# Spectrum Slicing for Multiple Access Channels with Heterogeneous Services
## 2 Related Work  
Orthogonal slicing has been widely explored and used in commercial systems [9]. It is a straightforward approach where independent resources are allocated to the different services, which allows one to treat them in an isolated manner. [PERSON] et al. [17] provided one of the first studies that compared orthogonal to non-orthogonal slicing. In particular, it investigated the benefits of OMA and NOMA schemes for the different combinations of 5G services in an uplink scenario: eMBB with URLLC and eMBB with mMTC. In the latter, orthogonal resources were allocated to each eMBB user, mMTC traffic was assumed to be Poisson distributed, and one URLLC user was considered. It was observed that NOMA may offer benefits with respect to OMA depending on the rate of the eMBB users and on the coexisting type of the intermittent traffic: with high URLLC, high data rates at the eMBB user were beneficial for NOMA, whereas the opposite is true with mMTC traffic. The work presented in [17] was extended to a multi-cell scenario with strict latency guarantees for URLLC traffic [18]. A single URLLC user per cell was considered, and it was observed that NOMA leads to a greater spectral efficiency with respect to OMA. A similar conclusion was drawn by [PERSON] et al. [10] in an uplink scenario with two users with the same service type that aimed to minimize the average AoI. It was also observed that a greater spectral efficiency does not directly translate into a lower average AoI. Another scenario that includes power control to simplify the reception of the intermittent packets was studied in [19], which derived analytical formulas for throughput and AoI with those settings. The selection of the multiple access scheme is essential when considering spectrum slicing with multiple intermittent users [9], and particularly so in MU-MIMO systems which can make MPR easier [20]. Slotted ALOHA and TDMA are two basic multiple access schemes that offer widely different benefits. Slotted ALOHA is simple, flexible, and effective for relatively low traffic loads. It is one of the most widely used random access protocols, implemented in a number of variants, e.g., multichannel slotted ALOHA in 5G [21; 22]. There is a vast literature on the performance evaluation of ALOHA-based schemes in terms of latency and reliability. For instance, grant-free ALOHA-based access has been studied for URLLC services [23; 24]. Besides, latency and reliability can be combined into a single performance indicator termed latency-reliability [25]. On the other hand, it is difficult to derive closed-form expressions of the probability distribution of the AoI. Hence, most papers in the literature examined it in terms of its mean value and in the context of queuing theory and often in ideal systems with Markovian service [26]. Only a few studies investigated the tail or the full distribution of AoI, event though these provide a clear measure for the reliability and stability of control systems. In particular, these are directly connected to control systems by the survival time, defined as the time that an application may continue to operate without receiving an anticipated message [27]. The distribution of AoI with packet preemption and memoryless servers was investigated in [28]. In [29], the Chernoff bound was used to derive an upper bound of the quantile function of the AoI for two queues in tandem with deterministic arrivals. The peak-age violation probability, defined as the probability of exceeding a pre-defined PAoI threshold, was derived for a single-hop link with fading and retransmissions, in the form of variable-length-stop-feedback [3]. So far, only a few studies considered the impact of physical layer and medium access control on the AoI. Among these, recent works compute the average AoI in Carrier Sense Multiple Access (CSMA) [30], ALOHA [31], and slotted ALOHA [32] networks, considering the impact of the different medium access policies on the age.