Queue dynamics of RED gateways under large number of TCP flows

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Abstract
We consider a stochastic model of a RED gate- way under competing TCP-like sources sharing the capacity. As the number of competing flows becomes large, the queue behavior of RED can be described by a two-dimensional re- cursion. We confirm the result by simulations and discuss their implications for the network dimensioning problem. lytic understanding of TCP and RED is yet to be found. The difficulties arise from the complex behavior of TCP congestion-control, and are further compounded by the random drop mechanism and queue averaging. Detailed modeling of these characteristics results in a number of states which explodes when the number of TCP flows in- crease, making the analysis untractable. In this paper, we present a stochastic model that captures the essential features of TCP, i.e., the gradual adaptive in- crease and the sudden decrease of transmission rate, com- bined with a random drop algorithm similar to RED. We analyze this ersatz model as the number of competing TCP flows becomes large, and show that the stochastic model simplifies in the limit to a two-dimensional recursion. This result suggests that with a large number of flows, it is easy for network operators to estimate the aggregate behavior of TCP flows and to dimension network resources accord- ingly. The remainder of the paper is organized as follows. Sec- tion II describes the stochastic model. Section III present the main asymptotic results for the large number of TCP flows whereby the stochastic model simplifies into a sim- plified limiting recursion. Simulation results supporting this behavior are shown in Section IV. The conclusions of the paper are given in Section V.

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