Many flow asymptotics for TCP with ECN/RED

We briefly review the dynamics of TCP when combined with explicit congestion notification/ECN/REDrandom early detection (ECN/RED). Under the assumption that ECN/RED is utilized at the bottleneck, the TCP congestion control algorithm dynamically adjusts the size of the congestion window (the amount of unacknowledged packets in the network per round-trip) by the following mechanism. In a round-trip, if all the packets transmitted are not marked, then the size of the congestion window is increased by one packet for the next round-trip. On the other hand, if at least one packet is marked in the roundtrip, the congestion window is halved. The probability that the router will mark packets in the buffer depends on the average queue length of the time of packet arrival. The average queue length is calculated by an exponential average filter with large memory to prevent RED from reacting too fast. As a result, consecutive incoming packets into RED are marked with almost identical probability. With these dynamics in mind, we construct a simple discrete-time model which captures basic features of the interaction between TCP and ECN/RED.