In a class of minimum cost flow control (MCFC) algorithms for adjusting session rates or window sizes congestion control is achieved through consideration of an incremental cost function that addresses link congestion, and an incremental cost function that addresses the cost of providing less than the desired transmission rate. A coarse version of the algorithm is geared towards implementation in the current Internet, relying on the end-to-end packet loss observations as indication of congestion. A more complete version anticipates an Internet where sessions can solicit explicit congestion information through a concise probing mechanism.