Skip to main content
SpringerLink
Log in

Stability Condition of a Multi-class Modified Erlang System

  • Conference paper
  • First Online:
Information Technologies and Mathematical Modelling. Queueing Theory and Applications (ITMM 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1391))

  • 252 Accesses

Abstract

We consider a modified Erlang loss system where the first priority customers (class-1) are lost if find all servers busy, while the second priority customers (class-2) form an infinite capacity queue. A new feature of this system is that sub-classes of class-1 customers are assigned on servers according to assignment probabilities. All customers follow Poisson inputs and have general class-dependent service time. We show how the product form of class-1 stationary probabilities can be used to obtain the stability condition of the whole system even when sub-classes of class-1 customers have different service rates. Also we perform discrete event simulation to confirm theoretical results.

The research is supported by Russian Foundation for Basic Research, projects 18-07-00147, 18-07-00156 and 19-07-00303.

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

Access this chapter

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Morozov, E., Rogozin, S., Nguyen, H.Q., Phung-Duc, T.: Modified Erlang loss system for cognitive wireless networks. J. Math. Sci. (2020, submitted)

    Google Scholar 

  2. Rogozin, S.: Simulation a modified Erlang loss system with multi-type servers and multi-type customers. In: Proceedings of the Second International Workshop on Stochastic Modeling and Applied Research of Technology (2020, submitted)

    Google Scholar 

  3. Adan, I., Hurkens, C., Weiss, G.: A reversible Erlang loss system with multitype customers and multitype servers. Probab. Eng. Inf. Sci. 24(4), 535–548 (2010)

    Article  MathSciNet  Google Scholar 

  4. Ostovar, A., Keshavarz, H., Quan, Z.: Cognitive radio networks for green wireless communications: an overview. Telecommun. Syst. 76, 129–138 (2020). https://doi.org/10.1007/s11235-020-00703-8

    Article  Google Scholar 

  5. Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003). https://doi.org/10.1007/b97236

    Book  MATH  Google Scholar 

  6. Morozov, E., Delgado, R.: Stability analysis of regenerative queues. Autom. Remote Control 70, 1977–1991 (2009). https://doi.org/10.1134/S0005117909120066

    Article  MathSciNet  MATH  Google Scholar 

  7. Akutsu, K., Phung-Duc, T.: Analysis of retrial queues for cognitive wireless networks with sensing time of secondary users. In: Phung-Duc, T., Kasahara, S., Wittevrongel, S. (eds.) QTNA 2019. LNCS, vol. 11688, pp. 77–91. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-27181-7_6

    Chapter  Google Scholar 

  8. Down, D.G., Lewis, M.E.: Dynamic load balancing in parallel queueing systems: stability and optimal control. Eur. J. Oper. Res. 168, 509–519 (2006)

    Article  MathSciNet  Google Scholar 

  9. Tsai, Y.C., Argon, N.T.: Dynamic server assignment policies for assembly-type queues with flexible servers. Naval Res. Logist. 55(3), 234–251 (2008)

    Article  MathSciNet  Google Scholar 

  10. Tekin, E., Hopp, W.J., Van Oyen, M.P.: Pooling strategies for call center agent cross-training. IIE Trans. 41(6), 546–561 (2009)

    Article  Google Scholar 

  11. Ahghari, M., Balcioglu, B.: Benefits of cross-training in a skill-based routing contact center with priority queues and impatient customers. IIE Trans. 41, 524–536 (2009)

    Article  Google Scholar 

  12. Agnihothri, S.R., Mishra, A.K., Simmons, D.E.: Workforce cross-training decisions in field service systems with two job types. J. Oper. Res. Soc. 54(4), 410–418 (2003)

    Article  Google Scholar 

  13. Ahn, H.-S., Duenyas, I., Zhang, Q.R.: Optimal control of a flexible server. Adv. Appl. Probab. 36, 139–170 (2004)

    Article  MathSciNet  Google Scholar 

  14. Stolyar, A.L., Tezcan, T.: Control of systems with flexible multi-server pools: a shadow routing approach. Queueing Syst. 66, 1–51 (2010). https://doi.org/10.1007/s11134-010-9183-0

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematical Research Karelian Research Centre RAS, Petrozavodsk, Russia

    Stepan Rogozin & Evsey Morozov

  2. Petrozavodsk State University, Petrozavodsk, Russia

    Stepan Rogozin & Evsey Morozov

  3. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991, Moscow, Russia

    Evsey Morozov

Authors
  1. Stepan Rogozin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evsey Morozov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Tomsk State University, Tomsk, Russia

    Alexander Moiseev

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Rogozin, S., Morozov, E. (2021). Stability Condition of a Multi-class Modified Erlang System. In: Dudin, A., Nazarov, A., Moiseev, A. (eds) Information Technologies and Mathematical Modelling. Queueing Theory and Applications. ITMM 2020. Communications in Computer and Information Science, vol 1391. Springer, Cham. https://doi.org/10.1007/978-3-030-72247-0_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-72247-0_19

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72246-3

  • Online ISBN: 978-3-030-72247-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation