Sojourn time distribution in polling systems with processor-sharing policy

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work-conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor-sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions.

Original languageEnglish
Pages (from-to)97-112
Number of pages16
JournalPerformance Evaluation
Volume114
DOIs
Publication statusPublished - 2017 Sep 1

Fingerprint

Polling Systems
Processor Sharing
Sojourn Time
Partial differential equations
Queue
Servers
Scheduling
Customers
Requirements
Partial differential equation
Transform
Policy
Scheduling Policy
Single Server
Poisson process
Server
Moment

Keywords

  • Exhaustive service
  • Polling system
  • Processor-sharing
  • Sojourn time distribution

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Networks and Communications

Cite this

Sojourn time distribution in polling systems with processor-sharing policy. / Kim, Bara; Kim, Jeongsim.

In: Performance Evaluation, Vol. 114, 01.09.2017, p. 97-112.

Research output: Contribution to journalArticle

@article{072a08dc490d4cd989569bb3f99830e0,
title = "Sojourn time distribution in polling systems with processor-sharing policy",
abstract = "We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work-conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor-sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions.",
keywords = "Exhaustive service, Polling system, Processor-sharing, Sojourn time distribution",
author = "Bara Kim and Jeongsim Kim",
year = "2017",
month = "9",
day = "1",
doi = "10.1016/j.peva.2017.06.002",
language = "English",
volume = "114",
pages = "97--112",
journal = "Performance Evaluation",
issn = "0166-5316",
publisher = "Elsevier",

}

TY - JOUR

T1 - Sojourn time distribution in polling systems with processor-sharing policy

AU - Kim, Bara

AU - Kim, Jeongsim

PY - 2017/9/1

Y1 - 2017/9/1

N2 - We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work-conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor-sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions.

AB - We consider a polling system with a single server and multiple queues where customers arrive at the queues according to independent Poisson processes. The server visits and serves the queues in a cyclic order. The service discipline at all queues is exhaustive service. One queue uses processor-sharing as a scheduling policy, and the customers in that queue have phase-type distributed service requirements. The other queues use any work-conserving policy, and the customers in those queues have generally distributed service requirements. We derive a partial differential equation for the transform of the conditional sojourn time distribution of an arbitrary customer who arrives at the queue with processor-sharing policy, conditioned on the service requirement. We also derive a partial differential equation for the transform of the unconditional sojourn time distribution. From these equations, we obtain the first and second moments of the conditional and unconditional sojourn time distributions.

KW - Exhaustive service

KW - Polling system

KW - Processor-sharing

KW - Sojourn time distribution

UR - http://www.scopus.com/inward/record.url?scp=85024866937&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85024866937&partnerID=8YFLogxK

U2 - 10.1016/j.peva.2017.06.002

DO - 10.1016/j.peva.2017.06.002

M3 - Article

AN - SCOPUS:85024866937

VL - 114

SP - 97

EP - 112

JO - Performance Evaluation

JF - Performance Evaluation

SN - 0166-5316

ER -