Idle-Period Approximations and Bounds

Abstract

Consider the GI/G/1 queue with generic inter-arrival time T and service time S, X=S-T. For this queue, the average delay can be written as [Image14.gif] where I is an idle period. Because closed-form expressions for the idle period do not exist, there is a large literature on approximations and bounds for such quantity in order to approximate or bound the average delayd. In this talk, after summarizing the existing results, we will first revisit a heavy-traffic approximation of the idle period that, we believe, deserves more attention. Then, we will prove and disprove a conjectured bound of D. J. Daley.