Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 4, Pages 371-392
Transient analysis of a queue with queue-length dependent MAP and its application to SS7 network
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.
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 th arrival packet. Before we study this complex
model, first we give a transient analysis of an 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.