Optimal routing with packet fragmentation in computer networks

The combined fragmentation-and-routing problem is addressed. Several possible fragmentation machines are discussed, and their equivalence is indicated. This allows the formulation of a comprehensive yet tractable flow model, whose performance measure is total delay. An analysis of this model leads to necessary and sufficient optimality conditions for the fragmentation-and-routing problem. The optimality conditions serve as a baseline for devising several optimal algorithms, both centralized and distributed. In order to deal with minimum first derivative length algorithms, the concept of minimum first derivative paths is generalized in order to accommodate them in the environment used. Several special cases of practical interest are discussed. It is shown the problem size and the running time of the algorithms are considerably shortened in networks in which packet sizes come in a limited number of sizes. The approach can accommodate performance measures other than total delay