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On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

Sergei Grishechkin
Sergei Grishechkin*
Affiliation:
Gubkin Institute of Oil and Gas, Moscow
*
∗Postal address: Warshavskoje shosse, d.88, kv. 43, 113 556 Moscow, Russia.
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Abstract

The M/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for the M/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerning M/G/1 queues with shortest residual processing time discipline.

Keywords

SHORTEST RESIDUAL PROCESSING TIME DISCIPLINEHEAVY TRAFFICOVERLOADED QUEUES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 653 - 698
Copyright
Copyright © Applied Probability Trust 1992 

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