Processor sharing

Processor sharing or egalitarian processor sharing is a service policy where the customers, clients or jobs are all served simultaneously, each receiving an equal fraction of the service capacity available. In such a system all jobs start service immediately (there is no queueing).

The processor sharing algorithm "emerged as an idealisation of round-robin scheduling algorithms in time-shared computer systems."^[1]^[2]

Queueing theory

A single server queue operating subject to Poisson arrivals (such as an M/M/1 queue or M/G/1 queue) with a processor sharing discipline has a geometric stationary distribution.^[1]

The sojourn time jobs experience has no closed form solution, even in an M/M/1 queue.^[3]

Generalized processor sharing

Main article: generalized processor sharing

Generalized processor sharing is a multi-class adaptation of the policy which shares service capacity according to positive weight factors to all non-empty job classes at the node, irrespective of the number of jobs of each class present. Often it is assumed that the jobs within a class form a queue and that queue is served on a first-come, first-served basis, but this assumption is not necessary for many GPS applications.^[1]

In processor scheduling, generalized processor sharing is "an idealized scheduling algorithm that achieves perfect fairness. All practical schedulers approximate GPS and use it as a reference to measure fairness."^[4]

==Multilevel processor

In multilevel processor sharing a finite set of thresholds are defined and jobs partitioned according to how much service they have received. The lowest level (containing jobs which have received the least service) has the highest priority and higher levels monotonically decreasing priorities. Within each level an internal discipline is used.^[1]

References

1 2 3 4 Aalto, S.; Ayesta, U.; Borst, S.; Misra, V.; Núñez-Queija, R. (2007). "Beyond processor sharing" (PDF). ACM SIGMETRICS Performance Evaluation Review. 34 (4): 36. doi:10.1145/1243401.1243409.
↑ Kleinrock, L. (1967). "Time-shared Systems: A theoretical treatment" (PDF). Journal of the ACM. 14 (2): 242. doi:10.1145/321386.321388.
↑ Borst, S.; Núñez-Queija, R.; Zwart, B. (2006). "Sojourn time asymptotics in processor-sharing queues" (PDF). Queueing Systems. 53: 31. doi:10.1007/s11134-006-7585-9.
↑ Li, T.; Baumberger, D.; Hahn, S. (2009). "Efficient and scalable multiprocessor fair scheduling using distributed weighted round-robin" (PDF). ACM SIGPLAN Notices. 44 (4): 65. doi:10.1145/1594835.1504188.

Queueing theory

Single queueing nodes	D/M/1 queue M/D/1 queue M/D/c queue M/M/1 queue Burke's theorem M/M/c queue M/M/∞ queue M/G/1 queue Pollaczek–Khinchine formula Matrix analytic method M/G/k queue G/M/1 queue G/G/1 queue Kingman's formula Lindley equation Fork–join queue Bulk queue

Arrival processes	Poisson process Markovian arrival process Rational arrival process

Queueing networks	Jackson network Traffic equations Gordon–Newell theorem Mean value analysis Buzen's algorithm Kelly network G-network BCMP network

Service policies	FIFO LIFO Processor sharing Round-robin Shortest job first Shortest remaining time

Key concepts	Continuous-time Markov chain Kendall's notation Little's law Product-form solution Balance equation Quasireversibility Flow-equivalent server method Arrival theorem Decomposition method Beneš method

Limit theorems	Fluid limit Mean field theory Heavy traffic approximation Reflected Brownian motion

Extensions	Fluid queue Layered queueing network Polling system Adversarial queueing network Loss network Retrial queue

Information systems	Data buffer Erlang (unit) Erlang distribution Flow control (data) Message queue Network congestion Network scheduler Pipeline (software) Quality of service Scheduling (computing) Teletraffic engineering

Category

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