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

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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.

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Authors and Affiliations

  1. Department of Mathematics and CEMAT, Instituto Superior Técnico–Technical University of Lisbon, Av. Rovisco Pais, 1049-001, Lisbon, Portugal

    António Pacheco

  2. ESTG, Department of Mathematics and CEMAT, Instituto Politécnico de Leiria, Campus 2, Morro do Lena–Alto do Vieiro, 2411-901, Leiria, Portugal

    Helena Ribeiro

Authors
  1. António Pacheco
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  2. Helena Ribeiro
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Correspondence to António Pacheco.

Additional information

This research was supported in part by Programa de Formação Avançada de Docentes do Ensino Superior Medida 5/Acção 5.3 (PRODEP III) and the Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) of the Fundação para a Ciência e a Tecnologia (FCT), cofinanced by the European Community fund FEDER, and the projects POSC/EIA/60061/2004, Euro-NGI, and Euro-FGI.

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Pacheco, A., Ribeiro, H. Consecutive customer losses in oscillating GI X/M//n systems with state dependent services rates. Ann Oper Res 162, 143–158 (2008). https://doi.org/10.1007/s10479-008-0313-6

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  • DOI: https://doi.org/10.1007/s10479-008-0313-6

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