Exponents for the tails of distributions in some polling models

Authors:
N. G. Duffield
Affiliations:
AT&T Laboratories, Room A175, 180 Park Avenue, Florham Park, NJ 07932-0971, USA E-mail: duffield@research.att.com
Venue:
Queueing Systems: Theory and Applications
Year:
1997

Citing 3
Cited 2

Analysis of polling systems

Analysis of polling systems
Computing distributions and moments in polling models by numerical transform inversion

Performance Evaluation
Waiting Lines and Times in a System with Polling

Journal of the ACM (JACM)

Asymptotics for M/G/1 low-priority waiting-time tail probabilities

Queueing Systems: Theory and Applications
Exact Asymptotics for ki-limited Exponential Polling Models

Queueing Systems: Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

The tail asymptotics of the distribution of the waiting-time W in some polling models is investigated. When this is of the form \mathrm{P}[Wx]\sim\alpha x^\beta\mathrm{e}^{-\eta x} for some \alpha, \beta, \eta, we show how to calculate the exponents \beta and \eta, and we establish the extent and form of their dependence on the distributions of the service-time and switchover-time. The exponents are expressed in terms of the fixed points and Lyapunov exponents of a dynamical system which we associate with the recursion which is used to calculate the moment generating functions of the waiting time.