Analysis of Discrete Time Queueing Networks under Buffer Threshold Scheme

This paper presents a framework for the performance analysis of queueing networks under active queue management scheme. The analysis is based on a queue-by-queue decomposition technique where each queue is modelled as a GGeo/GGeo/1/{N₁, N₂} queue with single server, R (R = 2) distinct traffic classes, N₁ as the buffer threshold and N₂ as full buffer capacity under first-come-first-serve (FCFS) service rule. Two classes of traffic represent the arrival of the single class Internet traffic before and after the threshold N₁, respectively. The use of queue thresholds is a well known technique for network traffic congestion control. The external traffic is modelled using the Generalised Geometric (GGeo) distribution which can capture the bursty property of network traffic. The analytical solution is obtained using the Maximum Entropy (ME) principle. The forms of the state probabilities and blocking probabilities are analytically established at equilibrium via appropriate mean value constraints. Initial numerical results demonstrate the credibility of the proposed analytical solution.