Versatile Stochastic Models for Networks with Asymmetric TCP Sources

In this paper we use stochastic Petri nets (SPNs) to study the interaction of multiple TCP sources that share one or two buffers. No analytical nor numerical results have been presented for such cases yet. We use SPNs in an unconventional way: the tokens in the SPN do not represent the packets being sent in the network, but merely model fractions of buffer occupancy and the congestion window sizes. In this way, we use the SPNs to obtain a discretisation of a fluid model for TCP dynamics. Thus, we pair the modelling flexibility of SPNs with the modelling efficiency of fluid models. In doing so, our approach also avoids the (numerical) solution of partial differential equations; instead, just the steady-state solution of a (large) continuous-time Markov chain is required. We first consider two TCP sources sharing a single buffer and evaluate the consequences of two popular assumptions for the loss process in terms of fairness and link utilization. The results obtained with this model are in agreement with existing analytic models. A comparison with (more costly) simulations in ns2 shows that the real loss process is somewhere in between the two loss models. Secondly, we consider a network consisting of three sources and two buffers and study how the sources share the capacity of the links. This leads to an interesting conjecture on fairness in large TCP networks.