Multiqueue Systems with Nonexhaustive Cyclic Service

Abstract

Queuing models with cyclic-type service are applicable for performance studies of polling mechanisms in data communication and switching systems or cyclic scheduling algorithms in real time computers. This paper provides an approximate analysis of the multiqueue system M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[x]</sup> /G/1 with batch Poisson input, general service times, general overhead (switchover) times, and a single server operating under a cyclic strategy with nonexhaustive service of queues. Based on a new concept of conditional cycle times, the generating function of the stationary probabilities of state, the Laplace-Stieltjes transforms of the delay distributions, and the mean waiting times are derived explicitly for each queue through an imbedded Markov chain approach and an independence assumption. The approximate analytic results are validated by computer simulations. Besides this analysis, a stability criterion is derived for the general case of GI/G/1 systems with cyclic priority service. The paper concludes with a number of studies of the behavior of cyclic queues discovering interesting properties such as the dependence of cycle times and waiting times on the arrival and service process types and on the efficiency of cyclic priorities.