RUS  ENG
Full version
JOURNALS // Dal'nevostochnyi Matematicheskii Zhurnal // Archive

Dal'nevost. Mat. Zh., 2002 Volume 3, Number 1, Pages 52–57 (Mi dvmg115)

Asymptotic invariants in one channel queueing system $G|G|1|\infty$

G. Sh. Tsitsiashvilia, N. V. Markovab

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
b The Birobidzhan teacher training college

Abstract: This paper is devoted to construction and investigation of invariant characteristics of stationary distribution tails of waiting time in queueing systems $M|M|1|\infty$, $G|G|1|\infty$ defined by subexponential distributions. Tails of these distributions are defined with accuracy of slowly varying multipliers. Stationary characteristics invariant to these multipliers are searched. Idea of invariant characteristics construction is based on classification of subexponential distributions suggested by Goldie and Kluppelberg and Karamata theorem and Embrechts-Veraverbeke formula.

UDC: 517.977

MSC: 60K25

Received: 30.12.2001



© Steklov Math. Inst. of RAS, 2025