Abstract: we present a reminder of the stochastic processes linked to the theory of queuing and the simple structure of the queue then some Markovian systems in continuous time and in discrete time. finally, we consider a discrete-time Queueing systems with retrials and working vacations and vacation interruption.
Assume requests in the orbit try to get service from the server with a constant retrial rate.
During the working vacation period, customers can be served at a lower rate. If there are customers in the system after a service completion instant, the vacation will be interrupted and the server comes back to the normal working level.
We use a quasi birth and death process to describe the considered system and derive a
condition for the stability of the model. Using the matrix-analytic method, we present the stationary probability distribution and some performance measures. Furthermore,
we prove the conditional stochastic decomposition for the queue length in the orbit.
keywords: discrete-time Queueing, retrials, working vacations, vacation interruption, quasi birth and death process, stability condition, matrix-analytic method, performance measures, stochastic decomposition.
- Enseignant: Lahcene Yahiaoui