Analysis of Power-law Queues Using Maximum Entropy Framework: An Application to Performance Evaluation of Network Systems

Abstract

Extensive research on traffic of modern communication networks including Internet and wireless establish the presence of power-law behavior. However, developing traffic models capturing power-law characteristics is a difficult task due to analytical intractability. Adopting maximum entropy approach, a theoretical model Pow/Pow/1/∞ has been proposed recently. The paper extends the framework to build two new theoretical models Pow/Pow/1/K and Pow/Pow/K/K where both inter-arrival and service times follow power law distribution. Closed form expressions of queue length distribution and various performance measures are derived in terms of traffic intensity ρ. An explicit expression for state probability distribution of Pow/Pow/K/K is also derived and compared with well-known Erlang loss formula. Both queue length distribution and blocking probability are found to depict power-law implying that increasing buffers have little impact on improving the performance of systems in these cases. Numerical computations reveal that the mean queue length explodes as ρ tends to 0.5 resulting in longer delay. The variance of number of packets also depicts sharp rise 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 models are useful in designing networks, dimensioning resources and developing congestion control algorithms.