Journal of Applied Mathematics and Stochastic Analysis
Volume 7 (1994), Issue 3, Pages 301-330
doi:10.1155/S1048953394000274
Large deviations for tandem queueing systems
Institute for Problems of Information Transmission, Russian Academy of Sciences, 19 Ermolovoj Str. GSP-4 , Moscow 101447, Russia
Received 1 May 1994; Revised 1 July 1994
Copyright © 1994 Roland L. Dobrushin and Eugene A. Pechersky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The crude asymptotics of the large delay probability in a tandem queueing
system is considered. The main result states that one of the two channels in the
tandem system defines the crude asymptotics. The constant that determines the
crude asymptotics is given. The results obtained are based on the large deviation
principle for random processes with independent increments on an infinite
interval recently established by the authors.