival queues. Queueing Syst 44: 51–67

    Article  MATH  MathSciNet  Google Scholar 

  • Bratiychuk MS, Kempa W (2004) Explicit formulae for queue length of batch arrival systems. Stochastic Models 20(4): 457–472

    Article  MATH  MathSciNet  Google Scholar 

  • Choudhury G, Kalita S (2002) Analysis of a batch arrival Poisson queue under single vacation policy. Calcutta Stat Assoc Bull 53(209–210): 81–91

    MATH  MathSciNet  Google Scholar 

  • Gupta UC, Sikdar K (2004) A finite capacity bulk service queue with single vacation and Markovian arrival process. J Appl Math Stochastic Anal 4: 337–357

    Article  MathSciNet  Google Scholar 

  • Kempa W (2004) The virtual waiting time for the batch arrival queueing systems. Stochastic Anal Appl 22(5): 1235–1255

    Article  MATH  MathSciNet  Google Scholar 

  • Loris-Teghem J (1990) On vacation models with bulk arrivals. Belg J Oper Res Stat Comput Sci 30(1): 53–66

    MathSciNet  Google Scholar 

  • Prabhu NU (1980) Stochastic storage processes. Springer, New York

    MATH  Google Scholar 

  • Sikdar K, Gupta UC (2005) Analytic and numerical aspects of batch service queues with single vacation. Comput Oper Res 32(4): 943–966

    Article  MATH  Google Scholar 

  • Takagi H (1983) Queueing analysis, vol 1: Vacation and priority systems, Part 1. North-Holland, Amsterdam

    Google Scholar 

  • Tang Y, Tang X (2000) The queue-length distribution for Mx/G/1 queue with single server vacation. Acta Math Sci (Engl Ed) 20(3): 397–408

    MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

    Wojciech M. Kempa

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  1. Wojciech M. Kempa
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Correspondence to Wojciech M. Kempa.

Additional information

This material is based upon work supported by the Polish Ministry of Scientific Research and Information Technology under Grant No. 3 T11C 014 26.

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Kempa, W.M. GI/G/1/∞ batch arrival queueing system with a single exponential vacation. Math Meth Oper Res 69, 81–97 (2009). https://doi.org/10.1007/s00186-008-0212-2

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  • DOI: https://doi.org/10.1007/s00186-008-0212-2

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