Min-max vs. max-min flow control algorithms for optimal computer network capacity assignment

摘要

The theory for optimally assigning capacities to the links of a store forward computer communication network is developed by the minimization of the maximum of two groupings of all link capacities previously assigned to the network. The MIN-MAX and MAX-MIN Algorithms developed have both local and global properties. The basic mathematical structure of the local section of the MIN-MAX Algorithm is derived from the Lagrange Multiplier technique for minimizing convex functions, or the Kuhn-Tucker method for constrained minimization solutions, and the constraints imposed by the functional structure definitions. Since the MIN-MAX Algorithm attains the optimal minimized delay assignment by minimization of the Min-Max assignment, the aspects of its relation to the MAX-MIN Algorithms, the Min-Max inequality and the of both algorithms offers an option for considering all possible, allowed link assignment combinations (2n - 2) of the n capacities available to further minimize delay.