Workload and waiting time in a fixed-time loop system

Abstract

Loop systems arise in many computer, communication, production, and similar stochastic systems. This work focuses on a loop system with Poisson traffic, arbitrary service times, and a non-Markovian fixed-time discipline. Extensive results for this protocol are presented. A workload analysis is performed to quantify queueing times, waiting times, preemption probabilities, and other important measures. A set of lower bounds for the steady-state mean workload is displayed, and from the set of bounds, it is shown that the mean workload obtained from a diffusion approximation is itself a lower bound. Necessary and sufficient conditions for this lower bound to become exact are given, and the maximum error incurred by using the diffusion approximation is also identified. Quantitative relationships between system sojourn time and system workload are established, and it has been found that with exponential service, this relationship depends only on the utilization, even with preemptive service. All results are evaluated by comparing them to simulations and related findings documented in related literature.