ISSN:
1572-9451
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract 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 infinite 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 server visits Q s for a maximum of T units of time. After visiting for T units 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 distribution. 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 type. We show that the resulting R matrix associated with this Markov chain has a very special structure which reduces to the solution of a smaller dimension matrix. We then show how to obtain the key performance measures for this system. Of interest is the approach used for obtaining the waiting time distribution. Some numerical examples are also presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019140005852
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