## 5 Results and Discussion  
In this section we provide simulation results that compare the performance of the proposed path selection schemes with the SP. In the evaluation of our strategies, results are plotted with burst loss values normalized to the number of bursts that enter the network backbone against the average load. The graphs presented in Figures 11 to 14 show the performance of our MCL, MEC and SBPR strategies applied to the four networks represented in Figure 7 having its nodes equipped with wavelength converters, _i.e._, where, on a contending situation, the contending burst can have its wavelength changed, as a measure of last resort, before being dropped. These graphs show that the plotted burst loss values for the proposed strategies are always bellow the reference curve for the SP routing, whose plotted values are in agreement with the ones generally presented in literature [10]. This means that the optimization effort required by the strategies is being productive in reducing contention, resulting clearly in better performance with respect to burst loss. These graphs show also that burst loss values decrease from Figure 11 to 14. Taking into account that simulations were done under absolutely similar conditions with regard to the number of bursts generated per source node (\(1\times 10^{6}\)), arrival pattern, traffic load variation, and number of \(K\) shortest paths per pair of nodes being provided to each strategy, we assume that the progressive gain of the proposed algorithms is also related with the way nodes are connected in OBS networks. In fact, these graphs are presented in ascending order of physical connectivity (see Table 1), which corroborates the work in [68] where the influence of nodal degree on the performance of OBS networks is analyzed. These algorithms are, therefore, more efficient in highly connected networks, and this explains why they provide better results for the COST239 topology than for the ARPANET topology. Among the three proposals the SBPR presents almost always the best performance, which means that reducing the number of upstream links competing for the same downstream link by balancing the potential load at the output links is more productive than the approaches in MCL and MEC. It is worth pointing out that this results from SBPR are obtained with an ILP problem that converges to an optimal solution in less then one second, like it is mentioned in Table 2 where the CPLEX total root+branch&cut time spent is reported (except for MEC). Results show also that MEC behaves almost always better than MCL, but the algorithm of MEC is significantly more expensive in terms of computation complexity,considering the sizes of the instances of the optimization problems both in terms of number of constraints and number of relevant variables involved (see Table 2). In fact, the ILP formulation of the MEC algorithm is so heavy that its optimization stage was intentionally terminated after a solution has been found bellow 1% of the optimal value, rendering what can be considered a _near-optimal_ solution obtained in some tens of minutes. The exception to the prevalence of MEC over MCL is the case of the COST239 network where the opposite happens, probably because its high connectivity makes it possible to obtain alternative paths with a similar reduced number of hops. In fact, alternative longer paths means more possibilities of contention, and potentially higher values of burst loss. For these reasons, and considering that the algorithm of SBPR is also light in terms of computation, SBPR can be considered the best choice for the networks under test, in particular for the more connected ones, where lower levels of burst loss can be achieved. This routing strategies may serve as a basis for the development of QoS policies.