Average Delay Approximation of M/G/1 Cyclic Service Queues with Bernoulli Schedules

Abstract

The Laplace Transform (and the first two moments) of the busy period of the recently introduced <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M/G/1</tex> vacation model with a Bernoulli schedule is completed exactly. This expression makes it possible to estimate the average waiting time of each queue for the Bernoulli schedule cyclic service queue. Consequently, the weighted average of the mean waiting time can be minimized over the class of Bernoulli schedules. The Bernoulli schedule has the advantage over exhaustive schedules (or classical priority schedules) in that the performance of one class of traffic is somewhat insulated from the adverse effects of high utilization in a different class of traffic. The analysis of cyclic service queues can be applied to processor schedules and token ring local area networks as well as components of other data communication systems.