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In a previous paper, algorithms for optimally routing a single vehicle were presented. In this paper, the problem of routing a fleet of M vehicles serving fixed demand for transportation from many origins to a single destination is considered. The M vehicle General Routing Problem (abbreviated M-GRP) is the core of many real routing problems, such as school bus routing for a single school (many-to-one) and garbage truck routing to a central dump. It is shown that the M-GRP on a given graph is equivalent to a GRP on a modified graph. From this result, it is shown that single vehicle routing algorithms can be applied to the M vehicle routing problem.

The problem of finding optimal routes in a packet-switched computer network can be formulated as a nonlinear multicommodity flow problem.

The functional equation technique has been employed to solve more general “routing” problems, when the route must pass through a number of specified nodes. The method is illustrated by an example.

This paper is concerned with the behavior of an adaptive routing system in a large communications network. The adaptive routing algorithm described uses stochastic switching matrices to automatically find and complete the traffic paths through a system. A realistic network and traffic which were derived from military field exercises are used to illustrate the real time behavior of the algorithm. Simulation experiments indicate that adaptive routing techniques can be effective in large communications networks.

The principles and practice of routing are well established and well known today, 12 years after the conception and 5 years after the introduction of the idea in Western European waters. It is the accelerated rate of change that makes it necessary to review the present situation and consider some permanent form of review, and plan development and improvement when necessary. The changes are technological, social, political and economic. The technological changes seem predictable, are measurable and can be caught in mathematical models, and consequently are ideally suitable for modern research techniques. The econometrist endeavours to do the same with economic changes. The much later application of mathematics to often empirical data is however bound to render results with greater variance in the answers.