Skip to main content
SpringerLink
Log in

Analysis of an \(M/M/1+G\) queue operated under the FCFS policy with exact admission control

  • Published:
Queueing Systems Aims and scope Submit manuscript

Abstract

In this article, we present an exact theoretical analysis of an \(M/M/1\) system, with arbitrary distribution of relative deadline for the end of service, operated under the first come first served scheduling policy with exact admission control. We provide an explicit solution to the functional equation that must be satisfied by the workload distribution, when the system reaches steady state. We use this solution to derive explicit expressions for the loss ratio and the sojourn time distribution. Finally, we compare this loss ratio with that of a similar system operating without admission control, in the cases of some common distributions of the relative deadline.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abdelzaher, T., Lu, C.: Schedulability analysis and utilization bounds for highly scalable real-time services. In: IEEE Real-Time Technology and Applications Symp, pp. 11–25 (2001)

  2. Baccelli, F., Boyer, P., Hebuterne, G.: Single-server queue with impatient customers. Adv. Appl. Probab. 16(4), 887–905 (1984)

    Article  Google Scholar 

  3. Barrer, D.Y.: Queueing with impatient customers and indifferent clerks. Oper. Res. 5(5), 644–649 (1957)

    Article  Google Scholar 

  4. Barrer, D.Y.: Queueing with impatient customers and ordered service. Oper. Res. 5(5), 650–656 (1957)

    Article  Google Scholar 

  5. Bekker, R.: Finite-buffer queues with workload-dependent service and arrival rates. Queueing Syst. 50, 231–253 (2005)

    Article  Google Scholar 

  6. Boxma, O.J., de Waal, P.R.: Multiserver queues with impatient customers. In: Proceedings of ITC, vol. 14, pp. 743–756. Elsevier, Amsterdam (1994)

  7. Boxma, O., Perry, D., Stadje, W.: The M/G/1+G queue revisited. Queueing Syst. 67, 207–220 (2011)

    Article  Google Scholar 

  8. Cohen, J.W.: Single server queues with restricted accessibility. J. Eng. Math. 3(4), 265–284 (1969)

    Article  Google Scholar 

  9. Daley, D.J.: General customer impatience in queue GI/G/1. J. Appl. Probab. 2(1), 186–205 (1965)

    Article  Google Scholar 

  10. Das, S., Jenkins, L., Sengupta, D.: Loss ratios of EDF and FCFS scheduling policies under a performance enhancing modification. In: Proceedings of International Conference on Real-Time and Embedded Systems, pp. 128–131, RTES (2010)

  11. Gavish, B., Schweitzer, P.: The Markovian queue with bounded waiting time. Manag. Sci. 23(12), 1349–1357 (1977)

    Article  Google Scholar 

  12. Haugen, R.B., Even, S.: Queueing systems with stochastic time out. IEEE Trans. Commun. 28(12), 1984–1989 (1980)

    Article  Google Scholar 

  13. Liu, L., Kulkarni, V.G.: Explicit solutions for the steady state distributions in M/PH/1 queues with workload dependent balking. Queueing Syst. 52, 251–260 (2006)

    Article  Google Scholar 

  14. Llamosi, A., Bernat, G., Burns, A.: Weakly hard real-time systems. IEEE Trans. Comput. 50(4), 308–321 (2001)

    Article  Google Scholar 

  15. Loris-Teghem, J.: On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times. J. Appl. Probab. 9, 642–649 (1972)

    Article  Google Scholar 

  16. Movaghar, A.: On queueing with customer impatience until the beginning of service. Queueing Syst. 29, 337–350 (1998)

    Article  Google Scholar 

  17. Movaghar, A.: On queueing with customer impatience until the end of service. Stoch. Models 22, 149–173 (2006)

    Article  Google Scholar 

  18. Palm, C.: Methods for judging the annoyance caused by congestion. Tele 2, 1–20 (1953)

    Google Scholar 

  19. Perry, D., Asmussen, S.: Rejection rules in the M/G/1 queue. Queueing Syst. 19, 105–130 (1995)

    Article  Google Scholar 

  20. Van Dijk, N.M.: Queueing systems with restricted workload: an explicit solution. J. Appl. Probab. 27, 393–400 (1990)

    Article  Google Scholar 

  21. Zwart, A.P.: Loss rates in the M/G/1 queue with complete rejection. Technische Universiteit Eindhoven, Technical report (2003)

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Science, Bangalore, 560012, India

    Sudipta Das & Lawrence Jenkins

  2. Applied Statistical Unit, Indian Statistical Institute, Kolkata, 7000108, India

    Debasis Sengupta

Authors
  1. Sudipta Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lawrence Jenkins
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Debasis Sengupta
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sudipta Das.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Das, S., Jenkins, L. & Sengupta, D. Analysis of an \(M/M/1+G\) queue operated under the FCFS policy with exact admission control. Queueing Syst 75, 169–188 (2013). https://doi.org/10.1007/s11134-013-9366-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11134-013-9366-6

Keywords

Mathematics Subject Classification (2000)

Search

Navigation