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

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Han S. Kim  and
Ness B. Shroff
Han S. Kim*
Affiliation:
Purdue University
Ness B. Shroff*
Affiliation:
Purdue University
*
∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA.
∗ Postal address: School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907-1285, USA.
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Abstract

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.

Keywords

Overflow probabilityloss ratioasymptotic relationship

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 4 , December 2001 , pp. 836 - 863
Copyright
Copyright © Applied Probability Trust 2001 

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