Asymptotic behavior of heterogeneous TCP flows and RED gateway

We introduce a stochastic model of a bottleneck ECN/RED gateway under a large number of heterogeneous TCP flows, i.e., flows with diverse round-trip delays and session dynamics. We investigate the asymptotic behavior of the system and show that as the number of flows becomes large, the buffer dynamics and aggregate traffic simplify and can be accurately described by simple stochastic recursions independent of the number of flows, resulting in a scalable model. Based on the Central Limit analysis in the paper, we identify the sources of fluctuations in queue size and describe the relationship between the system parameters such as the marking function and variance of queue size. A closed-form approximation for the mean queue size as a function of system parameters is provided from a simple steady-state analysis. Numerical examples are provided to validate our results.