# On the Evaluation of the NB-IoT Random Access Procedure in Monitoring Infrastructures
## 1 Introduction  
The Internet of Things (IoT) phenomenon is broadening at an astoundingly fast rate [1], which promoted the birth of several novel services in different application domains, including, but not limited to, Industry 4.0 [2], Smart Cities [3], Intelligent Transportation Systems [4], Precision Agriculture [5], healthcare [6] and environmental monitoring [7]. Hence, an increasing number of constrained smart devices are currently joining the worldwide Internet, asking for suitable wireless communication technology, capable of offering both extremely low power consumption and support for densely populated deployments. In general, these low-powered devices individually require low data transfer rates as well, even though a densely populated Machine Type Communication (MTC) deployment might become incredibly bandwidth-hungry. At the same time, devices generally require extremely low power, remaining idle for prolonged periods. Furthermore, reasonably numerous IoT applications involve the reporting of various events and data streaming to a central server in an efficient and robust way (e.g., video surveillance and emergency health services). Besides, either the physical location of devices in such scenarios may not be reached by fixed networks (e.g., basements) or the apparatuses have to be arbitrarily deployed or moved anywhere [8]. Low Power Wide Area networks (LPWANs) are an innovative communication pattern addressing the aforementioned requirements ofemerging IoT applications [9]. Essentially, they complement legacy cellular and short-range wireless technologies, offering exclusive features for low complexity devices. At the time of this writing, there are a number of LPWANs, each employing different techniques to meet the Machine-to-Machine (M2M) requirements. In the unlicensed spectrums, LoRa [10] and SigFox [11] are the most common. However, the licensed spectrum is widely known to supply a higher degree of reliability and Quality of Service. Among the licensed LPWANs, NarrowBand IoT (NB-IoT) has been recognized as a promising and effective technology offering wireless connectivity to smart devices. Standardized by the Third Generation Partnership Project (3 GPP) starting from Release 13 [12; 13], it natively supports the transmission of marginal amounts of data, while requiring low-energy consumption and limited bandwidth usage [14]. Moreover, the adoption of NB-IoT is able to satisfy most of the requirements of all the possible application scenarios, by dynamically adapting to different use cases. Therefore, the application based on the potentially enormous amount and variety of data generated by monitoring sensors is of particular interest. Such monitoring systems provide new services to citizens, companies, and public administrations as well. In a typical NB-IoT monitoring system, uplink transmissions prevail among the rest of exchanged messages. Here, the random access procedure is the primary relation established between devices and the base station. Built on top of a contention-based mechanism, it brings to performance degradation when a multitude of simultaneous transmissions takes place [15]. In fact, in high traffic conditions, only few devices can successfully complete the procedure. Consequently, analytical models and system-level simulation tools able to investigate the behavior of the aforementioned random access procedure are extremely important for driving current research activities related to the adoption of the NB-IoT technology in smart monitoring infrastructures. Nevertheless, at the time of this writing, scientific literature only provides splintered answers to these challenging open issues. For instance, analytical models for estimating the random access success probability are presented in [16; 17; 18; 19; 20; 21; 22], but they either do not fit the 3 GPP guidelines or overlook several aspects (see Section 2.4 for further details).