On the Fastest Route for Convoy-Type Traffic in Flowrate-Constrained Networks

Abstract

Flows of convoy-type traffic through networks whose arcs are characterized by both travel times and flowrate constraints are investigated. Suggested here, in particular, is the notion of a “flowrate-constrained fastest path”—a path by means of which the entirety of a volume of traffic, initially located at a source, node, can arrive at a sink in as short a time as possible when all traffic must flow along the same path and rates of flow along arcs are limited by flowrate constraints. Unlike the usual fastest path problems (those in networks without flowrate constraints), flowrate-constrained fastest times and paths both depend, in general, upon the initial volume of traffic at the source node. Several theorems about flowrate-constrained fastest times and paths are stated and proved; it is shown, for example, that such paths are independent of source volume whenever this volume is sufficiently large. Two algorithms for finding flowrate-constrained fastest times and paths are given.