Stability and Analysis of TCP Connections with RED Control and Exogenous Traffic

In this paper we study the stability and performance of a system involving several TCP connections passing through a tandem of RED controlled queues each of which has an incoming exogenous stream. The exogenous stream, representing the superposition of all incoming UDP connections into a queue, has been modeled as an MMPP stream. We consider both the TCP Tahoe and the TCP Reno versions. We start with the analysis of a single TCP connection sharing a RED controlled queue with an exogenous stream. The effect of the exogenous stream (which is almost always present in large networks) is to cause the system to converge to a stationary distribution from any initial conditions. This stability result holds good for any work conserving discipline. We also obtain the performance indices of the system; specifically the goodputs and the mean sojourn times of the various connections. The complexity involved in computation of performance indices for the system is reduced by approximating the evolution of the average queue length process of the RED queue by a deterministic ODE. Then, by using a decomposition approach of two time scales, we reduce the study of the system to that of a simplified one for which the performance measures can be obtained under stationarity. Finally, we extend the above results to the case when multiple TCP connections share a RED controlled queue with an exogenous stream and to the case when a TCP connection passes through several RED controlled tandem queues each of which has an incoming exogenous stream. We also consider an example of multiple TCPs passing through a tandem of queues. A number of simulation results have been provided which support the analysis.