In this paper, we discuss the discrete-time Geom/G/1 queue with multiple adaptive vacations and server setup/closedown times. We consider two types of closedown time policies which differ from each other in the completion instant of the closedown times and contrast the effects of them on the queueing system. We derive the probability generating functions (PGFs) and stochastic decomposition resu...

This paper introduces a generalization of the classical parallel-server fork-join queueing system in which arriving customers fork into multiple tasks, every task is uniquely assigned to one of the set of single-server queues, and each task consists of multiple iterations of different stages of execution, including task vacations and communication among sibling tasks. Several classes of dynamic...

This paper compares the equilibrium threshold strategies of customers with different decision criteria in an observable queue with multiple vacations. Customers are not informed of the service time distribution and the state of the server, whereas they are told that the expected service time is an alternative of two values or the variable service time belongs to an interval. We find that both t...

In this paper, we present a discrete-time single-server finite-buffer queue in which the server takes single/multiple vacations whenever the system becomes empty. The interarrival times are geometrically distributed and service, vacation times are independently identically distributed random variables and their durations are integral multiples of a slot duration. We obtain the state probabiliti...

1 Q I − − ) ( y , where the j th entry of the row vector y is the probability that the system state seen by the first arrival during a busy period is j and 1 Q I − − ) ( is the fundamental matrix associated with the standard GI/M/1 queue. In this paper, we present the entries of 1 Q I − − ) ( explicitly. Also, we illustrate how to find y by examples such as the N -policy GI/M/1 queue with or wi...

This paper considers a discrete-time Geo/G/1 queue with multiple adaptive vacations and variable input rate. The main purpose of this paper is to present a queuelength analysis of this system. Using a new analytic method, the late arrival system with delayed access (LAS-DA) and the early arrival system (EAS), have been examined. For both the cases, We derive the recursive solution for queue len...

We use the Method of Collective Marks to analyze some time-dependent processes in the M/G/1 queue with single and multiple vacations. With the server state specified at a fixed time t > 0, the Laplace transforms with respect to t of mixed transforms for the joint distribution of the number of departures by time t, the queue length, the virtual waiting time, the elapsed and remaining service/vac...

Abstract—This study considers the M/M/1/N queue with working breakdowns and server vacations. We assume that the arrivals occur according to a Poisson process. The server is subject to breakdowns and repairs while in operation. At failure times, the server still works at a lower service rate rather than completely stopping service. When there are no customers in the system, the server takes mul...