A discrete time-limited vacation model for the fair share scheduler

We present a vacation model which can be used as a component of the type of polling system encountered in a fair share scheduler. Consider two queues in tandem attended by one server. The primary queue Q(p), which has an infi nite buffer, has a preemptive priority over the secondary queue Q(s) which has a finite buffer. Jobs which complete service at the primary queue will go into the secondary queue for another service with a probability p. The s erver visits Q(s) for a maximum of T units of time. After visiting for T un its of time or after Q(s) becomes empty, whichever occurs first, the server goes on a vacation. The duration of this vacation has a phase type distrib ution. The vacation can also be interrupted in order to attend to the jobs in Q(p). The resulting Markov chain describing this system is of the QBD ty pe. We show that the resulting R matrix associated with this Markov chain h as a very special structure which reduces to the solution of a smaller dime nsion matrix. We then show how to obtain the key performance measures for t his system. Of interest is the approach used for obtaining the waiting time distribution. Some numerical examples are also presented.