Map/p h/1 queue with discarding customers having imperfect service

• Autores: Sindhu S, Achyutha Krishnamoorthy
• Localización: 3c Empresa: investigación y pensamiento crítico, ISSN-e 2254-3376, Vol. 11, Nº. 2, 2022, págs. 116-137
• Idioma: inglés
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• Resumen

  • In this paper, we consider two queueing models. Model I is on a single-server queueing system in which the arrival process follows MAP with representation D = (D0, D1) of order m and service time follows phase-type distribution (β,S) of order n. When a customer enters into service, a generalized Erlang clock is started simultaneously. The clock has k stages. The pth stage parameter is θp for 1 ≤ p ≤ k. If a customer completes the service in between the realizations of stages k1 and k2 (1 < k1 < k2 < k) of the clock, it is a perfect one. On the other hand, if the service gets completed either before the kth 1 stage realization or after the kth 2 stage realization, it is discarded because of imperfection. We analyse this model using the matrix-geometric method. We obtain the expected service time and expected waiting time of a tagged customer. Additional performance measures are also computed. We construct a revenue function and numerically analyse it. In Model II, a single server queueing system in which all assumptions are the same as in Model I except the assumption on service time, is considered. Up to stage k1 service time follows phase-type distribution (α′ , T′ ) of order n1 and beyond stage k1, the service time follows phase type distribution (β ′ , S′ ) of order n2. We compare the values of the revenue function of the two models