TY - JOUR
T1 - Sojourn time asymptotics in processor sharing queues with varying service rate
AU - Egorova, R.R.
AU - Mandjes, M.R.H.
AU - Zwart, B.
PY - 2007
Y1 - 2007
N2 - 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.
AB - 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.
U2 - 10.1007/s11134-007-9026-9
DO - 10.1007/s11134-007-9026-9
M3 - Article
VL - 56
SP - 169
EP - 181
JO - Queueing Systems: Theory and Applications
JF - Queueing Systems: Theory and Applications
SN - 0257-0130
IS - 3-4
ER -