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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 7871624, 8 pages
Research Article

Performance Analysis of Novel Overload Control with Threshold Mechanism

1Department of Applied Mathematics, Halla University, 28 Halla University-gil, Wonju-si, Gangwon-do 26404, Republic of Korea
2Department of System & Management Engineering, Kangwon National University, 1 Kangwondaehak-gil, Chuncheon-si, Gangwon-do 24341, Republic of Korea

Received 30 September 2015; Accepted 30 December 2015

Academic Editor: Jian Guo Zhou

Copyright © 2016 Doo Il Choi and Dae-Eun Lim. 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 propose a novel overload control method with hysteresis property; that is, we analyze the queueing system where the service and arrival rates are varied depending on the queue-length. We use two threshold values: and . When the queue-length increases by an amount between and , we apply one of the following two strategies to reduce the queue-length, either we decrease the mean service time or we decrease the arrival rate. If the queue-length exceeds with one strategy, we apply the other; thus, there are two models that depend on the method that was applied first. We derive the queue-length distribution at departure and at arbitrary epochs using the embedded Markov chain method and the supplementary variable method. We investigate performance measures including the loss probability and mean waiting time using various numerical examples.