School Seminars and Colloquia

Continuity theorems for the $M/M/1/n$ queueing system

Stochastic Processes Seminar Series

by Professor Vyacheslav M. Abramov

Institution: School of Mathematical Sciences, Monash University
Date: Thu 7th July 2005
Time: 1:15 AM
Location: Room 213, Richard Berry Building

Abstract: In this report continuity theorems are discussed for the number of
losses during a busy period of the $M/M/1/n$ queue, when the
service time probability distribution, slightly different in
certain sense from the exponential distribution, is approximated
by that exponential distribution. Continuity theorems are obtained
in the form of one or two-side stochastic inequalities. In this
discussion we show how the bounds of these inequalities are
changed if one or other assumption, associated with specific
properties of the service time distribution (precisely described
in the report), is done. Specifically, some parametric families of
service time distributions are discussed, and uniform estimations
(given for all possible values of the parameter) and local
estimations (where the parameter is fixed and takes only the given
value) are established. The analysis of the report is based on the
level crossing approach and some characterization properties of
exponential distribution.

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