Processor sharing: A survey of the mathematical theory

S. F. Yashkov · A. S. Yashkova

95 citations0/0 files storedAutomation and Remote Control

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Advanced Queuing Theory Analysis Probability and Risk Models Age of Information Optimization

Abstract

During last few decades the Egalitarian Processor Sharing (EPS) has gained a prominent role in applied probability, especially, in queueing theory and its computer applications. While the EPS paradigm emerged in 1967 as an idealization of round-robin (RR) scheduling algorithm in time-sharing computer systems, it has recently capture renewed interest as a powerful concept for modeling WEB servers. This paper summarizes the most important results concerning the exact solutions for the M/GI/1 queue with egalitarian processor sharing. The material is drawn, mainly, from recent authors’ papers which are supplemented, in small degree, by other related results. Many of the further results are established under the direct influence of our earlier papers. Our main purpose is to give a survey of state-of-the-art with regard to main achievements of the contemporary theory of the M/GI/1 queueing system with processor sharing. The focus is on the methods and techniques of exact and asymptotic analysis of this queueing system. In contrast to the standard surveys, the abridged proofs (or their ideas) of some key theorems and corollaries are included in the paper. We outline recent developments in exact analysis of the M/GI/1-EPS queue with further emphasis on time-dependent (transient) probability distributions of the main characteristics. In particular, the present paper includes the results on the joint time-dependent distribution of the sojourn time of a job arriving at time t with the service demand (length) u, and of the number of jobs at time t- in the M/GI/1 queue with egalitarian processor sharing, which obtained in form of multiple transforms. We also show how the non-stationary solutions can be used to obtain known and new results which allow to predict the behaviour of the EPS queue and to yield additional insights into its new unexpected properties. We also discuss a number of limit theorems arising under the study of the processor sharing queues.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 95 citations exist upstream.

References

1997Modelling Extremal Events 1994Modelling of extremal events in insurance and finance 1977Fundamentals of Queueing Theory.1987Applied Probability and Queues 1990The Asymptotic Theory of Extreme Order Statistics 1989Stochastic Modeling and the Theory of Queues 2003Applied Probability and Queues 1975Theory, Volume 1, Queueing Systems

Cited by

2015Congestion probabilities of elastic and adaptive calls in Erlang-Engset multirate loss models under the threshold and bandwidth reservation policies 2015Blocking probabilities of elastic and adaptive calls in the Erlang multirate loss model under the threshold policy 2022WCFS: a new framework for analyzing multiserver systems 2010Queuing system with processor sharing and limited resources 2016Sojourn Time Analysis for Processor Sharing Loss System with Unreliable Server 2016An algorithmic analysis of the BMAP/MSP/1 generalized processor-sharing queue

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.