Theory of uncontrollable flows – a new type of network-flow theory as a model for the 21st century of multiple values

A new type of network flow theory is proposed, where no cancellation of flows in an edge is admitted when two or more flows are superposed. It offers a general framework in which to discuss congestion, blocking flows, etc., in a network. We will call the flows in this framework ‘uncontrollable flows’ because they possess some basic properties of the flows which selfish and stubborn users, or users in emergency situations, generate in a network. The primary aim of this paper is not to develop ‘mathematics’ but to introduce a new viewpoint from which to give another look at network flow problems. However, a number of interesting and challenging mathematical problems naturally arise in so doing. What kind of practical problems will be the dual of the concept of uncontrollable flows is also briefly discussed.