Performance Analysis of Pow/Pow/1/∞ Queue Under Heavy Network Traffic Using Maximum Entropy Approach

A theoretical queueing model Pow/Pow/1/∞ with power law distributed inter-arrival and service times is proposed to investigate the performance of nodes in computer communication networks. Closed form expressions for queue length distribution and various performance measures such as mean queue length, variance of number of packets, overflow probability and average waiting time are derived in terms of traffic intensity ρ. The queue length distribution is found to depict power law. Numerical analysis of performance measures provide useful insights into the behavior of network nodes. Both mean queue length and average waiting time increase to infinite as ρ tends to 0.5 resulting in long delay at network nodes. The variance of number of packets also starts exploding as ρ approaches to 0.3. These results are in close agreement with the empirical studies carried out on real traffic traces in the past. The proposed model is useful in designing networks, dimensioning resources and developing congestion control algorithms.