## 1 Introduction  
5G networks are being designed with the objective to support a broad range of verticals such as manufacturing, transport, health, energy and entertainment. To this aim, important changes have been introduced to increase data rates (enhanced mobile broadband, or eMBB), efficiently support large amounts of devices (massive machine type communications, or mMTC) and guarantee unprecedented reliability and latency levels (Ultra-Reliable and Low-Latency Communications or URLLC) [1]. Supporting URLLC is particularly relevant for many Industry 4.0 manufacturing applications, such as motion control (requires a maximum latency of 1 ms and a reliability of 1-10\({}^{-6}\)[2]), control-to-control applications (maximum latency of 4 ms and a reliability of 1-10\({}^{-8}\)[1]) and factory automation (maximum latency between 0.25 ms and 2.5 ms and reliability requirements up to 1-10\({}^{-9}\)[3]). These applications require the exchange of information between sensors, actuators and controllers through an industrial sensor and control network. 5G has the potential to provide the connectivity required by the Industry 4.0 to digitalize factories and to support data-intensive services while ubiquitously guaranteeing low latency and reliable connections. This has actually been acknowledged through the establishment of the 5G Alliance for Connected Industries and Automation (5G-ACIA) [4]. 5G has introduced significant changes to support URLLC [5]. Some of these changes focus at the Radio Access Network level, since the medium access mechanisms account for an important part of the total end-to-end transmission delay [6]. This is for example the case of the grant-based scheduling process for uplink (UL) transmissions in legacy LTE (Long Term Evolution) 4G networks. Grant-based scheduling requires a User Equipment (UE) and a Base Station (BS) to exchange scheduling requests (SRs) and grant messages before transmitting any data. This process alone already results in an average delay of up to 11.5 ms when considering a Transmission Time Interval (TTI) equal to 1 ms and an SR periodicity of 10 ms [3]. Reducing the slot duration can reduce this delay. However, additional scheduling changes have been necessary to sustain the URLLC requirements that characterize some vertical applications, such as those in Industry 4.0. In particular, Release 15 and 16 of the 3 rd Generation Partnership Project (3 GPP) standards have introduced the concept of grant-free scheduling (also referred to as Configured Grant for 5G New Radio [7]) to support URLLC. With grant-free scheduling, the BS reserves resources for UL transmissions and informs the UEs of the reserved resources. When a UE wants to initiate a UL transmission, it directly utilizes the reserved resources, without sending an SR and waiting for the subsequent grant message from the BS. Recent studies have shown that grant-free scheduling in 5G NR considerably reduces the end-to-end latency [8]. The 3 GPP standards introduce the possibility for grant-free scheduling to reserve resources to dedicated UEs, or to a group of UEs. In the first case, each resource is reserved for a specific UE, and only this UE can utilize the resource at any time. This approach is adequate for periodic traffic since the resource allocations can be planned, and resources can then be utilized efficiently. Such planning is not possible in the case of aperiodic, sporadic or uncertain traffic. Sharing dedicated resources by a group of UEs is hence an interesting option to optimize the usage of the radio resources in the presence of aperiodic traffic. In this case, UEs have to contend for their usage, and collisions are possible. 5G NR introduces the possibility to transmit \(K\) replicas of the same packet in consecutive slots to combat potential collisions. However, relying on the transmission of \(K\) replicas to achieve a target reliability level can result in additional delays.