Skip to main content
SpringerLink
Log in

The queuing system GI/M/I with finite waiting space

  • Veröffentlichungen
  • Published:
Metrika Aims and scope Submit manuscript

Summary

Time dependent solution of the queuing system characterized by a general independent input, exponential service time distribution and a finite waiting space, has been first investigated by using the “phase method”. On finding the waiting room full, the customers then arriving may be turned away or the first customer may wait outside and the input process may be stopped till the customer then being served, completes its service. Steady state solutions of both these problems have been obtained and the difference in the operational behaviour of the two systems has been pointed out. For a 2-Erlang arrival distribution, the queuing parameters have been evaluated for different values ofρ r andN.

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

  1. Conolly, B.W. (1958): A difference equation technique applied to the queue with arbitrary arrival interval distribution. J. R. Statist. Soc B 20, 168–175.

    MATH  MathSciNet  Google Scholar 

  2. Finch, P.D. (1958): The effect of the size of the waiting room on a simple queue. J. R. Statist Soc B, 20, 182–186.

    MATH  MathSciNet  Google Scholar 

  3. Heathcote, C.R. & Moyal, J.E. (1959): The random walk (in continous time) and its application to the theory of queues. Biometrika 46, 400–411.

    MATH  MathSciNet  Google Scholar 

  4. Jaiswal, N.K.: Time dependent solution of the Bulk-service queuing problem (To be published).

  5. Jackson, J.R. (1958): Multiple servers with limited waiting space. Naval Res. Log. Quart. 5, 315–321.

    Google Scholar 

  6. Luchak (1956): The solution of the single channel queuing equations characterised by a time-dependent Poisson-distributed arrival rate and a general class of holding time opns. Res. 4, 711–732.

    MathSciNet  Google Scholar 

  7. Morse, P.M. (1958): Queues, Inventories and Maintenance, New York Wiley.

    Google Scholar 

  8. Wishart, D.M.G. (1956): A queuing system with service time distribution. Ann. Math. Stat. 27, 768–779.

    MathSciNet  MATH  Google Scholar 

  9. Wishart, D.M.G. (1959): A queuing system with service-time distribution of mixed chi-squared type. Opns. Res. 7. 174–179.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ministry of Defence, Defence Science Laboratory Metcalfe House, Delhi — 6, Indien

    N. K. Jaiswal

Authors
  1. N. K. Jaiswal
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaiswal, N.K. The queuing system GI/M/I with finite waiting space. Metrika 4, 107–125 (1961). https://doi.org/10.1007/BF02613872

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02613872

Keywords

Search

Navigation