Sojourn times in vacation and polling systems with Bernoulli feedback

Abstract

We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture of the three service disciplines.