Analysis of Generalized Processor Sharing Systems Using Matrix Analytic Methods

摘要

Generalized Processor Sharingrn(GPS) is an important scheduling discipline be-rncause it enables bandwidth sharing with workrnconservation and traffic isolation properties.rnAlthough Markov Modulated Fluid Processesrn(MMFP) captures the fne dynamics of thernsources and is expected to give tight performancernbounds, the analysis of MMFP sources with arnGPS server is usually di?cult because of thernlarge state space and the coupled services of thernclasses. Matrix analytic methods [8], which yieldrngreat numerical accuracy and stability, are eu000bec-rntive alternatives to the spectral analysis approachrn(e.g. [12]). In this paper, we apply Matrix An-rnalytic methods for ruid rows as introduced byrnRamaswami [11] to the analysis of GPS systemsrnfed by MMFP sources. We propose a new tech-rnnique to calculate the tail distributions of thernclasses where matrices processed are of smallerrnsizes, which greatly reduces the computation com-rnplexity. Numerical results illustrate the e?ciencyrnand accuracy of the technique. We also investi-rngate the Caudal Characteristics of GPS queuesrnwhich further illustrate the eu000bectiveness of thernGPS scheduling discipline.