An Information Theoretic Approach for Systems with Parallel Distributions: Case Studying Internet Traffic

The principle of Minimum Relative Entropy (MRE) is applied to characterize a ‘proportionality’ relationship between the state probabilities of infinite and finite capacity queues at equilibrium and thus, establish an information theoretic interpretation for the exact global balance solution of some finite capacity queues with or without correlated arrival processes. This result serves to establish the utility of the MRE inference technique and encourage its applicability to the analysis of more complex, and thus more realistic, queuing systems. The principles of Maximum Entropy (ME) and MRE are then employed, as least-biased methods of inference, towards the analysis of a Internet link carrying realistic TCP traffic, that exhibit this ‘proportionality’ relationship between a finite and infinite buffer system, as produced by a large number of connections. The analytic approximations are validated against exhaustive simulation experiments. Despite its simplicity, the methodology captures the behavior of the system under study both in the cases of finite and infinite buffers and finally and can easily be utilized for network management and design, capacity planning, and congestion control.