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1 results

  • On the asymptotic relationship between the overflow probability and the loss ratio

  • Part of
  • Han S. Kim, Ness B. Shroff
  • Journal:
    Advances in Applied Probability / Volume 33 / Issue 4 / December 2001
    Published online by Cambridge University Press:
    01 July 2016, pp. 836-863
    Print publication:
    December 2001

  • In this paper we study the asymptotic relationship between the loss ratio in a finite buffer system and the overflow probability (the tail of the queue length distribution) in the corresponding infinite buffer system. We model the system by a fluid queue which consists of a server with constant rate c and a fluid input. We provide asymptotic upper and lower bounds on the difference between log P{Q > x} and logPL(x) under different conditions. The conditions for the upper bound are simple and are satisfied by a very large class of input processes. The conditions on the lower bound are more complex but we show that various classes of processes such as Markov modulated and ARMA type Gaussian input processes satisfy them.