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1 results

  • Polling systems with periodic server routeing in heavy traffic: distribution of the delay

  • Part of
  • Tava Lennon Olsen, R. D. van der Mei
  • Journal:
    Journal of Applied Probability / Volume 40 / Issue 2 / June 2003
    Published online by Cambridge University Press:
    14 July 2016, pp. 305-326
    Print publication:
    June 2003

  • We consider polling systems with mixtures of exhaustive and gated service in which the server visits the queues periodically according to a general polling table. We derive exact expressions for the steady-state delay incurred at each of the queues under standard heavy-traffic scalings. The expressions require the solution of a set of only M—N linear equations, where M is the length of the polling table and N is the number of queues, but are otherwise explicit. The equations can even be expressed in closed form for several routeing schemes commonly used in practice, such as the star and elevator visit order, in a general parameter setting. The results reveal a number of asymptotic properties of the behavior of polling systems. In addition, the results lead to simple and fast approximations for the distributions and the moments of the delay in stable polling systems with periodic server routeing. Numerical results demonstrate that the approximations are highly accurate for medium and heavily loaded systems.