Abstract
In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.
Highlights
Queueing models with server vacation have been efficiently studied by many researchers in the last decades and successfully applied in various practical problems such as telecommunication system design and control, manufacturing industries, and other related systems
We provide the analysis of a multi-server feedback queue with a variant multiple vacation policy, balking and server’s states-dependent reneging
We studied an M /M /c feedback queue under synchronous K-variant vacations, balking, server’s states-dependent reneging and retention of reneged customers
Summary
Queueing models with server vacation have been efficiently studied by many researchers in the last decades and successfully applied in various practical problems such as telecommunication system design and control, manufacturing industries, and other related systems. A growing body of literature has emerged on the analysis of queueing systems with impatient customers [15]. This is due to their potential applications in many related areas, see for instance [16], [17]. Customers seem to get discouraged from receiving service when the server is absent and tend to leave the system without receiving service This phenomenon is very precisely observed when the server is on vacation. We provide the analysis of a multi-server feedback queue with a variant multiple vacation policy, balking and server’s states-dependent reneging.
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