  This paper discusses the problem of maximizing the total data transmission
utility of the computer network. The total utility is defined as the sum of the
individual (corresponding to each node in the network) utilities that are
concave functions of the data transmission rate. For the case of non-strongly
concave utilities, we propose an approach based on the use of a fast gradient
method to optimize a dually smoothed objective function. As an alternative
approach, we introduce stochastic oracles for the problem under consideration
and interpret them as the messages on the state of some individual node to use
randomized switching mirror descent to solve the problem above. We propose
interpretations of both described approaches allowing the effective
implementation of the protocols of their operation in the real-life computer
networks environment, taking into account the distributed information storage
and the restricted communication capabilities. The numerical experiments were
carried out to compare the proposed approaches on sythetic examples of network
architectures.
