A theory of convergence order of maxmin rate allocation and an optimal protocol

The problem of allocating maxmin rates with minimum rate constraints for connection-oriented networks is considered. This paper proves that the convergence of maxmin rate allocation satisfies a partial ordering in the bottleneck links. This partial ordering leads to a tighter lower bound for the convergence time for any maxmin protocol. An optimally fast maxmin rate allocation protocol called the distributed constraint precedence graph (CPG) protocol is designed based on this ordering theory. The new protocol employs bi-directional minimization and does not induce transient oscillations. The distributed CPG protocol is compared against ERICA, showing far superior performance.