Essay in the theory of uncontrolled flows and congestion
A new type of network flow theory is proposed, where only those flows which are representable as a positive sum of elementary-path (or elementary-cycle) flows are considered and 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 about congestion, blocking flows, etc. in a network. We will call the flows in this framework {open_quotes}uncontrollable flows{close_quotes} because they possess some basic properties of the flows which selfish and stubborn users, or users in emergency situations, generate in a network. Primarily, this is not a mathematics paper but one to introduce a new viewpoint from which to give another look at network flow problems. However, a number of interesting mathematical problems naturally arise in so doing: e.g., {open_quotes}Is a given flow uncontrollable{close_quotes}?, {open_quotes}How to determine a blocking flow or a bottleneck cut{close_quotes}?, {open_quotes}Can we design a network in which no congestion may occur{close_quotes}?, {open_quotes}Under what conditions does additional investment on a network improve its function in this framework{close_quotes}?, etc. What kind of practical problems will be the dual of the concept of uncontrollable flows will also be discussed.
- OSTI ID:
- 36152
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0429
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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