Consecutive customer losses in oscillating GIX/M//n systems with state dependent services rates |
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Authors: | António Pacheco and Helena Ribeiro |
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Affiliation: | (1) Department of Mathematics and CEMAT, Instituto Superior Técnico–Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisbon, Portugal;(2) ESTG, Department of Mathematics and CEMAT, Instituto Politécnico de Leiria, Campus 2, Morro do Lena–Alto do Vieiro, 2411-901 Leiria, Portugal |
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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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Keywords: | Consecutive customer losses GI X /M(m)//n system Oscillating system batch arrivals Busy period |
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