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Optimal capacity assignment in message-switched networks subject to end-to-end constraints

A problem of practical importance in the design of message-switched data-communication networks is that of optimal capacity assignment. The problem consists of specifying the capacity for each link in a network in order to minimize the average message delay subject to a constraint on the total capacity available for assignment. This problem, and its dual in which the total capacity is minimized subject to an average message delay constraint, have been treated in detail in [1-3]. In this short paper, we consider a version of the dual problem in which the minimization is subject to a set of one or more end-to-end average message delay constraints. The motivation for this work stems from the fact that satisfaction of an average message delay constraint may not always provide an acceptable delay for certain source-destination pairs. This would, in general, be the case for communication between nodes which are widely separated in terms of the number of links that messages must traverse from one node to the other.