This paper investigates a discrete-time impatient customer queue with Bernoullischedule vacation interruption. The vacation times and the service times during regular busy period and during working vacation period are assumed to follow geometric distribution. We obtain the steady-state probabilities at arbitrary and outside observer’s observation epochs using recursive technique. Cost analysis ...

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...

In this paper, we analyze a single-server vacation queue with a general arrival process. Two policies, working vacation and vacation interruption, are connected to model some practical problems. The GI/M/1 queue with such two policies is described and by the matrix analysis method, we obtain various performance measures such as mean queue length and waiting time. Finally, using some numerical e...

The goal of this paper is to establish a general approach for analyzing queueing models with repeated inhomogeneous vacations. The server goes on for a vacation if the inactivity prolongs more than the vacation trigger duration. Once the system enters in vacation mode, it may continue for several consecutive vacations. At the end of a vacation, the server goes on another vacation, possibly with...

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Stress in the work place has a detrimental effect on people's health. Sufficient recovery is necessary to counteract severe chronic negative load reactions. Previous research has shown that vacationing for at least seven consecutive days provided an efficient recovery strategy. Yet, thus far, the effects of short vacations and the mode of vacation (whether at home or in a new environment) have ...

We study a batch arrival queueing system with service interruption and Extended server vacation based on Bernoulli schedule. A single server provides essential service to all arriving customers with service time following general distribution. After every service completion the server has the option to leave for phase one vacation of random length with probability p or to continue staying in th...