We consider a queueing system with c servers and a threshold type vacation policy. In this system, when a certain number d<c of servers become idle at a service completion instant, these d servers will take a synchronous vacation of random length together. After each vacation, the number of customers in the system is checked. If that number is N or more, these d servers will resume serving the ...

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 Bi(v). After the completion of any of the n services, if the customer is di...

If you are reading this editorial in the week of publication, chances are that you do not work in one of the countries bordering the Mediterranean. If you are in Scandinavia, this is probably your first opportunity even to read my editorial from July. Most of Europe now takes a full four or five weeks of vacation, usually corresponding to the calendar month of July in the north or August in the...

In this paper we present the analysis of the BMAP/GI/1 phase dependent vacation model with decrementing-K service discipline. The exhaustive discipline is a special case of the decrementing-K discipline, where K = ∞. The generalization of the service discipline independent expressions of the vacation model [7] for phase dependent vacation enables the treatment of the BMAP/GI/1 queue as special ...

In this paper we present the analysis of BMAP/G/1 vacation models of non-M/G/1-type in a general framework. We provide new service discipline independent formulas for the vector generating function (GF) of the stationary number of customers and for its mean, both in terms of quantities at the start of vacation. We present new results for vacation models with gated and G-limited disciplines. For...

There are many practical situations that have both features of customer retrials and server vacations. The vacation policy is characterized by the vacation startup rules and vacation termination rules. The queueing system with retrials and vacations has been described in variety of ways according to the vacation rules and retrial policies such as constant retrial policy and linear retrial polic...

Abstract: We study the Nash equilibrium behavior of customers in a discrete-time single-server queue under multiple vacation policy or single vacation policy. Every arriving customer either joins the queue or balks based on his or her service utility. Using a Quasi-Birth-Death Processes (QBD) model, we obtain the stationary distribution of the queue length via the Matrix-Geometric Solution meth...