Skip to main content
SpringerLink
Log in

Performance evaluation of a queuing system with correlated packet-trains and server interruption

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

In this paper, we consider a practical queuing system with a finite number of input links and whose arrival process is correlated and consists of a train of a fixed number of fixed-length packets and a single server which is subjected to random interruptions. We model the server interruptions by a correlated Markovian on/off process with geometrically distributed on and off periods. We first derive an expression for the functional equation describing the transient evolution of this queuing system. This functional equation is then manipulated and transformed into a mathematical tractable form. This allows us to derive the probability generating function (pgf) of the system occupancy. From this pgf, closed-form expressions for various performance measures, such as mean and variance of system contents and customer delay can be derived. Finally, we illustrate our solution technique with some numerical examples, whereby we demonstrate the negative effect of correlation in the interruption process on the performance of the system. The paper presents new insights into the performance analysis of queuing systems with correlated arrivals and service interruption and it also covers some previously published results as a special case.

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. Takagi, H. (1987). A survey of queuing analysis of polling models. In Proceedings of the third IFIP international conference on data communication systems and their performance, Rio de Janeiro, Brazil, 22–25, June 1987.

  2. Takine, T., Sengupta, B., & Hasegawa, T. (1994). An analysis of a discrete-time queue for Broadband ISDN with priorities among traffic classes. IEEE Transactions on Communications, 42(2–4), 1837–1845.

    Article  Google Scholar 

  3. Walraevens, J., Steyaert, B., & Bruneel, H. (2002). Delay characteristics in discrete-time GI-G-1 queues with non pre-emptive priority queuing discipline. Performance Evaluation, 50(1), 53–75.

    Article  Google Scholar 

  4. Elloit, E. O. (1963). Estimates of error rates for codes on burst-noise channels. Bell System Technical Journal, 42, 1977–1997.

    Google Scholar 

  5. Van der Duyn Schouten, F. A., & Vanneste, S. G. (1995). Maintenance optimization of a production system with buffer capacity. European Journal of Operation Research, 82, 232–238.

    Google Scholar 

  6. Ibe, O. C., & Trivedi, K. S. (1990). Two Queues with alternating service and server breakdown. Queueing Systems, 7(3), 253–268.

    Article  Google Scholar 

  7. Fiems, D., Steyaert, B., & Bruneel, H. (2004). Discrete-time queues with generally distributed service times and renewal-type server interruption. Performance Evaluation, 55, 277–298.

    Article  Google Scholar 

  8. Doshi, B. (1986). Queueing systems with vacations—a survey. Queueing Systems, 1, 29–66.

    Article  Google Scholar 

  9. Takagi, H. (1991). Queueing Analysis; A foundation of performance evaluation, volume 1: Vacation and priority systems, part 1. Amsterdam: Elsevier.

    Google Scholar 

  10. Takagi, H. (1993). Queueing Analysis; A foundation of performance evaluation, volume 3: Discrete-time systems. Amsterdam: Elsevier.

    Google Scholar 

  11. Hsu, J. (1974). Buffer behavior with Poisson arrival and geometric output processes. IEEE Transactions on Communications, 22, 1940–1941.

    Article  Google Scholar 

  12. Heines, T. (1979). Buffer behavior in computer communication systems. IEEE Transactions on Communications, 28, 573–576.

    Article  Google Scholar 

  13. Bruneel, H. (1986). A general treatment of discrete-time buffers with one randomly interrupted output line. European Journal of Operational Research, 27(1), 67–81.

    Article  Google Scholar 

  14. Yang, O., & Mark, J. (1990). Performance analysis of integrated services on a single server system. Performance Evaluation, 11, 79–92.

    Article  Google Scholar 

  15. Woodside, C., & Ho, E. (1987). Engineering calculation of overflow probabilities in buffers with Markov-interrupted service. IEEE Transactions on Communications, 35(12), 1272–1277.

    Article  Google Scholar 

  16. Fiems, D., Steyaert, B., & Bruneel, H. (2003). Analysis of a discrete-time GI–G–1 queueing model subjected to bursty interruptions. Computers and Operations Research, 30, 139–153.

    Article  Google Scholar 

  17. Fiems, D., Steyaert, B., & Bruneel, H. (2001). Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue. Computers and Operations Research, 28(13), 1299–1313.

    Article  Google Scholar 

  18. Fiems, D., Steyaert, B., & Bruneel, H. (2004). Discrete-time queues with generally distributed service times and renewal-type server interruptions. Performance Evaluation, 55, 277–298.

    Article  Google Scholar 

  19. Fiems, D. (2004). Analysis of discrete-time queuing systems with vacations. Ph.D. thesis, Department of Telecommunications and Information Processing, Ghent University, Belgium.

  20. Pakes, A. G. (1974). On dams with Markovian inputs. Journal of Applied Probability, 10, 317–329.

    Article  Google Scholar 

  21. Gopinath, B., & Morrison, J. A. (1988). Single server queues with correlated inputs. In Proceedings of the international symposium on complex performance modeling: measurement and evaluation, August 1978 (pp. 263–278).

  22. Mehmet Ali, M., Zhang, X., & Hayes, J. F. (2003). A performance analysis of discrete-time queueing system with server interruption for modeling wireless ATM multiplexer. Performance Evaluation, 51, 1–31.

    Article  Google Scholar 

  23. Kamoun, F. (2006). Performance analysis of a discrete-time queuing system with a correlated train arrival process. Performance Evaluation, 63(4–5), 315–340.

    Article  Google Scholar 

  24. Xiong, Y., & Bruneel, H. (1992). Performance of statistical multiplexers with finite number of inputs and train arrivals. In Proceedings of INFOCOM (pp. 2036–2044).

  25. Bruneel, H. (1993). Packet delay and queue length of statistical multiplexers with low-speed access lines. Computer Networks and ISDN Systems, 25, 1267–1277.

    Article  Google Scholar 

  26. McKeown, N. (1997). A fast switched backplane for a gigabit switched router. Business Communications Review, 27(12).

  27. Bruneel, H., & Kim, B. G. (1993). Discrete-time models for communication systems including ATM. Boston: Kluwer Academic.

    Google Scholar 

  28. Kamoun, F. (2006). The discrete-time queue with auto-regressive inputs revisited. Queuing Systems, 54, 185–192.

    Article  Google Scholar 

  29. Kamoun, F. (2008). Performance analysis of a non-preemptive priority queuing system subjected to a correlated Markovian interruption process. Computers & Operations Research, 35(12), 3969–3988.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Information Technology, University of Dubai, P.O. Box 14143, Dubai, UAE

    Faouzi Kamoun

Authors
  1. Faouzi Kamoun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Faouzi Kamoun.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kamoun, F. Performance evaluation of a queuing system with correlated packet-trains and server interruption. Telecommun Syst 41, 267–277 (2009). https://doi.org/10.1007/s11235-009-9160-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-009-9160-2

Keywords

Search

Navigation