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Stability of multi-server polling system with server limits

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Abstract

We consider a multi-server polling system with server limits, that is the number of servers that can attend a queue simultaneously is limited. Stability conditions are available when service policies are unlimited. The definition of stability conditions when both server limits and limited service policies apply remains an open problem. We postulate a conjecture for the stability condition in this case that is supported by our simulation results. The study of this particular variant of the multi-server polling system is motivated by the performance evaluation of next generation passive optical access networks.

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References

  1. Antunes, N., Fricker, C., Robert, P., Roberts, J.: Traffic capacity of large WDM passive optical networks. In: 22th International Teletraffic Congress (ITC 22), Amsterdam, September 2010

    Google Scholar 

  2. Borst, S.C., van der Mei, R.D.: Waiting time approximations for multiple-server polling systems. Perform. Eval. 31, 163–182 (1998)

    Article  Google Scholar 

  3. Dai, J.G.: On positive Harris recurrence of multiclass queueing networks: a unified approach via fluid limit models. Ann. Appl. Probab. 5(1), 49–77 (1995)

    Article  Google Scholar 

  4. Delcoigne, F., Fayolle, G.: Thermodynamical limit and propagation of chaos in polling systems. Markov Process. Relat. Fields 5(1), 89–124 (1999)

    Google Scholar 

  5. Down, D.: On the stability of polling models with multiple server. J. Appl. Probab. 35(4), 925–935 (1998)

    Article  Google Scholar 

  6. Foss, S., Kovalevskii, A.: A stability criterion via fluid limits and its application to a polling system. Queueing Syst. 32, 131–168 (1999)

    Article  Google Scholar 

  7. Fricker, C., Jaibi, M.R.: Monotonicity and stability of periodic polling models. Queueing Syst. 15, 211–238 (1994)

    Article  Google Scholar 

  8. Fricker, C., Jaibi, M.R.: Stability of multi-server polling models. INRIA Research report, No. 3347, January 1998. Available at ftp://ftp.inria.fr/INRIA/publication/dienst/RR-3347.pdf

  9. Kovalevskii, A.P.: Positive recurrence and optimization of polling systems with several servers. Aktual. Probl. Sovrem. Mat. 3, 75–86 (1997)

    Google Scholar 

  10. Maier, M.: WDM passive optical networks and beyond: the road ahead [invited]. IEEE/OSA J. Opt. Commun. Netw. 1(4), C1–C16 (2009)

    Article  Google Scholar 

  11. van der Mei, R.D., Borst, S.C.: Analysis of multiple-server polling systems by means of the power-series algorithm. Stoch. Models 13(2), 339–369 (1997)

    Article  Google Scholar 

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Authors and Affiliations

  1. University of Algarve/CEMAT and INRIA Paris-Rocquencourt, Campus de Gambelas, 8005-139, Faro, Portugal

    Nelson Antunes

  2. INRIA Paris-Rocquencourt, Domaine de Voluceau, 78153, Le Chesnay, France

    Christine Fricker & James Roberts

Authors
  1. Nelson Antunes
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  2. Christine Fricker
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  3. James Roberts
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Correspondence to Christine Fricker.

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Antunes, N., Fricker, C. & Roberts, J. Stability of multi-server polling system with server limits. Queueing Syst 68, 229–235 (2011). https://doi.org/10.1007/s11134-011-9254-x

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  • DOI: https://doi.org/10.1007/s11134-011-9254-x

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