# Modeling Network-Controlled Device-to-Device Communications in SimuLTE
## 6 Performance Evaluation
### Scenario 3--Selection of the P2 MP transmission horizon  
We now evaluate the impact of setting a finite transmission horizon for P2 MP D2D communications, according to the scenario in Figure 25 and the parameters in Table 4, _Scenario 3_. Five hundred UEs are placed four meters apart along a straight line, covering a distance of 2 km. Radio coverage is provided by five eNBs located at 400 m from each other. The leftmost UE sends 1000 largely spaced packets (one per second), using P2 MP D2D transmissions. All UEs are members of the same multicast group. We recall that P2 MP transmissions are modeled by invoking a sendDirect() for each potential receiver that is within a predefined distance. We initially use an infinite horizon, i.e., all the UEs in the network are added as targets of the sendDirect(). Every configuration is repeated ten times and the reported results are obtained as the average of such repetitions. Figure 26 reports the measured reception probability as a function of the distance from the transmitting UE, along with three vertical lines at 250, 500 and 750 m, representing possible values of the transmission horizon. Setting the horizon to 250 m excludes UEs that would receive with a probability of 20%. With \(h\) = 500 m, instead, we exclude UEs that would receive with 1% probability. With \(h\) = 750 m, only UEs with a reception probability around 0.1% are excluded.  
Figure 24: Application-level throughput of the TCP connection at a MS.  
Figure 25: Simulation scenario for P2 MP D2D transmissions.  
Note, however, that even small differences may be amplified in a multihop scenario. Assume now that we want to ensure that every UE in the first 1000 m receives a message, and program all UEs to relay the message (still using P2 MP D2D transmissions) if they are within 1000 m of the originator. To avoid excessive flooding, the Trickle duplicate suppression protocol is used, so that a UE that receives more than three copies of the message within a 10 ms time window assumes that the neighborhood is already well covered and suppresses relaying [6]. We test what happens by configuring a horizon of 250, 500 and 750 m for each transmission, compared to a baseline with an infinite horizon. Here, we run 10 repetitions with 100 s of simulated time. Figures 27-29 show the probability of reception of UEs outside the 1000 m radius (those within the radius always receive with 100% probability), with a varying horizon \(h\). Obviously, no UE located to the right of \(1000+h\) will receive any packet by definition, since no sendDirect() will target it. Figure 27 shows that setting \(h=250\) m completely overlooks the fact that UEs at, e.g., 1300 m, will receive nearly always in practice. Setting \(h=500\) m, as shown in Figure 28, overlooks UEs whose reception probability is around 10%, 10 times more than in the single-hop case. Finally, setting the horizon to 750 m overlooks UEs whose reception probability is 1%, as depicted in Figure 29. Figure 30 reports the simulation time as a function of the horizon \(h\). We observe that the baseline employs just below 120 min, whereas introducing the transmission horizon abates the simulation time. In particular, the time is reduced by 37% when setting \(h=750\) m.  
The take-home lesson is that limiting the transmission horizon may save a considerable amount of time in dense scenarios. However, the horizon should be set based on the expected residual reception probability, also accounting for multihop effects.  
Figure 26: Reception probability of a P2 MP D2D transmission.  
Figure 27: Reception probability in the multihop case, \(h=250\) m.