Skip to main content
SpringerLink
Log in

Performance and cost analysis of a Geom/G/1 (G, SV) system

  • Published:
Optimization and Engineering Aims and scope Submit manuscript

Abstract

In this paper, a gate service Geom/G/1 queue system with single vacation is analyzed. Firstly, a gate service policy and single vacation are introduced in detail, the expected number of customers in the system at the beginning instant of a service period is obtained. Next, the Probability Generating Function (P.G.F.) of the stationary queue length is obtained by using regeneration cycle approach. Then the P.G.F. of the waiting time is derived under the condition of the independence between the arrival process and the waiting time. Moreover, the P.G.Fs. of the service period, the vacation period and the idle period are obtained, and the mean length of three periods are also obtained. Cost model is formulated to determine the optimal expected vacation length. Finally, based on numerical results, the relations of the performance measures and traffic intensity are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alfa A (1998) Discrete time analysis of MAP/PH/1 vacation queue with gated time-limited service. Queueing Syst 29:35–54

    Article  MATH  MathSciNet  Google Scholar 

  • Boxma O, Yechiali U (1997) An M/G/1 queue with multiple types of feedback and gated vacations. J Appl Probab 34:773–784

    Article  MATH  MathSciNet  Google Scholar 

  • Fiems D, Walraevens J, Bruneel H (2004) The discrete-time gated vacation queue revisited. Int J Electron Commun 58:136–141

    Article  Google Scholar 

  • Hunter J (1983) Mathematical techniques of applied probability, vol 2: discrete time models: techniques and applications. Academic Press, New York

    Google Scholar 

  • Leung K, Eisenberg M (1990) A single-server queue limited vacation and gated time-limited service. IEEE Trans Commun 38:1454–1462

    Article  MATH  Google Scholar 

  • Takagi H (1991) Queueing analysis, vol 1: vacation and priority systems. North-Holland, Amsterdam

    Google Scholar 

  • Takagi H (1993) Queueing analysis, vol 3: discrete-time systems. North-Holland, Amsterdam, pp 90–199

    Google Scholar 

  • Tian N, Zhang G (2006) Vacation queueing models-theory and applications. Springer, New York

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Science, Yanshan University, Qinhuangdao, 066004, China

    Zhanyou Ma & Naishuo Tian

  2. Department of Intelligence and Informatics, Konan University, Kobe, 658-8501, Japan

    Wuyi Yue

Authors
  1. Zhanyou Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wuyi Yue
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Naishuo Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanyou Ma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ma, Z., Yue, W. & Tian, N. Performance and cost analysis of a Geom/G/1 (G, SV) system. Optim Eng 10, 239–251 (2009). https://doi.org/10.1007/s11081-008-9074-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11081-008-9074-y

Keywords

Search

Navigation