We study the problem of congestion control in a communication network that is supporting remote estimation of multiple processes. A stochastic rate control protocol is developed using the network utility maximization (NUM) framework. This decentralized protocol avoids congestion by regulating the transmission probabilities of the sources. The presence of estimation costs poses new challenges; however, for low congestion levels, the form of rate controller resembles that of the standard TCP rate controller. Stability of the protocol is analyzed in the presence of fixed network delays. (C) 2013 Elsevier Ltd. All rights reserved.