Linear programming based routing design for a class of positive systems with piecewise constant capacity constraints

We present a technique to design routing parameters for positive compartmental conservative systems with capacity constraints. Such systems describe the flow of material through a network of interconnected reservoirs and have become popular, in particular, as models of air traffic flows. The technique presented here is a Linear Programming based method to design time varying routing parameters to satisfy piecewise constant capacity constraints. Under these routing parameters, the resulting system is positive, conservative and exhibits the desired interconnection.