# Resource Allocation in 5G Cellular IoT Systems with Early Transmissions at the Random Access Phase
## 2 Related Work  
Most studies where the authors addressed mMTC using CIoT technologies primarily focused on the RA phase. Since modern mMTC technologies, including both NB-IoT and LTE-M, utilize multichannel ALOHA mechanisms at the RA phase, most of the studies investigated them in detail under different traffic arrival patterns. The authors in [5] showed that, for multichannel slotted ALOHA under Poisson arrivals, the optimal transmission probability is inversely proportional to \(\min(l/N_{t},1)\), where \(l\) is the number of preambles, and \(N_{t}\) is the number of active EDs. The studies in [8; 9] proposed a method for approximating the value of \(N_{t}\). The NB-IoT RA phase performance under batch arrivals was addressedin [4]. Among others, the authors demonstrated that, under such types of arrival, capacity of the NB-IoT systems decreased by multiple orders of magnitude. A mixture of stochastic and regular arrivals was addressed in [10], in which the authors derived the mean delay for both traffic types. Unlike models of other types of traffic, such as enhanced Mobile BroadBand (eMBB) broadband traffic or Ultra Reliable Low Latency Communications (URLLC) traffic [11], RA mechanisms play a key role in the context of machine-to-machine (M2M) communications. In addition, various algorithms have been developed for the RA phase to adaptively adjust access its parameters based on estimating the time-varying number of access requests [12; 13; 14; 15; 16]. In [13; 14], an analytical model is presented to determine the expected total delay at the RA phase. Specifically, the mean number of non-conflicting preambles allocated by ED was reported in [12], the mean number of preambles experiencing collisions--in [13], and the mean number of EDs that successfully complete the RA phase--in [14]. The studies in [15; 16; 17; 18] proposed the queuing theoretic models incorporating the queuing behavior of individual EDs. Another important characteristic in addition to transmission delay is the age of the information (AoI), which is investigated in [19; 20; 21]. Having identified that the NB-IoT and LTE-M RA designs are suitable for achieving high capacity at the RA phase for asynchronous EDs, researchers started to characterize the capacity at the DT phase under different deployments. The authors in [22] considered the optimal DT phase capacity for a given arrival rate of EDs having different resource requirements. Joint service deployment utilizing LTE and NB-IoT for surveillance applications was considered in [23]. Studies accounting for both the RA and DT phases have appeared only recently. Specifically, such systems were addressed in [24] for IEEE 802.16 [25] systems and, more recently, in [26; 27] in the context of general random access systems. Specifically, the authors in [27] extended the model originally proposed in [24] and developed a method for determining the optimal ratio of resources at RA and DT phases to maximize the system throughput. Coexistence between mMTC and human-to-human (H2H) services was considered in [28], where the authors explicitly accounted for RA and DT phases for mMTC traffic and DT phase only--for H2H traffic. As mMTC technology bounds the ED battery lifetime, in [29], the authors explore the possibility that choosing among several low-power wide-area network (LPWAN) technologies integrated at a single ED may improve its lifetime. An early data transmission regime (EDT) for the NB-IoT system introduced in 3 GPP Release 16 [6] has received significant attention thus far. Specifically, the authors in [30] utilized computer simulations to show that, under careful choice of early and normal transmission probability, the capacity of the NB-IoT system can be maximized. The authors in [7] investigated the use of EDT operation in industrial environments, showing that it can enhance the system capacity compared to the traditional operational regime. However, no studies published so far addressed EDT performance when resources allocated to both the RA and DT phases may vary.