By Gianni Gilardi

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**Example text**

3. 3), respectively.

For each vertex v with multiple outgoing arcs we introduce time-dependent distribution rates Av,e (t), v ∈ Vd , where Vd ⊂ V denotes the set of dispersing intersections. The functions Av,e (t) are required to satisfy 0 ≤ Av,e (t) ≤ 1 and e∈δv+ Av,e (t) = 1 for all times t > 0. Those rates describe the distribution of the incoming flux among the outgoing processors and are later subject to optimization; see Chapter 7. 2. 2. Network with distribution rates A1,2 (t) and A2,6 (t). Before we pay attention to detailed application of distribution rates we focus on the different equations governing the flow on the network.

In other words, we have the following proposition. 7. 9). Then the production rate vector M converges to a vector (µ, ¯ . . , µ) ¯ for some µ¯ > 0. 5 Summary We have introduced a model for supply networks consisting of a finite set of variables representing good inventory levels and supplier production rates. Interactions among these variables are given by the network structure, while their evolution is ruled by ordinary differential equations. Such an approach has the advantage of representing the network status in a quite compact way, still leaving the possibility of managing oscillations in production rates and inventory levels.