On M[x]G1G21 queue with optional re-service

Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan
Applied Mathematics and Computation (Impact Factor: 1.55). 04/2004; 152(1):71-88. DOI: 10.1016/S0096-3003(03)00545-9
Source: DBLP


We study a single server queue with batch arrivals and two types of heterogeneous service with different general (arbitrary) service time distributions. The server provides either type of service to customers, one by one, on a first come, first served basis. Just before a service starts, a customer has the option to choose either type of service after completion of which the customer may leave the system or may opt for re-service of the service taken by him. We obtain steady-state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue and the system, the average number of customers and the average waiting time in the queue as well as the system. Some special cases of interest are discussed and some known results have been derived. A numerical illustration is provided.

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Available from: Amjad Al-Nasser, Feb 11, 2015
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    • "Choudhary and Templeton, 1983; in their book provided a comprehensive review on bulk queues and their applications. Madan et al., 2004; included the concept of an optional re-service for M X /G1, G 2 /1 queue. A twostage batch arrival queueing system with modified Bernoulli schedule vacation under N-policy was investigated by Choudhury and Madan, 2005. "
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    ABSTRACT: In this paper we use the maximum entropy principle(MEP) to find the approximate waiting time of an M X /G/1 model with 'k' services; the first being essential (first essential service FES) whereas remaining 'k-1' of them as optional services (multiple optional service MOS). The server is subject to breakdown while rendering service to the customers. The customers arrive in the system in Poisson fashion in batches with arrival rate. After getting FES, the customer may opt for first of MOS, with some probability; after completing it, he may opt for next MOS with some other probability and so on. The service time of FES is generally distributed, while service times of MOS are exponentially distributed. The noble feature of the present study is to employ MEP which helps us in finding precise performance measures. The derived approximate results based on MEP, are compared with exact results obtained in previous studies for different distributions as special cases. It is noticed that MEP provides an alternative approach for solving complex queueing systems, in particular when queue size distribution is to be computed.
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    ABSTRACT: This paper investigates the queueing process of a bulk service queueing system under Bernoulli schedule. It also generalizes some known scenarios concerning the choice of service and re-service types. The queueing process is studied both in discrete time and in continuous time. Performance measures are derived and used to implement an optimal management policy of the system.
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