Advertisement

Acta Informatica

, 48:243 | Cite as

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

  • Tien Van DoEmail author
  • Ram Chakka
  • Nam H. Do
  • László Pap
Original Article

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.

Keywords

Fading Channel User Equipment Universal Mobile Telecommunication System Steady State Probability Channel Quality Indicator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    3GPP Technical Report 25.214, version 7.0.0. Physical layer procedures (FDD). The 3GPP project, March (2006)Google Scholar
  2. 2.
    Assaad M., Zeghlache D.: Analytical model of hsdpa throughput under nakagami fading channel. IEEE Trans. Vehicul. Technol. 58(2), 610–624 (2009)CrossRefGoogle Scholar
  3. 3.
    Auckland Internet Traffic Capture. http://www.wand.net.nz/wand/wits/auck/6/20010612-060000-e1 (2001)
  4. 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)Google Scholar
  5. 5.
    Chakka, R.: Performance and Reliability Modelling of Computing Systems Using Spectral Expansion. PhD thesis, University of Newcastle upon Tyne (Newcastle upon Tyne) (1995)Google Scholar
  6. 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)CrossRefGoogle Scholar
  7. 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. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Chakka R., Harrison Peter G.: The MMCPP/GE/c queue. Queueing Syst. Theory Appl. 38, 307–326 (2001)zbMATHCrossRefGoogle Scholar
  10. 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)Google Scholar
  11. 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. 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)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 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)Google Scholar
  14. 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)MathSciNetGoogle Scholar
  15. 15.
    Gelenbe E.: Réseaux neuronaux aléatoires stables. Comptes Rendus de l’Acad. Sci. 310 (II), 177–180 (1990)MathSciNetGoogle Scholar
  16. 16.
    Gelenbe E., Pujolle G.: Introduction to Queuing Networks. Wiley, New York (1998)Google Scholar
  17. 17.
    Gelenbe Erol.: Random neural networks with positive and negative signals and product form solution. Neural Comput. 1(4), 502–510 (1989)CrossRefGoogle Scholar
  18. 18.
    Gelenbe E.: The first decade of G-networks. Eur. J. Oper. Res. 126(2), 231–232 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    Gelenbe E.: Dealing with software viruses: a biological paradigm. Inf. Secur. Tech. Rep. 12(4), 242–250 (2007)MathSciNetCrossRefGoogle Scholar
  20. 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)Google Scholar
  21. 21.
    Gelenbe, E., Kahane, J.-P. (eds): Fundamental Concepts in Computer Science. Imperial College Press, London (2009)zbMATHGoogle Scholar
  22. 22.
    Gelenbe E., Mitrani I.: Analysis and Synthesis of Computer Systems World Scientific. Imperial College Press, London (2010)CrossRefGoogle Scholar
  23. 23.
    Gelenbe E., Shachnai H.: On G-networks and resource allocation in multimedia systems. Eur. J. Oper. Res. 126(2), 308–318 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Kouvatsos D.: Entropy maximisation and queueing network models. Ann. Oper. Res. 48, 63–126 (1994)zbMATHCrossRefGoogle Scholar
  25. 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)Google Scholar
  26. 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)CrossRefGoogle Scholar
  27. 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)zbMATHCrossRefGoogle Scholar
  28. 28.
    Norros I.: A storage model with self-similar input. Queueing Syst. Appl. 16, 387–396 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    Paxman V., Floyd S.: Wide-area traffic: the failure of Poisson modelling. IEEE/ACM Trans. Network. 3(3), 226–244 (1995)CrossRefGoogle Scholar
  30. 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)Google Scholar
  31. 31.
    Simon Marvin K., Alouini M.-S.: Digital Communication over Fading Channels, 2nd edn. Wiley, London (2005)Google Scholar
  32. 32.
    The Internet Traffic Archive. http://ita.ee.lbl.gov/.
  33. 33.
    Wang, H.S., Moayeri, N.: Finite-state Markov channel—a useful channels. IEEE Trans. Vehicul. Technol. pp. 163–171 (1995)Google Scholar
  34. 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)Google Scholar
  35. 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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Tien Van Do
    • 1
    Email author
  • Ram Chakka
    • 1
    • 2
  • Nam H. Do
    • 1
  • László Pap
    • 1
  1. 1.Department of TelecommunicationsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.Meerut Institute of Engineering and Technology (MIET)MeerutIndia

Personalised recommendations