Bimodal packet distribution in loss systems using maximum Tsallis entropy principle

A theoretical model of loss system is proposed and analysed within the framework of maximum Tsallis entropy principle. The study provides an explicit expression for state probability distribution of packets in presence of long-range dependent traffic. The unimodal state probability distribution corresponding to well-known Erlang's loss formula is recovered for Tsallis entropy parameter q = 1. As the parameter q is lowered from unity, it is shown that the state probability distribution makes a transition from unimodal to bimodal. The emergence of bimodality can be regarded as a consequence of long-range dependence. The implication of the model in the design of loss systems is discussed.