This paper considers a stochastic model of a window flow control scheme with Explicit Congestion Notification (ECN). Routers detect incipient congestion by computing the average queue size, and set the ECN bit in the packet headers when the average queue size exceeds a certain threshold. Then, the ECN bit sometimes may not be set from router error. If the ECN bit is not set from the absence of congestion, the number of packets, which corresponds to a window size, is successively transmitted to a client by a web server. If it is set from the presence of congestion, the number of packets, which correspond to half of the first window size, are transmitted. The mean time-until packet transmissions succeed is derived. An optimal policy which maximizes the amount of packets per unit of time until the transmission succeeds is analytically discussed. Finally, numerical examples axe given. been already proposed [3]. A window flow control scheme with ECN mechanism has also been discussed in our previous work [4]. Routers detect incipient congestion by computing the average queue size, and set the ECN bit in the packet headers when the average queue size exceeds a certain threshold. Then, if the ECN bit is not set from router error, the error of ECN message may cause a mistake of the window flow control. This paper considers a stochastic model of a communication system using a window flow control scheme considering error of ECN message: If the ECN bit is not set from the absence of congestion, the number of packets, which corresponds to a window size, is successively transmitted to a client by a web server. If it is set from the presence of congestion, the number of packets, which correspond to half of the first window size, are transmitted. The mean time until packet transmissions succeed is derived. An optimal policy which maximizes the amount of packets per unit of time until the transmission succeeds is analytically discussed. Finally, numerical examples are given.
