Two-level processor-sharing scheduling disciplines

Abstract

Inspired by several recent papers that focus on scheduling disciplines for network flows, we present a mean delay analysis of Multilevel Processor Sharing (MLPS) scheduling disciplines in the context of M/G/1 queues. Such disciplines have been proposed to model the effect of the differentiation between short and long TCP flows in the Internet. Under MLPS, jobs are classified into classes depending on their attained service. We consider scheduling disciplines where jobs within the same class are served either with Processor Sharing (PS) or Foreground Background (FB) policy, and the class that contains jobs with the smallest attained service is served first. It is known that the FB policy minimizes (maximizes) the mean delay when the hazard rate of the job size distribution is decreasing (increasing). Our analysis, based on pathwise and meanwise arguments of the unfinished truncated work, shows that Two-Level Processor Sharing (TLPS) disciplines, e.g., FB+PS and PS+PS, are better than PS scheduling when the hazard rate of the job size distribution is decreasing. If the hazard rate is increasing and bounded, we show that PS outperforms PS+PS and FB+PS. We further extend our analysis to study local optimality within a level of an MLPS scheduling discipline.

Stability of size-based scheduling disciplines in resource-sharing networks

“…While this implies that the LAS discipline improves the performance for a rich class of highly variable service requirement distributions, there is no guarantee that it will do better than FCFS or PS in general, and in fact it performs worse for distributions with increasing failure rates. A discrete-class version of LAS that has recently attracted renewed attention is the Multi-Level Processor Sharing (MLPS) discipline [1,2,5,15,22]. The performance gains from size-based scheduling disciplines have been thoroughly analyzed in the literature for single-server systems.…”

On the performance of multi-level time sharing policy under heavy-tailed workloads

“…(N -----+ (0) [2,3]. There exist only a few prior works that investigate the performance of a multi-level time sharing under non-exponential service time distributions for the case of positive quanta and finite number of levels, see for example [19].…”

“…As a result many recent works are based on the assumptions that the quanta are infinitely small and the number of levels are infinite (Multi-level processor sharing). A few recent studies on multi-level processor sharing policies include [1,2,3]. In [1], authors prove that multi-level scheduling disciplines are better than the processor sharing discipline with respect to the mean delay provided that the failure rate of the service time distribution is decreasing.…”

“…In [1], authors prove that multi-level scheduling disciplines are better than the processor sharing discipline with respect to the mean delay provided that the failure rate of the service time distribution is decreasing. In [3], it has been shown that the two-level processor sharing disciplines are better than processor sharing scheduling when the hazard rate of the job size distribution is decreasing. A few existing work that assumes positive quanta and finite levels, are not applicable for heavytailed distributions [8].…”

“…Though the Poisson arrival pattern (this implies exponentially distributed inter-arrival times) can be justified for many computer workloads [7], extensive research carried out in the last few years clearly indicates that the service times of many computer workloads do not follow exponential distributions, rather they follow heavy-tail distributions [4,5,6]. A few recent works that looks at the performance of time sharing (multi-level and single level) policies under non-exponential service time distributions, assume infinitely small quanta or infinite levels [1,2,3]. Neither infinitely small quanta nor infinite levels can be implemented on real computer systems.…”