Stability of periodic polling system with BMAP arrivals

Zsolt Saffer, M. Telek

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

This paper considers the stability of BMAP/GI/1 periodic polling models with mixed service disciplines. The server attends the N stations in a repeating sequence of stages. Customers arrive to the stations according to batch Markov arrival processes (BMAPs). The service times of the stations are general independent and identically distributed. The characterization of global stability of the system, the order of instability of stations and the necessary and sufficient condition for the stability are given. Our stability analysis is based on the investigation of the embedded Markovian chains at the polling epochs, which allows a much simpler discussion than the formerly applied approaches. This work can also be seen as a survey on stability of a quite general set of polling models, since the majority of the known results of the field is a special case of the presented ones.

Original languageEnglish
Pages (from-to)188-195
Number of pages8
JournalEuropean Journal of Operational Research
Volume197
Issue number1
DOIs
Publication statusPublished - Aug 16 2009

Fingerprint

Polling Systems
Polling
Time varying systems
Periodic Systems
Batch
Global Stability
Identically distributed
Stability Analysis
Server
Customers
Necessary Conditions
Sufficient Conditions
Model
Markov process
Servers

Keywords

  • BMAP
  • Polling model
  • Queueing
  • Service discipline
  • Stability

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Modelling and Simulation
  • Information Systems and Management

Cite this

Stability of periodic polling system with BMAP arrivals. / Saffer, Zsolt; Telek, M.

In: European Journal of Operational Research, Vol. 197, No. 1, 16.08.2009, p. 188-195.

Research output: Contribution to journalArticle

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