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Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates

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  • António Pacheco
  • Helena Ribeiro

Abstract

We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI X /M//n systems with state dependent services rates, also denoted as GI X /M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear system of equations. The results derived are illustrated for specific sets of parameters. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.
    • Handle: RePEc:spr:annopr:v:162:y:2008:i:1:p:143-158:10.1007/s10479-008-0313-6
    DOI: 10.1007/s10479-008-0313-6
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    1. J. R. Artalejo & A. Economou, 2005. "Markovian Controllable Queueing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 353-378, September.
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    Cited by:

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    2. Souvik Ghosh & A. D. Banik & Joris Walraevens & Herwig Bruneel, 2022. "A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service," 4OR, Springer, vol. 20(2), pages 241-272, June.
    3. Pawel Mrozowski & Andrzej Chydzinski, 2018. "Queues with Dropping Functions and Autocorrelated Arrivals," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 97-115, March.
    4. M. L. Chaudhry & A. D. Banik & A. Pacheco, 2017. "A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: $$ GI ^{[X]}/C$$ G I [ X ] / C - $$ MSP /1/\infty $$ M S P / 1 / ∞," Annals of Operations Research, Springer, vol. 252(1), pages 135-173, May.

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