## 4 Conclusions and Trends
This had in mind the fact that these routing models are common in multiple situations. Note that the models of the two latter types appear typically in routing methods where the route/path calculation and selection cannot be mathematically separated from the assignment of node-to-node traffic flows to the selected paths. This happens in routing models for which the routing method embodies a teletraffic engineering mechanism requiring some form of optimization of the bandwidth demand (associated with different end-to-end services) assignment to the arcsof the paths, seeking, on the one hand, the satisfaction of the demand under certain QoS requirements and, on the other hand, the achievement of some form of global network performance optimization, in terms of different network metrics. Concerning trends and challenges in this research area, as noted above, we begin by noting that the nature of real telecommunication networks is very complex, having in mind that they are organized, in functional, operational and management/control terms, in several interrelated layers, which leads to the necessity of considering them as _multilayer networks_. This raises difficulties in terms of routing modeling when some inter-layer representation is at stake that also may affect the formulation of the corresponding path problems. An example of the way in which this issue could be tackled, in the context of resilient routing models with path protection, is the concept of Shared Risk Link Group that corresponds to the definition, for each possible failure risk in an element of the physical/transport layer, of the set of arcs in the logical layer which are affected by that risk. The specification of these sets assumes that the mapping of the physical layer onto the logical layer is known, so that this information can be incorporated in the mathematical formulation of the path pair (active path and protection path) problem. This of course has a strong impact in the form of the addressed path problem (either single or multiobjective) and in the corresponding resolution approach (as described in some references referred to in the previous section) since it requires that discrete objective functions specified in terms of operations on finite sets be used. In more complex multilayer modelling situations, a useful mathematical tool may be the definition of'multilevel graphs', as proposed in [192]. In most papers concerning applications of MOPP algorithms to multiobjective telecom network routing models, computational experiments considering different types of network environments are presented. Many of these studies are focused on the performance evaluation of the algorithms in terms of CPU times, usually in reference to topological network structures. In multiple cases, these computational studies also analyze the effects of the application of the proposed routing methods in terms of the resulting network performance measures, using some type of simulation of end-to-end service demands, depending on the network technological and architectural context and on relevant features of the network environment. Specific examples of such computational studies are in references [18; 157; 170; 171]. Also, in a few of the methodological papers in Section 2, real-world applications are presented, see for instance [33; 118]. Furthermore, it would be clearly important to evaluate the possible merits and disadvantages of the multiple types of multiobjective routing methods proposed in the literature, in real-world network applications. This would require further empirical studies desirably involving collaborations with network and service operators, on a case by case basis, in the context of future applied research tasks.