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

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.