Slowdown in the M/M/1 discriminatory processor-sharing queue

We consider a queue with multiple K job classes, Poisson arrivals, and exponentially distributed required service times in which a single processor serves according to the discriminatory processor-sharing (DPS) discipline. For this queue, we obtain the first and second moments of the slowdown, which is a measure for queueing fairness. We then provide numerical examples and discuss aspects of the slowdown in the DPS queue.

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

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

[3]  Eitan Altman,et al.  A survey on discriminatory processor sharing , 2006, Queueing Syst. Theory Appl..

[4]  Richard J. Boucherie,et al.  Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues , 2005, Perform. Evaluation.

[5]  T. M. O'Donovan.  Direct Solutions of M/G/1 Processor-Sharing Models , 1974, Oper. Res..

[6]  S. F. Yashkov,et al.  Processor-sharing queues: Some progress in analysis , 1987, Queueing Syst. Theory Appl..

[7]  Adam Wierman,et al.  Classifying scheduling policies with respect to unfairness in an M/GI/1 , 2003, SIGMETRICS '03.

[8]  Benjamin Avi-Itzhak,et al.  SQF: A slowdown queueing fairness measure , 2007, Perform. Evaluation.

[9]  Valerie Isham,et al.  Non‐Negative Matrices and Markov Chains , 1983 .

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

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

[12]  Bara Kim,et al.  Comparison of DPS and PS systems according to DPS weights , 2006, IEEE Communications Letters.

[13]  Richard J. Boucherie,et al.  Insensitive bounds for the moments of the sojourn time distribution in the M/G/1 processor-sharing queue , 2006, Queueing Syst. Theory Appl..

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

[15]  Bara Kim,et al.  Sojourn time distribution in the M/M/1 queue with discriminatory processor-sharing , 2004, Perform. Evaluation.

[16]  R. Núñez-Queija,et al.  Sojourn times in a processor sharing queue with service interruptions , 1999 .

[17]  Adam Wierman,et al.  Asymptotic convergence of scheduling policies with respect to slowdown , 2002, Perform. Evaluation.