Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 371-392
doi:10.1155/S1048953399000325

Transient analysis of a queue with queue-length dependent MAP and its application to SS7 network

Bong Dae Choi,1,4 Sung Ho Choi,1 Dan Keun Sung,2 Tae-Hee Lee,3 and Kyu-Seog Song3

1KAIST, Department of Mathematics and Center for Applied Math, 373-1 Kusong-Dong, Yusong-Gu, Taejon 305-701, Korea
2KAIST, Department of Electrical Engineering, 373-1 Kusong-Dong, Yussong-Gu, Taejon 305-701, Korea
3Korea Telecom, Telecommunications Network Laboratory, 463-1, Junmin-Dong, Yusong-Gu, Taejon 305-390, Korea
4Department of Mathematics, Korea University, Seoul, Korea

Received 1 March 1999; Revised 1 August 1999

Copyright © 1999 Bong Dae Choi et al. 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

We analyze the transient behavior of a Markovian arrival queue with congestion control based on a double of thresholds, where the arrival process is a queue-length dependent Markovian arrival process. We consider Markov chain embedded at arrival epochs and derive the one-step transition probabilities. From these results, we obtain the mean delay and the loss probability of the nth arrival packet. Before we study this complex model, first we give a transient analysis of an MAP/M/1 queueing system without congestion control at arrival epochs. We apply our result to a signaling system No. 7 network with a congestion control based on thresholds.