A Push-Pull Network with Infinite Supply of Work

Anat Kopzon; Yoni Nazarathy; Gideon Weiss

doi:10.1007/s11134-009-9121-1

A Push-Pull Network with Infinite Supply of Work

Anat Kopzon, Yoni Nazarathy, Gideon Weiss

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between the servers positive recurrent. We analyze two specific policies in detail, obtaining steady state distributions. We perform extensive calculations of expected queue lengths under these policies. We compare this network with the Kumar-Seidman-Rybko-Stolyar network, in which there are two random streams of arriving jobs rather than infinite supply of work.

Original language	English
Pages (from-to)	75-111
Number of pages	37
Journal	Queueing Systems
Volume	62
Issue number	1-2
DOIs	https://doi.org/10.1007/s11134-009-9121-1
State	Published - 2009

Bibliographical note

Funding Information:
Research supported in part by Israel Science Foundation Grants 249/02 and 454/05 and by European Network of Excellence Euro-NGI.

Keywords

Infinite supply of work
Infinite virtual queues
Kumar-Seidman-Rybko-Stolyar network
Manufacturing
Markovian multiclass queueing networks
Maximum pressure policies
Queueing
Threshold policies

ASJC Scopus subject areas

Statistics and Probability
Computer Science Applications
Management Science and Operations Research
Computational Theory and Mathematics

Access to Document

10.1007/s11134-009-9121-1

Cite this

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title = "A Push-Pull Network with Infinite Supply of Work",

abstract = "We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between the servers positive recurrent. We analyze two specific policies in detail, obtaining steady state distributions. We perform extensive calculations of expected queue lengths under these policies. We compare this network with the Kumar-Seidman-Rybko-Stolyar network, in which there are two random streams of arriving jobs rather than infinite supply of work.",

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AU - Nazarathy, Yoni

AU - Weiss, Gideon

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AB - We consider a two-node multiclass queueing network with two types of jobs moving through two servers in opposite directions, and there is infinite supply of work of both types. We assume exponential processing times and preemptive resume service. We identify a family of policies which keep both servers busy at all times and keep the queues between the servers positive recurrent. We analyze two specific policies in detail, obtaining steady state distributions. We perform extensive calculations of expected queue lengths under these policies. We compare this network with the Kumar-Seidman-Rybko-Stolyar network, in which there are two random streams of arriving jobs rather than infinite supply of work.

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A Push-Pull Network with Infinite Supply of Work

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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