M/G/1 queue with exponential working vacation and gated service

Zsolt Saffer, M. Telek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Citations (Scopus)

Abstract

In this paper we consider the analysis of an M/G/1 queue with working vacation. In contrast to the previous literature where the working vacation starts when all customers are served (exhaustive discipline) we consider the case where the vacation period starts when the customers present at the system at beginning of the service period are served (gated discipline). The analysis of the model with gated discipline requires a different approach than the one with exhaustive discipline. We present the probability-generating function of the number of customers in the system and the Laplace-Stieljes transform of the stationary waiting time.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages28-42
Number of pages15
Volume6751 LNCS
DOIs
Publication statusPublished - 2011
Event18th International Conference on Analytical and Stochastic Modelling and Applications, ASMTA 2011 - Venice, Italy
Duration: Jun 20 2011Jun 22 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6751 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other18th International Conference on Analytical and Stochastic Modelling and Applications, ASMTA 2011
CountryItaly
CityVenice
Period6/20/116/22/11

Fingerprint

Working Vacation
M/G/1 Queue
Laplace transforms
Customers
Vacation
Probability generating function
Waiting Time
Laplace transform
Model

Keywords

  • queueing theory
  • vacation model
  • working vacation

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Saffer, Z., & Telek, M. (2011). M/G/1 queue with exponential working vacation and gated service. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6751 LNCS, pp. 28-42). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6751 LNCS). https://doi.org/10.1007/978-3-642-21713-5_3

M/G/1 queue with exponential working vacation and gated service. / Saffer, Zsolt; Telek, M.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6751 LNCS 2011. p. 28-42 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6751 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Saffer, Z & Telek, M 2011, M/G/1 queue with exponential working vacation and gated service. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 6751 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6751 LNCS, pp. 28-42, 18th International Conference on Analytical and Stochastic Modelling and Applications, ASMTA 2011, Venice, Italy, 6/20/11. https://doi.org/10.1007/978-3-642-21713-5_3
Saffer Z, Telek M. M/G/1 queue with exponential working vacation and gated service. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6751 LNCS. 2011. p. 28-42. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-21713-5_3
Saffer, Zsolt ; Telek, M. / M/G/1 queue with exponential working vacation and gated service. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 6751 LNCS 2011. pp. 28-42 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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