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Busy period distribution of a batch arrival retrial queue

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This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.

Abstract

This paper is concerned with the analysis of the busy period distribution in a batch arrival $M^X/G/1$ retrial queue. The expression for the Laplace-Stieltjes transform of the length of the busy period is well known, but from this expression we cannot compute the moments of the length of the busy period by direct differentiation. This paper provides a direct method of calculation for the first and second moments of the length of the busy period.

참고문헌 (12)

  1. J. R. Artalejo, "A classified bibliography of research on retrial queues: Progress in 1990–1999", Top, 7(2), pp.187~211 (1999)
  2. J. R. Artalejo, "Accessible bibliography on retrial queues", Math. Comput. Modelling, 30, pp.1~6 (1999)
  3. J. R. Artalejo, "Accessible bibliography on retrial queues: Progress in 2000–2009", Math. Com-put. Modelling, 51(9-10), pp.1071~1081 (2010)
  4. J. R. Artalejo, "Retrial Queueing Systems" (2008), Springer
  5. J. R. Artalejo, "On the busy period of the M", G, Naval Res. Logist, pp.2000, 47(2)[DOI]
  6. G. I. Falin, "A single-line system with secondary orders", Engrg. Cybernetics Review, 17, pp.76~83 (1979)
  7. G. I. Falin, "Functioning under nonsteady conditions of a single-channel system with group arrival of requests and repeated calls", Ukrainian Math. J, 33, pp.429~432 (1981)
  8. G. I. Falin, "A survey of retrial queues", Queueing Syst, 7(2), pp.127~168 (1990)
  9. G. I. Falin, "Retrial Queues" (1997), Chapman & Hall
  10. J. Kim, "A survey of retrial queueing systems", Ann. Oper. Res, 247(1), pp.1~36 (2016)
  11. V. G. Kulkarni, "Frontiers in Queueing:Models and Applications in Science and Engineering", pp.19~34 (1997), CRC Press
  12. T. Yang, "A survey on retrial queues", Queueing Systems, 2, pp.201~233 (1987)

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