Abstract
This paper deals with the stationary analysis of a fluid queue driven by anM/M/1queueing model subject to Bernoulli-Schedule-Controlled Vacation and Vacation Interruption. The model under consideration can be viewed as a quasi-birth and death process. The governing system of differential difference equations is solved using matrix-geometric method in the Laplacian domain. The resulting solutions are then inverted to obtain an explicit expression for the joint steady state probabilities of the content of the buffer and the state of the background queueing model. Numerical illustrations are added to depict the convergence of the stationary buffer content distribution to one subject to suitable stability conditions.
Highlights
In many real time situations, the server in the background queueing model may become unavailable for a random period of time to perform a secondary task, when there are no customers in the waiting line at the service completion epoch
This paper presents an analytical solution for the fluid queue driven by an M/M/1 queue subject to BernoulliSchedule-Controlled Vacation and Vacation Interruption in stationary regime
Markov Modulated Fluid Flows (MMFF) are a class of fluid models wherein the rates at which the content of the fluid buffer varies are modulated by the Markov process evolving in the background
Summary
In many real time situations, the server in the background queueing model may become unavailable for a random period of time to perform a secondary task, when there are no customers in the waiting line at the service completion epoch. Such period of server absence is termed as server vacation. A better modeling assumption would be to assume that the server works at a slower rate during vacation periods in comparison to that of a regular working period Such models are classified as queues subject to working vacations [4,5,6]. The vacation duration of the server during working vacation epoch may be interrupted due to vacation interruption
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