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Extension of the loss probability formula to an overloaded queue with impatient customers

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  • Kim, Bara
  • Kim, Jeongsim

Abstract

We consider a batch arrival MX∕G∕1 queue with impatient customers. The loss probability is expressed in terms of the stationary waiting time distribution for the standard MX∕G∕1 queue with no impatience. But this expression is only applicable when the offered load ρ is less than 1. We give a formula for the loss probability applicable for any values of ρ>0, by proving that the loss probability is analytic in ρ on (0,∞) through a Girsanov-type change of measure.

Suggested Citation

  • Kim, Bara & Kim, Jeongsim, 2018. "Extension of the loss probability formula to an overloaded queue with impatient customers," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 54-62.
    • Handle: RePEc:eee:stapro:v:134:y:2018:i:c:p:54-62
    DOI: 10.1016/j.spl.2017.10.007
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    References listed on IDEAS

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    1. Nam Kyoo Boots & Henk Tijms, 1999. "A Multiserver Queueing System with Impatient Customers," Management Science, INFORMS, vol. 45(3), pages 444-448, March.
    2. Stephen C. Graves, 1982. "The Application of Queueing Theory to Continuous Perishable Inventory Systems," Management Science, INFORMS, vol. 28(4), pages 400-406, April.
    3. Nam Boots & Henk Tijms, 1999. "AnM/M/c queue with impatient customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 213-220, December.
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