# Markov-Modulated Poisson Process Modeling for Machine-to-Machine Heterogeneous Traffic
## 4 CHANAL Model and Performance Metrics  
### CHANAL Model  
Remember from [11] that by enabling both M2M and H2H devices to access network resources efficiently, we aimed to maintain a sustainable level of services with minimal congestion during emergency events while measuring the mutual impact of M2M homogeneous traffic and H2H traffic in various scenarios. This use case is summarized in Table 1. In order to accomplish this, we use the assumption that the observation time intervals are so short that, at any given time, only one event may happen (either one M2M or one H2H request/completed service). Although this simplification used in our previous CANAL model helps in studying homogeneous M2M traffic, it may not be suitable to represent a real case with heterogeneous M2M traffic. To this end, we extend our work to study the arrival of two requests per time slot. These two requests are attempting to access the network. In case of a system overload, some of the requests will be pushed to the queue and processed following a pre-defined priority. In this publication, we have updated our earlier model, labeled \"CANAL\" [11], with a new architecture termed \"CHANAL\", which detects the homogeneity of M2M traffic and automatically manages both H2H and M2M traffic. In order to achieve this, the model operates based on the load state of M2M requests in various scenarios. A single uplink cell in an eNodeB with total network resource blocks (c) is represented by CHANAL. M2M and H2H traffic are examples of heterogeneous traffic types. According to [PERSON]'s distributions, both types of traffic are expected to have arrival rates of \(\lambda_{\text{(m)}}\) and \(\lambda_{\text{(h)}}\), respectively [20]. Consider that the exponential distributions for M2M and H2H service rates, respectively, are represented by \(\mu_{\text{(m)}}\) and \(\mu_{\text{(h)}}\). Resource Allocation Control (RAC) is another feature of CHANAL that is utilized to manage, control, and grant access to network requests in accordance with the resources that are available. In network congestions brought on by catastrophic occurrences, RAC is essential because it adaptively manages resources to manage the overwhelming demands of M2M devices while limiting H2H requests to reasonable levels. An eNodeB bandwidth in the LTE-A specification varies as follows, according to the requirements of the operator: 1.4, 3, 5, 10, 15, and 20 MHz. Our CHANAL model subtracts an LTE-M bandwidth of 1.4 MHz (6 PRBs) from the overall bandwidth (e.g., 20 MHz) allowed for H2H traffic to reserve it for M2M traffic. It continues to reduce the H2H bandwidth and widen the M2M bandwidth until it absorbs all of the M2M accumulative storms. It resets the M2M and H2H bandwidths to their initial settings upon the retreat of all M2M storms. For instance, \(\text{rb}_{\text{(m)}}\) is set aside for LTE-M networks where \(\text{rb}_{\text{(h)}}+\text{rb}_{\text{(m)}}=\text{c}\), while \(\text{rb}_{\text{(h)}}\) is set aside for LTE-A networks for their maximum resource blocks. Both \(\text{rb}_{\text{(h)}}\) and \(\text{rb}_{\text{(m)}}\) typically hold onto the starting number of resources (e.g., for a bandwidth network,LTE-A = 10 MHz, \(\rm{rb}_{(h)}\) = 50, and for an LTE-M network, \(\rm{rb}_{(m)}\) = 6). The utilization of \(\rm{rb}_{(m)}\) peaks at the moment of a sudden event. Thus, in order to satisfy the temporary H2H requests, the RAC offers an extra six resources. As a result, with LTE-A bandwidth of 10 MHz, there are 6 more resources set aside for M2M (\(\rm{rb}_{(m)}\) = 12) and 6 fewer resources set aside for H2H (\(\rm{rb}_{(h)}\) = 44). Until the sudden event passes or all storms are absorbed, more resources will be repeatedly loaned. Furthermore, CHANAL has a Queuing Control Unit (QCU) that consists of two independent queues with queue sizes of n and o for H2H and M2M, respectively (H2H-Q, M2M-Q).