Skip to main content
SpringerLink
Log in
Book cover

Multidimensional Queueing Models in Telecommunication Networks pp 1–33Cite as

Multidimensional Loss Models of Queueing Systems and Their Applications in Telecommunication Networks

  • Chapter
  • First Online:

  • 497 Accesses

Abstract

This chapter presents the foundations of multidimensional Erlang’s models, and the discussion has been concentrated on Markov models with pure losses. Both single-rate and multi-rate Erlang’s loss models with uncontrolled access schemes are considered. Effective computational procedures to calculate the main quality of service (QoS) metrics are shown.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Ahmed M, Yanikomeroglu H (2005) Call admission control in wireless networks. IEEE Commun Surv 7(1):50–69

    Article  Google Scholar 

  2. Beigy H, Meybody MR (2003) Used-based call admission control policies for cellular mobile systems: a survey. J CSI Comput Sci Eng 10:45–58

    Google Scholar 

  3. Burman DY, Lehoczky JP, Lim Y (1984) Insensitivity of blocking probabilities in a circuit switched network. J Appl Probab 21(4):850–859

    Article  MATH  MathSciNet  Google Scholar 

  4. Buzen JP (1973) Computational algorithms for closed networks with exponential servers. Commun Assoc Comput Mach 16(9):527–531

    MATH  MathSciNet  Google Scholar 

  5. Cruz-Perez FA, Toledo-Marin R, Hernandez-Valdez G (2011) Approximated mathematical methods of guard-channel-based call admission control in cellular networks. In: Melikov A (ed) Cellular networks: positioning, performance analysis, reliability. Intech, India, pp 151–168

    Google Scholar 

  6. Delaire M, Hebuterne G (1997) Call blocking in multi-services systems on one transmission link. In: 5th international workshop on performance model and evaluation of ATM networks, July, UK, pp 253–270

    Google Scholar 

  7. Erlang AK (1909) The theory of probabilities and telephone conversations. Nyt Tidsskrift for Matematik B-20:33–39

    Google Scholar 

  8. Fang Y (2003) Thinning schemes for call admission control in wireless networks. IEEE Trans Comput 52(5):371–382

    Google Scholar 

  9. Fang Y, Chlamtac I (1999) Teletraffic analysis and mobility modelling for PCS networks. IEEE Trans Commun 47:1062–1072

    Article  Google Scholar 

  10. Fang Y, Chlamtac I, Lin YB (1998) Channel occupancy times and handoff rate for mobile computing and PCS networks. IEEE Trans Comput 47:679–692

    Article  Google Scholar 

  11. Fang Y, Zhang Y (2002) Call admission control schemes and performance analysis in wireless mobile networks. IEEE Trans Veh Technol 51(2):371–382

    Article  MathSciNet  Google Scholar 

  12. Firouzi Z, Beigy H (2009) A new call admission control scheme based on new call bounding and thinning II schemes in cellular mobile networks. In: Proceedings of IEEE conference on electro/information technology, June 2009, pp 40–45. doi:978-1-4244-3355-1/09

    Google Scholar 

  13. Gelenbe E, Pujolle G (1998) Introduction to queueing networks. Wiley, New York

    Google Scholar 

  14. Gnedenko BV, Kovalenko IN (1989) Introduction to queueing theory. Birkhauser, Boston

    Book  Google Scholar 

  15. Goswami V, Swain PK (2012) Analysis of finite population limited fractional guard channel call admission control in cellular networks. Procedia Eng 30:759–766

    Article  Google Scholar 

  16. Gross D, Harris C (1985) Fundamentals of queueing theory. Wiley, New York

    MATH  Google Scholar 

  17. Kaufman JS (1981) Blocking in shared resource environment. IEEE Trans Commun 10(2):1474–1481

    Article  Google Scholar 

  18. Kim HM, Melikov A, Fattakhova M, Kim CS (2012) An analytical approach to the analysis of guard-channel-based call admission control in wireless cellular networks. J Appl Math 12:Article ID 676582, 14 pages, doi:10.1155/2012/676582

  19. Kim K (2008) A computation method in performance evaluation in cellular communication network under general distribution model. J KSIAM 12(2):119–131

    Google Scholar 

  20. Kleinrock L (1975) Queueing systems, Vol. 1. Theory. Wiley, New York

    Google Scholar 

  21. Kleinrock L (1976) Queueing systems, Vol. 2. Computer applications. Wiley, New York

    Google Scholar 

  22. Kolmogorov A (1936) Zum theorie der Markoffschen ketten. Mathematische Annalen B112:155–160

    Article  MathSciNet  Google Scholar 

  23. Korolyuk VS, Korolyuk VV (1999) Stochastic model of systems. Kluwer, Boston

    Book  Google Scholar 

  24. Kovalenko IN (1963) On independence of stationary distributions of the form of the service time distribution law. Probl Pered Inform 11:104–113

    Google Scholar 

  25. Leoung CW, Zhuang W (2003) Call admission control for wireless personal communications. Comput Commun 26(6):522–541

    Article  Google Scholar 

  26. Melikov AZ, Babayev AT (2006) Refined approximations for performance analysis and optimization of queuing model with guard channels for handovers in cellular networks. Comput Commun 29(9):1386–1392

    Article  Google Scholar 

  27. Melikov AZ, Ponomarenko LA (2014) Methods for analysis and optimization of a new access strategy in cellular communication networks. J Autom Inform Sci 46(3):70–82

    Article  MathSciNet  Google Scholar 

  28. Neuts M (1984) Matrix-geometric solutions in stochastic models: an algorithmic approach. John Hopkins University Press, Baltimore

    Google Scholar 

  29. Ponomarenko L, Kim CS, Melikov A (2010) Performance analysis and optimization of multi-traffic on communication networks. Springer, Heidelberg

    Book  MATH  Google Scholar 

  30. Pioro M, Lubacs J, Korner U (1990) Traffic engineering problems in multi-service circuit-switched networks. Comput Netw ISDN Syst 1–5:127–136

    Article  Google Scholar 

  31. Roberts JW (1981) A service system with heterogeneous user requirements application to multi-service telecommunication systems. In: Pujolle G (ed) Performance of data communication systems and their application. North Holland, Amsterdam, pp 423–431

    Google Scholar 

  32. Schneps-Schneppe M, Iversen VB (2012) Call admission control in cellular networks. In: Ortiz JH (ed) Mobile networks. Intech, India, pp 111–136

    Google Scholar 

  33. Vazquez-Avilla JL, Cruz-Perez FA, Ortigoza-Guerrero L (2006) Performance analysis of fractional guard channel policies in mobile cellular networks. IEEE Trans Wireless Commun 5(2):301–305

    Article  Google Scholar 

  34. Wang X, Fan P, Pan Y (2008) A more realistic thinning scheme for call admission control in multimedia wireless networks. IEEE Trans Comput 57(8):1143–1148

    Article  MathSciNet  Google Scholar 

  35. Wei L, Fang Y (2008) Performance evaluation of wireless cellular networks with mixed channel holding times. IEEE Trans Wireless Commun 7(6):2154–2160

    Article  Google Scholar 

  36. Wolff RW (1992) Poisson arrivals see time averages. Oper Res 30(2):223–231

    Article  Google Scholar 

  37. Yavuz EA, Leung VCM (2006) Computationally efficient method to evaluate the performance of guard-channel-based call admission control in cellular networks. IEEE Trans Veh Technol 55(4):1412–1424

    Article  Google Scholar 

  38. Zeng H, Chlamtac I (2003) Adaptive guard channel allocation and blocking probability estimation in PCS networks. Comput Netw 43:163–176

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Teletraffic Theory, Institute of Cybernetics, National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

    Agassi Melikov

  2. International Research and Training Center for Information Technologies and Systems of the National Academy of Sciences of Ukraine and Ministry of Education and Science of Ukraine, Kiev, Ukraine

    Leonid Ponomarenko

Authors
  1. Agassi Melikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leonid Ponomarenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Melikov, A., Ponomarenko, L. (2014). Multidimensional Loss Models of Queueing Systems and Their Applications in Telecommunication Networks. In: Multidimensional Queueing Models in Telecommunication Networks. Springer, Cham. https://doi.org/10.1007/978-3-319-08669-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08669-9_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08668-2

  • Online ISBN: 978-3-319-08669-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation