On the Discrete-Time GeoXG1 Queues under N-Policy with Single and Multiple Vacations

الملخص EN

We consider the discrete-time GeoX/G/1 queue under N-policy with single and multiple vacations.

In this queueing system, the server takes multiple vacations and a single vacation whenever the system becomes empty and begins to serve customers only if the queue length is at least a predetermined threshold value N.

Using the well-known property of stochastic decomposition, we derive the stationary queue-length distributions for both vacation models in a simple and unified manner.

In addition, we derive their busy as well as idle-period distributions.

Some classical vacation models are considered as special cases.