Skip to main content
SpringerLink
Log in

A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment

  • Original Article
  • Published:
Acta Informatica Aims and scope Submit manuscript

Abstract

Inspired by the need for performability models for HSDPA user equipment, a Markovian queue with varying number of servers is conceived. The arrival and the service processes, the number of allocated or active servers of the queue are inherently, and independently (or jointly) Markov modulated. Batch arrivals, batch services, autocorrelation of inter-arrival times, and autocorrelation of batch sizes can be accommodated in the queue, by a suitable use of Markov modulation and generalized exponential distribution. The queue has a provision for negative customers too. Transformations of the balance equations into a computable form are proposed in order to obtain the steady state probabilities with the Spectral Expansion method. This queue is used to model the High Speed Downlink Packet Access (HSDPA) wireless networks. The model is an integrated one with respect to HSDPA, capable of accommodating many of the intricate aspects of HSDPA such as, channel allocation policy, loss of packets due to channel fading, bursty and correlated traffic. Good agreement is observed between the numerical results of the proposed analytical model and those of an independent simulator of real HSDPA and radio channel behaviors. The comparison of the terminal categories specified by the 3rd Generation Partnership Project (3GPP) is also presented.

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. 3GPP Technical Report 25.214, version 7.0.0. Physical layer procedures (FDD). The 3GPP project, March (2006)

  2. Assaad M., Zeghlache D.: Analytical model of hsdpa throughput under nakagami fading channel. IEEE Trans. Vehicul. Technol. 58(2), 610–624 (2009)

    Article  Google Scholar 

  3. Auckland Internet Traffic Capture. http://www.wand.net.nz/wand/wits/auck/6/20010612-060000-e1 (2001)

  4. Brouwer, F., de Bruin, I., Silva, J.C., Souto, N., Cercas, F., Correia, A.: Usage of link-level performance indicators for HSDPA network-level simulations in E-UMTS. In: ISSSTA2004, Sydney, Australia, augustus-september (2004)

  5. Chakka, R.: Performance and Reliability Modelling of Computing Systems Using Spectral Expansion. PhD thesis, University of Newcastle upon Tyne (Newcastle upon Tyne) (1995)

  6. Chakka R., Do T.V.: The MM \({{\sum_{k=1}^{K} {CPP_k}}/GE/c/L\,G}\)-queue with heterogeneous servers: steady state solution and an application to performance evaluation. Perform. Eval. 64, 191–209 (2007)

    Article  Google Scholar 

  7. Chakka R., Do T.V., Pandi Z.: A generalized Markovian queue and its applications to performance analysis in telecommunications networks. In: Kouvatsos, D. (eds) Performance Modelling and Analysis of Heterogeneous Networks, pp. 371–387. River Publisher, Aalborg (2009)

    Google Scholar 

  8. Chakka R., Harrison Peter G.: A Markov modulated multi-server queue with negative customers—the MM CPP/GE/c/L G-queue. Acta Inform. 37, 881–919 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chakka R., Harrison Peter G.: The MMCPP/GE/c queue. Queueing Syst. Theory Appl. 38, 307–326 (2001)

    Article  MATH  Google Scholar 

  10. Do, T.V., Chakka, R., Harrison Peter, G.: An integrated analytical model for computation and comparison of the throughputs of the UMTS/HSDPA user equipment categories. In: MSWiM’07: Proceedings of the 10th ACM Symposium on Modeling, analysis, and simulation of wireless and mobile systems, pp. 45–51. ACM, New York (2007)

  11. Do T.V., Papp D., Chakka R., Truong Mai X.T.: A performance model of MPLS multipath routing with failures and repairs of the LSPs. In: Kouvatsos, D. (eds) Performance Modelling and Analysis of Heterogeneous Networks, pp. 27–43. River Publisher, Aalborg (2009)

    Google Scholar 

  12. Fourneau J.M., Gelenbe E., Suros R.: G-networks with multiple classes of negative and positive customers. Theor. Comput. Sci. 155, 141–156 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fretwell, R.J., Kouvatsos, D.D.: ATM traffic burst lengths are geometrically bounded. In: Proceedings of the 7th IFIP Workshop on Performance Modelling and Evaluation of ATM & IP Networks, Antwerp. Chapman and Hall, Belgium (1999)

  14. Gelenbe E.: Réseaux stochastiques ouverts avec clients négatifs et positifs, et réseaux neuronaux. Comptes Rendus de l’Acad. Sci. 309 (II), 979–982 (1989)

    MathSciNet  Google Scholar 

  15. Gelenbe E.: Réseaux neuronaux aléatoires stables. Comptes Rendus de l’Acad. Sci. 310 (II), 177–180 (1990)

    MathSciNet  Google Scholar 

  16. Gelenbe E., Pujolle G.: Introduction to Queuing Networks. Wiley, New York (1998)

    Google Scholar 

  17. Gelenbe Erol.: Random neural networks with positive and negative signals and product form solution. Neural Comput. 1(4), 502–510 (1989)

    Article  Google Scholar 

  18. Gelenbe E.: The first decade of G-networks. Eur. J. Oper. Res. 126(2), 231–232 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gelenbe E.: Dealing with software viruses: a biological paradigm. Inf. Secur. Tech. Rep. 12(4), 242–250 (2007)

    Article  MathSciNet  Google Scholar 

  20. Gelenbe, E.: Network of interacting synthetic molecules in steady state. In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol. 464(2096), pp. 2219–2228 (2008)

  21. Gelenbe, E., Kahane, J.-P. (eds): Fundamental Concepts in Computer Science. Imperial College Press, London (2009)

    MATH  Google Scholar 

  22. Gelenbe E., Mitrani I.: Analysis and Synthesis of Computer Systems World Scientific. Imperial College Press, London (2010)

    Book  Google Scholar 

  23. Gelenbe E., Shachnai H.: On G-networks and resource allocation in multimedia systems. Eur. J. Oper. Res. 126(2), 308–318 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. Kouvatsos D.: Entropy maximisation and queueing network models. Ann. Oper. Res. 48, 63–126 (1994)

    Article  MATH  Google Scholar 

  25. Kolding T., Frederiksen F., Mogensen P.: Performance aspects of WCDMA systems with high speed downlink packet access (HSDPA). VTC Vancouver. vol. 1, 477–481 (2002)

  26. Liu Q., Zhou S., Giannakis Georgios B.: Queuing With adaptive modulation and coding over wireless links: cross-layer analysis and design. IEEE Trans. Wireless Commun. 4(3), 1142–1153 (2005)

    Article  Google Scholar 

  27. Mitrani I., Chakka R.: Spectral expansion solution for a class of Markov models: application and comparison with the matrix-geometric method. Perform. Eval. 23, 241–260 (1995)

    Article  MATH  Google Scholar 

  28. Norros I.: A storage model with self-similar input. Queueing Syst. Appl. 16, 387–396 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  29. Paxman V., Floyd S.: Wide-area traffic: the failure of Poisson modelling. IEEE/ACM Trans. Network. 3(3), 226–244 (1995)

    Article  Google Scholar 

  30. Pedersen K.I., Lootsma T.F., Stottrup M., Frederiksen F., Kolding T.E., Mogensen P.E.: Network performance of mixed traffic on high speed downlink packet access and dedicated channels in WCDMA. VTC Vancouver. vol. 6, 4496–4500 (2004)

  31. Simon Marvin K., Alouini M.-S.: Digital Communication over Fading Channels, 2nd edn. Wiley, London (2005)

    Google Scholar 

  32. The Internet Traffic Archive. http://ita.ee.lbl.gov/.

  33. Wang, H.S., Moayeri, N.: Finite-state Markov channel—a useful channels. IEEE Trans. Vehicul. Technol. pp. 163–171 (1995)

  34. Yang, L.-L., Hanzo, L.: Improving the throughput of DS-CDMA systems using adaptive rate transmissions based on variable spreading factors. In: Proceeding of VTC 2002, Vancouver, vol. 1, pp. 1816–1820 (2002)

  35. Zorzi M., Rao Ramesh R., Milstein Laurence B.: Error statistics in data transmission over fading channels. IEEE Trans. Commun. 46(11), 1468–1477 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Telecommunications, Budapest University of Technology and Economics, 1117 Magyar tudósok körútja 2, Budapest, Hungary

    Tien Van Do, Ram Chakka, Nam H. Do & László Pap

  2. Meerut Institute of Engineering and Technology (MIET), Meerut, 250005, India

    Ram Chakka

Authors
  1. Tien Van Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ram Chakka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nam H. Do
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. László Pap
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tien Van Do.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Do, T.V., Chakka, R., Do, N.H. et al. A Markovian queue with varying number of servers and applications to the performance comparison of HSDPA user equipment. Acta Informatica 48, 243–269 (2011). https://doi.org/10.1007/s00236-011-0138-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00236-011-0138-7

Keywords

Search

Navigation