MAP/PH/1 QUEUE WITH DISCARDING CUSTOMERS HAVING IMPERFECT SERVICE

被引:1
作者
Sindhu, S. [1 ]
Krishnamoorthy, Achyutha [2 ,3 ]
机构
[1] Model Engn Coll, Dept Math, Ernakulam, India
[2] CMS Coll, Ctr Res Math, Kottayam, India
[3] Cent Univ Kerala, Dept Math, Kasargod, India
来源
3C EMPRESA | 2022年 / 11卷 / 02期
关键词
Markovian Arrival Process; Phase-type distribution; Erlang Clock; Imperfect Service; G-NETWORKS; VACATIONS;
D O I
10.17993/3cemp.2022.110250.116-137
中图分类号
F [经济];
学科分类号
02 ;
摘要
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 (beta, 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 theta p 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 k2th 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 (alpha ', T ') of order n1 and beyond stage k1, the service time follows phase type distribution (beta ', S ') of order n2. We compare the values of the revenue function of the two models
引用
收藏
页码:116 / 137
页数:22
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