Exact and approximate analysis of sojourn times in finite discriminatory processor sharing queues

Exact analysis of discriminatory processor sharing (DPS) systems has proven to be extremely hard. We describe how the sojourn time distribution can be obtained in closed-form for exponential service requirement distributions when there is admission control. The computational complexity suffers from the usual state-space explosion when the number of customer classes becomes large, or if the admission control allows for many concurrent customers. Through numerical experiments, we show that a time-scale decomposition approach provides an approximation that requires much less computational effort, while giving accurate results even when the classes do not have different time scales and are distinguished through the relative service shares only.

[1]  Alexandre Proutière,et al.  Modeling integration of streaming and data traffic , 2004, Perform. Evaluation.

[2]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[3]  R. Núñez Queija,et al.  Discriminatory processor sharing revisited , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[4]  Sem C. Borst,et al.  Differentiated bandwidth sharing with disparate flow sizes , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[5]  Sem C. Borst,et al.  Asymptotic regimes and approximations for discriminatory processor sharing , 2004, PERV.

[6]  R. Núñez Queija,et al.  Processor-Sharing Models for Integrated-Services Networks , 2000 .

[7]  Shoichi Noguchi,et al.  An Analysis of the M/G/1 Queue Under Round-Robin Scheduling , 1971, Oper. Res..

[8]  Jaroslav Kožešnk,et al.  Information Theory, Statistical Decision Functions, Random Processes , 1962 .

[9]  Kiran M. Rege,et al.  Queue-Length Distribution for the Discriminatory Processor-Sharing Queue , 1996, Oper. Res..

[10]  J. W. Cohen,et al.  The multiple phase service network with generalized processor sharing , 1979, Acta Informatica.

[11]  Eitan Altman,et al.  DPS queues with stationary ergodic service times and the performance of TCP in overload , 2004, IEEE INFOCOM 2004.

[12]  Hans van den Berg,et al.  TheM/G/1 queue with processor sharing and its relation to a feedback queue , 1991, Queueing Syst. Theory Appl..

[13]  Isi Mitrani,et al.  Sharing a Processor Among Many Job Classes , 1980, JACM.

[14]  Duan-Shin Lee.  Generalized longest queue first: an adaptive scheduling discipline for ATM networks , 1997, Proceedings of INFOCOM '97.

[15]  Sem C. Borst,et al.  The impact of the service discipline on delay asymptotics , 2003, Perform. Evaluation.

[16]  Laurent Massoulié,et al.  Bandwidth sharing: objectives and algorithms , 2002, TNET.

[17]  Sem C. Borst,et al.  Tail asymptotics for discriminatory processor-sharing queues with heavy-tailed service requirements , 2005, Perform. Evaluation.

[18]  Alexandre Proutière,et al.  On Stochastic Bounds for Monotonic Processor Sharing Networks , 2004, Queueing Syst. Theory Appl..

[19]  Kiran M. Rege,et al.  A decomposition theorem and related results for the discriminatory processor sharing queue , 1994, Queueing Syst. Theory Appl..

[20]  Sara Oueslati,et al.  Integrated Admission Control for Streaming and Elastic Traffic , 2001, QofIS.

[21]  Leonard Kleinrock,et al.  Time-shared Systems: a theoretical treatment , 1967, JACM.

[22]  Laurent Massoulié,et al.  Arguments in favour of admission control for TCP flows , 1999 .

[23]  N. Hegde,et al.  Sojourn times in finite-capacity processor-sharing queues , 2005, Next Generation Internet Networks, 2005.

[24]  Walter L. Smith,et al.  Proceedings of the Symposium on Congestion Theory , 1967 .