The present investigation deals with analysis of non-Markovian queueing model with multistage of services. When the server is unavailable during the system breakdown (or) vacation periods, we consider reneging to prevail. Supplementary variable techniques have been adopted to obtain steady state system length distributions. The numerical illustrations are provided to validate the tractability of performance measures as far as computational aspect is concerned. Numerical results in the form of graphical representation are also presented. Practical large scale industry applications are described to justify our model.
In this paper, a multi phase M/G/1queueing system with Bernoulli feedback where the server takes multiple vacation is considered. All the poisson arrivals with mean arrival rate will demand any of the multi essential services.. The service times of the first essential service are assumed to follow a general distribution B i (v). After the completion of any of the n services, if the customer is dissatisfied he can join the tail of the queue for receiving another regular service with probability p. Otherwise the customer may depart from the system with the probability q=1-p. If there is no customer in the queue, then the server can go for vacation and vacation periods are exponentially distributed with mean vacation time .On returning from vacation , if the server again founds no customer waiting in the queue, then it again goes for vacation. The server continues to go for vacation until he finds at least one customer in the system. We find the time dependent probability generating function in terms of Laplace transforms and derive explicitly the corresponding steady state results.
Mathematics Subjects Classification: 60K25,62K30.
This Paper studies batch arrival queue with two stages of service. Random breakdowns and Bernoulli schedule server vacations have been considered here .After a service completion, the server has the option to leave the system or to continue serving customers by staying in the system. It is assumed that customers arrive to the system in batches of variable size, but served one by one. After completion of first stage of service, the server must provide the second stage of service to the customers. Vacation time follows general distribution, while we consider exponential distribution for repair time.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, average number of customers ,and the average waiting time in the queue.
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