## 5 Performance Evaluation
It is important to remember that \(L\) establishes the maximum number of replicas \(K\) that can be transmitted. The results (the number of supported UEs) for each value of \(L\) in Figure 5 have been obtained for the maximum value of \(K\) permitted by \(L\) (\(K\) equal to 2, 4, 6 and 8 for \(L\) equal to 0.25, 0.5, 0.75 and 1 ms, respectively). The Release 15 of the 3 GPP standards [22] establishes URLLC requirements with a latency of \(L\) = 1 ms and a reliability target of 1-10-5. Figure 5 shows that grant-free scheduling with \(K\)-repetitions and shared resources can achieve a reliability equal to 1-10-5 with only \(K\) = 2 if we do not consider self-collisions. Grant-free scheduling with \(K\) = 2 can also guarantee a latency as low as 0.25 ms. For low values of the packet generation rate (i.e., \(\lambda\) = 0.1 packets), grant-free scheduling with 2 repetitions can support up to 34 UEs with a reliability of 1-10-5 and \(L\) = 0.25 ms if we do not consider self-collisions. The number of UEs that can be supported decreases with \(\lambda\), since the risk of collision with other UEs increases when each UE transmits more packets per second. For example, only 4 UEs can be supported with \(L\) = 0.25 ms and a reliability of 1-10-5 when \(\lambda\) = 1 packet. If the latency requirement is relaxed to 0.5 ms or even higher, grant-free scheduling can support more than 500 UEs with only \(K\) = 4 when \(\lambda\) = 0.1 packets. If \(\lambda\) increases, grant-free scheduling can only guarantee the required reliability for 500 UEs if the latency requirement is 1 ms, and each UE can transmit 8 replicas of the same packet. These results show that the reliability and latency levels that can be achieved with grant-free scheduling depend upon configuration parameters (e.g., \(K\)), the traffic (e.g., \(\lambda\)) and the number of UEs supported. An adequate configuration and optimization of grant-free scheduling based on the network conditions could help support stringent reliability and latency levels. However, it is important to note that these results are achieved without considering self-collisions. The impact of self-collisions might be non-negligible when, for example, \(K\) and/or \(\lambda\) increase. The Release 16 of 3 GPP standards for 5G NR [2] defines use cases with higher reliability requirements (up to 1-10-6). Some Industry 4.0 applications (e.g., factory automation) require even  
Figure 4: \(P_{c}\) as function of the number of User Equipments (UEs) and for different latency requirements \(L\): (a) \(\lambda\) = 0.1 packets; (b) \(\lambda\) = 1 packet. higher reliability levels (up to 1-10\({}^{-9}\)), as discussed in [3]. It is then important analyzing whether grant-free scheduling with \(K\)-repetitions and shared resources can guarantee reliability levels of the order of 1-10\({}^{-9}\). Figures 4 and 5 show that grant-free scheduling can only guarantee very high reliability levels with high values of \(K\), which limits the latency requirements (\(L\)) that can be satisfied. For example, a probability to correctly receive a packet equal to 1-10\({}^{-7}\) cannot be guaranteed when \(L<0.5\) ms, even for the lower packet generation rates. If the reliability requirement increases to \(P_{rel}=1\)-10\({}^{-9}\), grant-free scheduling can only support 5 UEs with \(L=0.75\) ms and \(\lambda=0.1\) packets. It can support 86 UEs if the latency requirement is relaxed to 1 ms. However, if \(\lambda\) increases to 1 packet then grant-free scheduling can only support 10 UEs with a reliability of 1-10\({}^{-9}\) even if \(L\) is equal to 1 ms. Figure 6 shows the impact of \(U\) upon the performance of the grant-free scheduling scheme with \(K\)-repetitions and shared resources. \(U\) is the number of available RBs (Resource Blocks) per \(T_{slot}\).