# A Privacy-Preserving Routing Protocol Using Mix Networks in Opportunistic Networks
## 4 Evaluation
### Results  
Running the simulations, we could measure the introduced penalty by using the opportunistic-mixnet approach in the three above mentioned scenarios. Figure 2 shows the delivery ratio for each scenario. In each case, the figure shows the delivery ratio based on the number of nodes used in cascade to communicate. 0 mix nodes correspond to the case of not using our opportunistic-mixnet approach. Each line corresponds to a different size for the set \(\mathcal{M}\) of mix nodes. We used sizes corresponding to 100%, 80%, 60%, 40%, and 20% of the total nodes. This size was randomly selected from the whole set of nodes of the network. Similarly, Figure 3 shows the same data, but the selection of the set of mix nodes was performed using node centrality. In general, the selection of nodes with higher centrality as mix nodes provided slightly better results in terms of delivery ratio. This improvement was, however, relatively small in most cases. Using a higher number of nodes as mix nodes, that is, a larger size for set \(\mathcal{M}\), usually provided lower delivery ratios. This is because increasing the number of mix nodes also increases the delay introduced by each. A source node randomly selects mix nodes from \(\mathcal{M}\). With more possible nodes, the distribution of messages for each mix node decreases, and mix nodes need more time to receive their corresponding \(k_{i}\) messages to be able to flush them. Increasing the size of \(\mathcal{M}\) increases the privacy provided by the system, but on the other hand introduces a clear observable penalty. In Figures 4 and 5, we show the latency of delivered messages for each scenario using different sizes for set \(\mathcal{M}\). Those sizes are 80%, 60%, 40%, and 20% of the total number of the node for each case. The delay is also shown for a different number of cascaded mix nodes. As per the previous figures, the 0 number of mix nodes is the case of sending messages without the opportunistic mixnet. Again, Figure 4 shows the case when the set of mix nodes was chosen randomly, and Figure 5 when those nodes were selected by their centrality. Figure 3: Delivery ratio with centrality mix nodes. Figure 2: Delivery ration with random mix nodes. The obtained results in this case are analogous to the ones observed for the delivery ratio. When using nodes on the basis of their centrality as mix nodes, we obtained slightly better results. The same happens for smaller sizes of set \(\mathcal{M}\). Overall, the introduced penalty by using the opportunistic-mixnet approach was not very large, and could easily be tolerable in most scenarios and applications of opportunistic networks. In Tables 2 and 3, we can see the overhead ratio of our proposed mix networks methods with random and centrality mix nodes. The overhead ratio can be exploited to present the volume of used network resources to deliver a message to its receiver. From the result, we can see that the overhead ratio of the Taxis scenario was much higher than those of the Cambridge and Info5 scenarios. The main reason is that there are more nodes in the Taxis scenario compared with in the two other scenarios, which leads to more relayed messages during transmission. This also shows that the number of mixes had more of an effect on the overhead ratio of the Taxis scenario than those of the Cambridge and Info5 scenarios. We can also check the average routing-step path length in each case, that is, the number of hops that a message needs to traverse between each mix node. This is shown in Tables 4 and 5 when selecting mix nodes randomly or on the basis of their centrality, respectively. In general, the path length for each step is kept constant, and the use of the mix nodes does not increase such length. Obviously, as the number of nodes increases, the number of paths from source to destination also increases, e.g., if we have an average step-path length of 4, using one mix node results in path length of 8, and using 3 results in overall path length of 12.