Necessary and sufficient conditions for optimal flow control in multirate multicast networks

Abstract

The authors consider the optimal flow control problem in multirate multicast networks where all receivers of the same multicast group can receive service at different rates with different QoS. The objective is to achieve the fairness transmission rates that maximise the total receiver utility under the capacity constraint of links. They first propose necessary and sufficient conditions for the optimal solution to the problem, and then derive a new optimal flow control strategy using the Lagrangian multiplier method. Like the unicast case, the basic algorithm consists of a link algorithm to update the link price, and a receiver algorithm to adapt the transmission rate according to the link prices along its path. In particular if some groups contain only one receiver and become unicast, the algorithm will degrade to their previously proposed unicast algorithm.

Utility max–min fair resource allocation for communication networks with multipath routing

“…Among them, the most successful result in the area of network congestion control and resource allocation is the "Optimal Flow Control"(OFC) approach proposed by Kelly [1]. This pioneer work was further advanced by the researches in single path networks [2,3,4,5,6], multipath networks [7,8,9] and multirate multicast networks [10,11,12].…”

Application-Oriented Flow Control: Fundamentals, Algorithms and Fairness

“…Theorem 1: Suppose the step size is selected to be then the sequence generated by the flow control algorithm (13) and (14) will converge to a limit point , and is the unique optimal solution for the maximization problem (16), (17).…”

“…Therefore, must be increasing and strictly concave. If the step size in (13) is selected to be appropriately small, the sequence generated by the dual algorithm (13) and (14) will solve the maximization problem (16), (17). Let…”

“…Let , any sequence generated by the gradient projection algorithm (13) converges to a limit point , which is the optimal solution for the dual problem . Meanwhile, is the unique solution for the primal problem (16), (17) (see [31, p. 214]). Thus, the proof of Theorem 1 is complete.…”

“…In [2], the network flow control problem is formulated, for the first time, as an optimization problem and explicit rate flow control algorithm is derived by solving the optimization problem via a link congestion pricing policy. Following this pioneering work, an extensive study of network flow control based on optimization method and game theory has been carried out by network researchers, e.g., [3]- [13] for single-path networks, [14], [15] for multiple-path networks and [16], [17] for multirate multicast networks.…”