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Moments of losses during busy-periods of regular and nonpreemptive oscillating \(M^X/G/1/n\) systems

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Abstract

This work addresses loss characteristics associated to busy-periods of regular and nonpreemptive oscillating \(M^X/G/1/n\) systems. By taking advantage of the Markov regenerative structure of the number of customers in the system and resorting to results on moments of compound mixed Poisson distributions, it proposes a fast and easy to implement recursive procedure to compute integer moments of the number of customers lost in busy-periods initiated with multiple customers in the system.

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Acknowledgments

This research was partially supported by Fundação para a Ciência e a Tecnologia (FCT), in particular through projects UID/Multi/04621/2013, PEst-OE/MAT/UI0822/2014, and PEst-OE/MAT/UI4080/2014. The authors are grateful to the anonymous referees, whose suggestions contributed to improve a previous version of the paper.

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Authors and Affiliations

  1. Departamento de Matemática, CM-UTAD and CEMAT, Universidade de Trás-os-Montes e Alto Douro (UTAD), Quinta dos Prados, 5000-801, Vila Real, Portugal

    Fátima Ferreira

  2. CEMAT and Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    António Pacheco

  3. Escola Superior de Tecnologia e Gestão and CEMAT, Instituto Politécnico de Leiria, Campus 2, Morro do Lena - Alto do Vieiro, 2411-901, Leiria, Portugal

    Helena Ribeiro

Authors
  1. Fátima Ferreira
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  2. António Pacheco
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  3. Helena Ribeiro
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Correspondence to Fátima Ferreira.

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Ferreira, F., Pacheco, A. & Ribeiro, H. Moments of losses during busy-periods of regular and nonpreemptive oscillating \(M^X/G/1/n\) systems. Ann Oper Res 252, 191–211 (2017). https://doi.org/10.1007/s10479-015-1901-x

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