Analysis of a feedback fluid model for heterogeneous TCP sources

In this paper we consider a bottleneck link and buffer used by one or two fluid sources that are subject to feedback. The feedback is such that the model captures essential aspects of the behavior of the Transmission Control Protocol as used in the Internet. During overflow, the buffer sends negative feedback signals to the sources to indicate that the sending rate should be reduced. Otherwise the buffer sends positive signals so as to increase the rate. In this context we find closed form expressions for the solution of the one-source case. The two-source case extends the single-source model considerably: we can control the behavior and parameters of each source individually. This enables us to study the impact of these parameters on the sharing of links and buffers. For the two-source case we solve the related two-point boundary value problem in the stationary case. We also establish a numerically efficient procedure to compute the coefficients of the solution of the differential equations. The numerical results of this model are presented in an accompanying paper.