In Chapter 9, we introduced the conceptual basis of network design problems, and we illustrated this with the help of a generic model:

{*Find, on an initial network G* = *(X,E), which defines a support topology, an infrastructure vector z ≥ 0 ∈ Z and a multiflow f = (f _{i} i in I) ≥ 0 such that:*

– *C1(z) (structural constraints on z, which can be discrete or real and constrained for security reasons; we could for example require of z that it allows the transit of a certain type of message by at least two arc disjoint paths)*.

– *For every arc e in E, z*_{e} ≥ f*_{e} or f* returns an aggregate vector (more often than not the sum) constructed from the components of the multiflow f

– *Each component f*_{i} of the multiflow f transfers a certain average demand Mi from a set of origin vertices O_{i} to a set of destination vertices D_{i}.

*Zmin = U(z) (installation cost) + V(z,f) (operational cost linked to y) + W(z,f) (measure of service failure associated with y) is the smallest possible*.}

We then proposed a taxonomy of network design problems, based on the fact that:

– the importance taken by the *quality of service* (QoS) leads us to introduce performance functions W(x,f) that are more and more complex;

– taking into account the variations in traffic over time leads to the introduction of *dynamic* or *timed* networks [ARO 89, CHAR 96, YAG 73];

– introducing *real and virtual networks ...*

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