Light traffic derivatives via likelihood ratios

Author

Reiman, Martin I. ; Weiss, Alan

Author_Institution

AT&T Bell Lab., Murray Hill, NJ, USA

Volume

35

Issue

3

fYear

1989

fDate

5/1/1989 12:00:00 AM

Firstpage

648

Lastpage

654

Abstract

The steady-state behavior of open queuing systems with Poisson arrival processes in light traffic, that is, as the arrival rate tends to zero, is considered. Expressions are provided for the derivatives with respect to the arrival rate of various quantities of interest (such as moments of steady-state sojourn times and queue lengths), evaluated at an arrival rate of zero. These expressions are obtained using the regenerative structure of the queuing system and a change-of-measure formula based on likelihood ratios. The derivatives, which can be used in interpolation approximations, can be evaluated analytically in simple cases and by simulation in general

Keywords

queueing theory; telecommunication traffic; Poisson arrival processes; arrival rate; change-of-measure formula; interpolation approximations; light traffic derivatives; likelihood ratios; open queuing systems; queue lengths; regenerative structure; steady-state behavior; steady-state sojourn times; Analytical models; Extraterrestrial measurements; Interpolation; Q measurement; Random variables; Steady-state; Stochastic processes; Stochastic systems; Time measurement; Traffic control;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.30987

Filename

30987