Sojourn time asymptotics in Processor Sharing queues with varying service rate

  • Authors:
  • Regina Egorova;Michel Mandjes;Bert Zwart

  • Affiliations:
  • CWI, Amsterdam, The Netherlands 1090 GB;CWI, Amsterdam, The Netherlands 1090 GB and Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands 1018 TV;Stewart School of Industrial and Systems Engineering, Georgia University of Technology, Atlanta, USA GA 30332

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper addresses the sojourn time asymptotics for a GI/GI/驴 queue operating under the Processor Sharing (PS) discipline with stochastically varying service rate. Our focus is on the logarithmic estimates of the tail of sojourn-time distribution, under the assumption that the job-size distribution has a light tail. Whereas upper bounds on the decay rate can be derived under fairly general conditions, the establishment of the corresponding lower bounds requires that the service process satisfies a sample-path large-deviation principle. We show that the class of allowed service processes includes the case where the service rate is modulated by a Markov process. Finally, we extend our results to a similar system operation under the Discriminatory Processor Sharing (DPS) discipline. Our analysis relies predominantly on large-deviations techniques.