q-Exponential product-form solution of packet distribution in queueing networks: Maximization of Tsallis entropy

A maximum Tsallis entropy solution is presented to examine the effect of long-range dependence (LRD) of packet traffic on network of queues. An important finding is that usual product form solution of queueing networks does not hold. However, it is possible to preserve the product like structure in terms of q-product of q-exponential functions. A special case is considered when normalized q-expectation values of first moment and queue utilization at each node are available as the constraint. The joint state probability distribution is shown to depict asymptotically power law behavior.