Performance Analysis of Novel Overload Control with Threshold Mechanism

Abstract

We propose a novel overload control method with hysteresis property; that is, we analyze theM/G/1/Kqueueing system where the service and arrival rates are varied depending on the queue-length. We use two threshold values:L1(≤L2)andL2(≤K). When the queue-length increases by an amount betweenL1andL2, 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 exceedsL2with 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.