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Stability and continuity of polling systems

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The stability of a polling system with exhaustive service and a finite number of users, each with infinite buffers is considered. The arrival process is more general than a Poisson process and the system is not slotted. Stochastic continuity of the stationary distributions, rates of convergence and functional limit theorems for the queue length and waiting time processes have also been proved. The results extend to the gated service discipline.

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  1. [1]

    E. Altman, P. Konstantopoulos and Z. Liu, Stability, monotonicity and invariant quantities in general polling systems. Queueing Syst. 11 (1992) 35–57.

  2. [2]

    S. Asmussen,Applied Probability and Queues (Wiley, 1987).

  3. [3]

    P. Billingsley,Convergence of Probability Measures (Wiley, 1968).

  4. [4]

    A.A. Borovkov,Asymptotic Methods in Queueing Theory (Wiley, 1984).

  5. [5]

    A.A. Borovkov, Limit theorems for queueing networks I, Theory Prob. Appl. 31 (1986).

  6. [6]

    W. Bux, Token ring local area networks and their performance, Proc. IEEE 77 (1989) 238–256.

  7. [7]

    P. Franken, D. Konig, V. Arndt and V. Schmidt,Queues and Point Processes (Akademie Verlag, Berlin, 1981).

  8. [8]

    L. Georgiadis and W. Szpankowski, Stability of token passing ring, Queueing Syst. 11 (1992) 7–33.

  9. [9]

    D. Grillo, Polling mechanism models in communication systems-some application examples, in:Stochastic Analysis of Computer and Communications Systems, ed. H. Takagi (Eisevier Science, 1990).

  10. [10]

    A. Gut,Stopped Random Walks (Springer, New York, 1988).

  11. [11]

    O. Hashida, Analysis of multiqueue, Rev. Electr. Commun Labs. 20 (1972) 189–199.

  12. [12]

    V.V. Kalashnikov, Regenerative queueing processes and their qualitative and quantitative analysis, Queueing Syst. 6 (1990) 113–136.

  13. [13]

    J. Keilson,Markov Chain Models-Rarity and Exponentiality (Springer, New York, 1979).

  14. [14]

    A.G. Konheim and B. Meister, Waiting lines and times in a system with polling, J. ACM 21 (1974) 470–490.

  15. [15]

    P.J. Kuehn, Multiqueue systems with nonexhaustive cyclic service, Bell Syst. Tech. J. 58 (1979) 671–698.

  16. [16]

    H. Levy and M. Sidi, Polling systems: Applications, modelling and optimization, IEEE Trans. Commun. COM-38 (1990) 1750–1760.

  17. [17]

    H. Levy, M. Sidi and O.J. Boxma, Dominance relations in polling systems, Queueing Syst. 6 (1990) 155–172.

  18. [18]

    V. Sharma, Stability and continuity analysis of computer networks with nonstationary and/or nonindependent input, Final Report, for ISRO-IISc Space Technology Cell, Bangalore, India (Dec. 1990).

  19. [19]

    V. Sharma, Invariance principles for regenerative and Markov processes with application to queueing networks, submitted.

  20. [20]

    G.B. Swartz, Polling in a loop system, J. ACM 27 (1980) 42–59.

  21. [21]

    H. Takagi,Analysis of Polling Systems (MIT Press, Cambridge, MA, 1986).

  22. [22]

    H. Takagi, Queueing analysis of polling models: An update, in:Stochastic Analysis of Computer and Communication Systems, ed. H. Takagi (Elsevier Science, 1990).

  23. [23]

    H. Thorisson, H., The queueGI/G/1: finite moments of the cycle variables and uniform rates of convergence, Stochast. Proc. Appl. 19 (1985) 85–99.

  24. [24]

    V.S. Zhdenov and E. A. Saksonov, Conditions for existence of steady state modes in cyclic queueing systems, Avt. i. Telemekhania (Feb. 1979) 176–184.

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Sharma, V. Stability and continuity of polling systems. Queueing Syst 16, 115–137 (1994). https://doi.org/10.1007/BF01158952

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  • Polling systems
  • stability
  • stochastic continuity
  • general arrival process
  • functional limit theorems.