An approximate calculation of max-min fair throughputs for non-persistent elastic flows

The general problem we consider is the analysis of a model in which there are several routes in a network, on each route elastic flows arrive randomly according to some arrival process, and each flow transfers a finite volume of data sampled from some distribution. We are interested in computing a measure of average flow throughput on each route, for a given bandwidth sharing mechanism. Such models arise in problems of network dimensioning and traffic engineering. In this paper, we assume Poisson arrivals of file transfer requests on each route, the transfer volumes are fluid and arbitrarily distributed. At each instant the network shares the bandwidth among the ongoing flows according to the max-min fair bandwidth sharing mechanism, i.e., Instantaneous Max-Min Fair (IMMF) sharing. The measure of performance we consider is the time average bandwidth obtained by flows on each route. We propose a heuristic algorithm for obtaining an approximation for this performance measure for arbitrary routes in an arbitrary network topology. Simulations with various network topologies are used to evaluate the proposal. In spite of its simplicity, we find that the approximation works quite well in a variety of topologies that we have studied.