We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Sojourn time asymptotics in Processor Sharing queues with varying service rate.
- Authors
Regina Egorova; Bert Zwart
- Abstract
  This paper addresses the sojourn time asymptotics for a GI/GI/⋅ 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.
- Subjects
LOCAL times (Stochastic processes); STOCHASTIC processes; MARKOV processes; PROBABILITY theory; ASYMPTOTIC distribution; NUMERICAL analysis; LOGARITHMIC functions; MATHEMATICAL statistics; ESTIMATION theory; DEVIATION (Statistics); ERROR analysis in mathematics
- Publication
Queueing Systems, 2007, Vol 56, Issue 3/4, p169
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-007-9026-9