On utility‐optimised router‐level bandwidth allocation

Kelly's network utility maximisation (NUM) problems and solutions are aimed to maximise the aggregate utility subject to link capacity constraints. They are formulated and solved by using the individual flow rate vector. Because of the architecture of the current networks such as the Internet, the individual flow rates are generally not measurable directly at the routers for the network service provider. However, the aggregate flow rates are more convenient to obtain and to adjust. In this paper, we still study the NUM problems for communication networks but from a router-level bandwidth allocation standpoint. With the use of the generalised matrix inverse, we propose a general model of utility-optimised router-level bandwidth allocation and its solution, where the objective function and the constraints are formulated in terms of the aggregate flow rate vector rather than from the individual flow rate vector as in the usual NUM problem. We find that the new proposed models are equivalent to Kelly's NUM model in the sense that they lead to the same optimum and their solutions satisfy the given routing scheme. We also discuss the special cases where the routing matrix is of full row rank and where there is one single-hop flow in every link in the network. We suggest a direct application to Internet Protocol-based virtual private network of the latter case. We present the mathematical models and solution procedures that lead to the utility-optimised aggregate flow rate vector and further illustrate them by numerical examples. We believe our approach is promising for deployment in communication networks. Copyright © 2012 John Wiley & Sons, Ltd.