On the accurate performance evaluation of the LTE-A random access procedure Israel Leyva-Mayorga, Luis Tello-Oquendo, Vicent Pla, Jorge Martinez-Bauset and Vicente Casares-Giner ITACA, Universitat Politècnica de València, Spain email: {isleyma, luiteloq, vpla, jmartinez, vcasares}@upv.es Abstract—The performance evaluation of the random access (RA) procedure in LTE-A has recently become a major research topic as these networks are expected to play a major role in future 5G networks. Up to now, the key performance indicators (KPIs) of the RA in LTE-A have been obtained either by performing a large number of simulations or by means of analytic models that sacrifice precision in exchange of simplicity. In this paper, we present an analytic model for the performance evaluation of the LTE-A RA procedure. By means of this model, each and every one of the key performance indicators suggested by the 3GPP can be obtained with minimal error when compared to results obtained by simulation. To the best of our knowledge, this is the most accurate analytic model of the LTE-A RA procedure. Index Terms—Analytic model; LTE-A; performance evalua- tion; random access (RA). I. I NTRODUCTION The current LTE-A system has a widely deployed infras- tructure, which provides with ubiquitous coverage and global connectivity [1]. As such, LTE-A networks present the best solution for the interconnection of mobile devices (known as user equipments, UEs, in LTE-A) and will serve as a base for the future development of the Internet of things (IoT) [2], [3]. The UEs access the cellular base station (eNB) by means of the random access (RA) procedure; it is performed through the random access channel (RACH) and comprises a four-message handshake: preamble transmission (only allowed in predefined time-frequency resources called random access opportunities, RAOs), random access response (RAR), connection request and contention resolution messages. The RA procedure of LTE-A was not designed to handle a large number of synchronized access requests. This is a typical behavior in machine-to-machine (M2M) applications, in which the devices communicate autonomously [2], [3], [4]. Consequently, M2M applications may lead to severe congestion in the RACH and, due to the rapid increase in the number of interconnected devices, the frequency and severity of congestion will surely increase in the coming years. In order to develop efficient solutions to congestion in the RACH, the correct performance evaluation of the LTE-A RA procedure is of prime importance. The performance evaluation of the RA procedure is of- tentimes conducted by means of simulations [4] because it is difficult to model analytically. However, simulations may be highly time-consuming and the obtained results are not easily reproducible. One of the first efforts to model the RA procedure was presented in [5], but only the first step: preamble transmission, is considered. In fact, there are just a few analytic models for the performance evaluation of the complete RA procedure and their accuracy suffers when compared to simulations [6], [7], [8]. The access delay of UEs is the KPI that is most neglected by the existing analytic models. For instance, a general model for the RACH is presented in [8]. Some of the shortcomings of this model, as described by the authors, are: a) the error of the presented model increases at certain traffic intensities and; b) the KPI with the largest relative error is the access delay. Furthermore, only the average access delay is calculated. Clearly, evaluating the access delay by means of its average value is not suitable for time-constrained applications, e.g., health care [9]; instead, the probability mass function (pmf) of delay should be obtained. To the best of our knowledge, the most detailed analytic model for the performance evaluation of the RA procedure was presented in [6]. While this work was later extended in [7] to incorporate the model of an access control scheme, the basic model of the RA procedure remained. In fact, the model presented in [6] is of similar nature as the one presented in [8]; hence, both models present similar shortcomings. One of the main contributions of [6], [7] is that the probability distribution of access delay can be calculated, but its accuracy is poor. The main reason for this is the use of the expected value of the number of preambles decoded by the eNB instead of its pmf; this issue is described in detail in [10]. In this paper, we present a novel analytic model for the performance evaluation of the RA procedure. We describe the process for calculating the following key performance indicators (selected from the ones suggested by the 3GPP [4]): 1) Success probability, defined as the probability to success- fully complete the RA procedure within the maximum number of preamble transmissions. 2) Probability distribution of the number of preamble trans- missions performed by the UEs that successfully com- plete the RA procedure. 3) Probability distribution of the access delay. The accuracy of our model is evaluated by comparing the results obtained with both, our model and the one presented in [6] with the ones obtained by simulation. Results show that the error obtained by means of our model is minimal and surpasses the accuracy of the model presented in [6]. In addition, results can be obtained within a few tens of seconds.