# Selecting Remote Driving Locations for Latency Sensitive Reliable Tele-Operation
## 3 Selecting Driving Locations for Multiple Paths
### Selecting a Fixed Number of Driving Locations for Smallest Distance
The base stations along the shortest path are considered as the list of based stations between the origin and the destination. Finally, it is well known that the network distances do not belong to a metric space, where a direct distance between two points is always shorter than or equal to an indirect distance through a third point. However, in this evaluation, instead of using the network distance as the distance between a driver location and a base stations, we use the Euclidean distance between the two positions as the distance. The reason is because the network distance is mostly proportional to the geographical distance. However, it should be note that the algorithms proposed in the previous section do not have any specific assumption of the distance space. Thus, the algorithms can be applied to distances from a non-metric space. Now, we evaluate the performance of the proposed algorithms with the environment information generated by the above procedure. ### Performance of the Algorithms for Objective I

As we mentioned earlier, in the first objective, we assume that the remote driving is safe if the latency is under a certain threshold. Under this assumption, we want to minimize the number of remote driving locations. By this way, we can reduce the management cost because we may need to manage fewer number of driving facilities. Thus, we first investigate the performances of RDSMP and ERDSMP whether they find the same number of driving locations or not. Figure 4 shows the average number of remote driving locations found for 1000 randomly selected paths over \(L\) varying from 300 to 500. The number of candidate remote driving locations is 500, i.e., \(|\mathcal{F}|=500\). Both RDSMP and ERDSMP find the same number of remote drivers. \"LAF (Longest Advance First)\" is the algorithm to find the smallest number of remote drivers for a single path [8]. In this evaluation, we just repeat LAF over the multiple paths in \(P\). Then, we compute the union of the results of the repeated LAF executions. As can be seen in Figure 4, LAF generates more remote driving locations over various latency constraints, \(L\). Thus, it clearly shows that running LAF multiple times over \(P\) may not be used for Objective I. Furthermore, since the main objective of proposing ERDSMP is to reduce the average distance for the same number of remote driving locations, we evaluate the average distances of the algorithms. Figure 5 shows the average distances of the three algorithms: RDSMP, ERDSMP, and LAF. Since LAF generates more remote driving locations, it is easily understood that LAF shows smaller average distances. Thus, it is meaningful to compare RDSMP and ERDSMP only. As can be seen in Figure 5, ERDSMP shows smaller average distance from some cases. It is quite intuitive from the design of ERDSMP because in ERDSMP, we check more alternatives in selecting the first remote driving location from the candidate driving locations. Similar distance reduction is found for different numbers of candidate driving locations. We vary the number of candidate remote driving locations from 100 to 500, i.e., \(|\mathcal{F}|=100,\cdots,500\) to see whether this number may affect the result. We fix \(L=300\). Figure 6 shows the average distance over various \(|\mathcal{F}|\). We can see that ERDSMP shows slightly lower average distances over various \(|\mathcal{F}|\). Furthermore, the average distances decrease as the number of candidate remote driving locations increases. It is quite intuitive because as the number of candidate remote driving locations increases, there are more choices to select better remote driving locations. Figure 4: Average number of remote driving locations found for various latency constraints. Figure 5: Average network distance for various latency, L.

### Performance of the Algorithms for Objective II

In Objective II, we want to find the set of \(k\) remote driving locations that shows smaller distance to the base stations.