Sharing a Processor Among Many Job Classes

Abstract

A single-server processor-sharing system with M job classes is analyzed in the steady state. The scheduling strategy considered divides the total processor capacity in unequal fractions among the different job classes. More precisely, if there are N~jobs of classj in the system, j = 1, 2 ..... M, each class k job receives a fraction gh/(~M.~ giN~) of the processor capacity.Earlier analyses of this system are shown to be incorrect and new expressions for the conditional expected response times Wk(t) of class k jobs with required service time t are obtained (for general required service time distributions). These yield the asymptotic behavior of W~(t) as t ~ oo and rather simple formulas in the exponential case. The unconditional average response times are also obtained.

Tail asymptotics for discriminatory processor-sharing queues with heavy-tailed service requirements

“…In a seminal paper, Fayolle, Mitrani & Iasnogorodski [8] obtain the conditional mean sojourn times as the solution of a system of integro-differential equations. For the case of exponentially distributed service requirements, they derive closed-form expressions and also determine the unconditional mean sojourn times from a system of linear equations.…”

Moment-Generating Algorithm for Response Time in Processor Sharing Queueing Systems

“…Some of the earliest significant work on PS queues is by Coffman et al in 1970 [4], which analysed waiting time means and variance of PS systems compared to FCFS. In 1980, Fayolle et al [37] summarised results of Kleinrock and Mitrani for DPS and also obtained average response time (both conditionally and unconditionally on job request sizes) in M/M/1-DPS queueing systems. Further, Laplace transforms provided average waiting time for multiple class types and asymptotic behaviour of service demand was also obtained, but no results on higher response time moments were given.…”

Differentiated bandwidth sharing with disparate flow sizes

“…The DPS discipline was first studied by Kleinrock [21] and O'Donovan [25]. In a seminal paper, Fayolle, Mitrani & Iasnogorodski [14] obtain the conditional mean sojourn times as the solution of a system of integro-differential equations.…”