Mathematical Sciences - Colloquium

 
A model of a `flexible manufacturing system' under such scheduling policies as `clearing' or `first come, first served' gives an interesting class of dynamical systems. Formerly, it was conjectured that a simple capacity condition sufficed to ensure stability [boundedness, uniform in t, for the state for any initial conditions]. However, it has been possible to construct examples, for each of these policies, which are unstable even though the natural capacity condition is satisfied. On the other hand, for simple flow geometries it is possible to show stability (and estimate performance) for a variety of simple control policies.

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