## 6 Conclusions  
This paper has analyzed the capacity of 5G NR grant-free scheduling to support URLLC services with strict reliability and latency levels such as those demanded by Industry 4.0. The study has focused on aperiodic or sporadic traffic and an implementation of 5G NR grant-free scheduling with \(K\)-repetitions and shared radio resources. This implementation has been chosen, since sharing radio resources is an attractive option for aperiodic traffic. In addition, the \(K\)-repetitions scheme can combat possible packet collisions between UEs that share radio resources. This study has analyzed the reliability and latency levels that can be achieved with existing 5G NR grant-free scheduling with shared radio resources as a function of the number of UEs, the number of reserved radio resources, and the number of replicas \(K\). To this aim, this study has derived analytical expressions that quantify the exact probability of collision with packets transmitted by other UEs, and the impact of self-collisions. It is important to emphasize that this study is the first one that has evaluated the impact of self-collisions. Packet collisions and self-collisions have then been taken into account to derive analytically the reliability that can be achieved by existing 5G NR grant-free scheduling with shared resources. The derived analytical expressions have been validated against simulations. These expressions are a valuable contribution to the community, since they can be easily utilized to evaluate 5G NR grant-free scheduling.  
This study has demonstrated that current 5G NR grant-free scheduling solutions cannot guarantee high reliability levels with strong latency requirements. This is partly due to the fact that strong latency requirements limit the number of replicas \(K\) that can be transmitted. In addition, self-collisions have a non-negligible impact that even limits the reliability that can be achieved when \(K\) increases. The impact of self-collisions also increases with the latency requirements. The obtained results demonstrate that new solutions are necessary for 5G NR grant-free scheduling to be able to support applications with stringent URLLC latency and reliability requirements under the presence of aperiodic traffic. In particular, the transmission of \(K\) replicas per packet might be inadequate to support aperiodic traffic with very low latency levels due to the impact of self-collisions. Consequently, other approaches should be designed to minimize collisions between UEs sharing radio resources. This study has shown that these new solutions cannot be based either on grant-based or semi-persistent scheduling. Grant-based scheduling introduces additional latency due to the exchange of messages between the UEs and the BS for assigning the radio resources. Semi-persistent scheduling with dedicated resources inefficiently utilizes the available resources when considering dedicated resources and aperiodic traffic. Innovative grant-free scheduling solutions are hence necessary to meet the URLLC requirements identified for 3 GPP Release 16 and beyond. This could include, for example, the use of sensing mechanisms or full duplex techniques that can reduce packet collisions.  
Conceptualization, M.C.L.-E. and J.G.; methodology, M.C.L.-E. and J.G.; validation, M.C.L.-E. and J.G.; formal analysis, M.C.L.-E., J.G. and M.S.; investigation, M.C.L.-E.; writing--original draft preparation, M.C.L.-E.; writing--review and editing, J.G. and M.S.; funding acquisition, J.G. and M.S.  
This work has been funded by the European Commission through the FoF-RIA Project AUTOWARE: Wireless Autonomous, Reliable and Resilient Production Operation Architecture for Cognitive Manufacturing(No. 723909), and the Spanish Ministry of Economy, Industry, and Competitiveness, AEI, and FEDER funds (TEC2017-88612-R).  
The authors declare no conflict of interest.