Bi-Path Networks and Multicommodity Flows

This paper considers the feasibility of simultaneous multicommodity flows with specified values in a capacity-limited communication network. A class of "bi-path networks" is defined and some basic topological properties of such networks are derived. It is shown that a bi-path network
B
satisfies a requirement matrix
\bar{R}
if, and only if, the value of each simple cutset in
B
is no smaller than the corresponding cutset value in the "requirement network"
R
. This result can be readily extended to the case with time-varying requirements. The optimal synthesis can be solved using linear programming techniques if linear cost can be assumed.