We present methods for analyzing continuous-time multi-channel queueing systems with Gated, Exhaustive, or Globally-Gated service regimes, and with Cyclic, Hamiltonian or Elevator-type polling mechanisms. We discuss issues of dynamically controlling the server's order of visits to the channels, and derive easily implementable index-type rules that optimize system's performance. Future directions of research are indicated.


Multi-channel queueing systems polling gated exhaustive globally-gated conservation laws Hamiltonian tours Elevator polling dynamic control 


  1. 1.
    Altman, E., Blanc, H., Khamisy, A., Yechiali, U.: Gated-type polling systems with walking and switch-in times. Technical Report, Dept. of Statistics & OR, Tel Aviv University 1992.Google Scholar
  2. 2.
    Altman, E., Khamisy, A., Yechiali, U.: On elevator polling with globally-gated regime. Queueing Systems 11 (1992) 85–90.Google Scholar
  3. 3.
    Altman, E., Yechiali, U.: Polling in a closed network. Technical Report SOR-92-14, Dept. of Statistics & OR, New York University 1992.Google Scholar
  4. 4.
    Altman, E., Yechiali, U.: Cyclic Bernoulli polling. ZOR-Methods and Models of Operations Research 38 (1993).Google Scholar
  5. 5.
    Boxma, O.J.: Workloads and waiting times in single-server systems with multiple customer classes. Queueing Systems 5 (1989) 185–214.Google Scholar
  6. 6.
    Boxma, O.J.: Analysis and optimization of polling systems. In: Cohen, J.W., Pack, CD. (Eds.) Queueing, Performance and Control in ATM. North-Holland, 1991, pp.173–183.Google Scholar
  7. 7.
    Boxma, O.J., Groenendijk, W.P.: Pseudo conservation laws in cyclic service systems. Journal of Applied Probability 24 (1987) 949–964.Google Scholar
  8. 8.
    Boxma, O.J., Levy, H., Yechiali, U.: Cyclic reservation schemes for efficient operation of multiple-queue single-server Systems. Annals of Operations Research 35 (1992) 187–208.Google Scholar
  9. 9.
    Boxma, O.J., Weststrate, J.A., Yechiali, U.: A globally gated polling system with server interruptions, and applications to the repairman problem. Probability in the Engineering and Informational Sciences 7 (1993).Google Scholar
  10. 10.
    Browne, S., Yechiali, U.: Dynamic priority rules for cyclic-type queues. Advances in Applied Probability 21 (1989a) 432–450.Google Scholar
  11. 11.
    Browne, S., Yechiali, U.: Dynamic routing in polling systems. In: M. Bonatti (Ed.) Teletraffic Science for New Cost-Effective Systems, Networks and Services. North-Holland, 1989b, pp.1455–1466.Google Scholar
  12. 12.
    Browne, S., Yechiali, U.: Scheduling deteriorating jobs on a single processor. Operations Research 38 (1990) 495–498.Google Scholar
  13. 13.
    Browne, S., Yechiali, U.: Dynamic scheduling in single-server multiclass service systems with unit buffers. Naval Research Logistics 38 (1991) 383–396.Google Scholar
  14. 14.
    Browne, S., Weiss, G.: Dynamic priority rules when polling with multiple parallel servers. Operations Research Letters 12 (1992) 129–137.Google Scholar
  15. 15.
    Cooper, R.B. Murray, G.: Queues served in cyclic order. Bell System Technical Journal 48 (1969) 675–689.Google Scholar
  16. 16.
    Cooper, R.B.: Queues served in cyclic order: waiting times. Bell System Technical Journal 49 (1970) 399–413.Google Scholar
  17. 17.
    Eisenberg, M.: Queues with periodic service and changeover time. Operations Research 20 (1972) 440–451.Google Scholar
  18. 18.
    Ferguson, M.J., Aminetzah, Y.J.: Exact results for nonsymmetric token ring systems. IEEE Transactions on Communications 33 (1985) 223–231.Google Scholar
  19. 19.
    Kleinrock, L.: Queueing Systems, Vol. 1: Theory. John Wiley, 1975.Google Scholar
  20. 20.
    Konheim, A.G., Levy, H., Srinivasan: Descendant set: an efficient approach for the analysis of polling systems. IEEE Transactions on Communications (to appear 1993a).Google Scholar
  21. 21.
    Konheim, A.G., Levy, H., Srinivasan: The individual station technique for the analysis of polling systems. Technical Report, 1993b.Google Scholar
  22. 22.
    Levy, H., Sidi, M.: Polling systems: applications, modeling and optimization. IEEE Transactions on Communications 8 (1990) 1750–1760.Google Scholar
  23. 23.
    Sarkar, D., Zangwill, W.I.: Expected waiting time for nonsymmetric cyclic queueing systems — exact results and applications. Management Science 35 (1989) 1463–1474.Google Scholar
  24. 24.
    Shoham, R., Yechiali, U.: Elevator-type polling systems. Technical Report, Dept. of Statistics & OR, Tel Aviv University, 1992.Google Scholar
  25. 25.
    Takagi, H.: Analysis of Polling Systems. MIT Press, 1986.Google Scholar
  26. 26.
    Takagi, H.: Queueing analysis of polling models: an update. In: Takagi, H. (ed.) Stochastic Analysis of Computer and Communications Systems. North Holland, 1990, pp.267–318.Google Scholar
  27. 27.
    Yechiali, U.: A new derivation of the Khintchine-Pollaczek formula. In: Haley, K.B. (Ed.) Operational Research '75. North Holland, 1976, pp.261–264.Google Scholar
  28. 28.
    Yechiali, U.: Optimal dynamic control of polling systems. In: Cohen, J.W., Pack, C.D. (Eds.) Queueing, Performance and Control in ATM. North Holland, 1991, pp.205–217.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Uri Yechiali
    • 1
  1. 1.Department of Statistics & Operations Research, School of Mathematical Sciences, Sackler Faculty of Exact SciencesTel Aviv UniversityTel AvivIsrael

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