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Ergodicity of a polling network

Author

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  • Borovkov, A. A.
  • Schassberger, R.

Abstract

The polling network considered here consists of a finite collection of stations visited successively by a single server who is following a Markovian routing scheme. At every visit of a station a positive random number of the customers present at the start of the visit are served, whereupon the server takes a positive random time to walk to the station to be visited next. The network receives arrivals of customer groups at Poisson instants, and all customers wait until served, whereupon they depart from the network. Necessary and sufficient conditions are derived for the server to be able to cope with the traffic. For the proof a multidimensional imbedded Markov chain is studied.

Suggested Citation

  • Borovkov, A. A. & Schassberger, R., 1994. "Ergodicity of a polling network," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 253-262, April.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:253-262
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    Cited by:

    1. Menshikov, Mikhail & Zuyev, Sergei, 2001. "Polling systems in the critical regime," Stochastic Processes and their Applications, Elsevier, vol. 92(2), pages 201-218, April.
    2. Saffer, Zsolt & Telek, Miklós, 2009. "Stability of periodic polling system with BMAP arrivals," European Journal of Operational Research, Elsevier, vol. 197(1), pages 188-195, August.

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