Optimization network flow control and price coordination with feedback: proposal of a new distributed algorithm

The usage of price instruments was found to offer an interesting opportunity for reactive congestion flow control in communication or computer networks where the objective is to maximize the total utility of all traffic sources over their transmission rates. The proposed control mechanisms were, amongst others, based on the Price Method—known also as the Interaction Balance Method—and both synchronous and asynchronous versions were developed. It was, however, so far assumed that the transmission network model was known exactly and that no traffic was lost and the traffic routes were fixed and known to the transmitting sources. In this paper, we formulate the flow control problem in a modified form, allowing in particular for the routing decisions to be hidden from the sources, and recall the concept of the Price Coordination with Feedback (known also under the name of the Interaction Balance Method with Feedback—IBMF). It is then shown that the use of this approach allows for proposing the new distributed algorithm for pricing of network services. The existence of an optimal solution in steady state is proved under reasonable assumptions and the convergence issues are discussed. Two examples are provided to illustrate the operation of the proposed algorithm and to compare its performance with the usage of classical price coordination.