# Markov-Modulated Poisson Process Modeling for Machine-to-Machine Heterogeneous Traffic
## 2 Traffic Modeling  
Stochastic processes that mimic the behavior of measured data traffic for physical quantities can be used to characterize traffic modeling [12]. There are two types of traffic models: aggregated traffic models (such as high-speed links, backbone networks, and the internet) and source traffic models (such as voice, video, and data traffic). Packets that replicate real traffic behavior at different sizes and intervals are generated by source traffic simulations, such as the SimuLTE simulator [13], OPNET [14], OMNeT [15], etc. Several common sources of traffic models, including as two-state MMPP, ON/OFF, and Interrupted Poisson Process (IPP) models, are analyzed in [16] using the OPNET model. An example of an ON-OFF model is an MMPP or IPP (Interrupted Poisson Process). The Poisson process is modulated by a Markov chain that contains two states: ON and OFF. These states correspond to two values of the Poisson process's intensity; this model is called the ON-OFF model since the intensity is frequently 0 in the off state. The article in [17] states that during a disaster, it is estimated that there would be more than \(5\times 10^{4}\) devices per cell that may send their payloads simultaneously. We understand that in these situations, source traffic models become very difficult to execute, which makes the usage of aggregated traffic modeling necessary. Finding a fair approximation of the arrival process of several devices while maintaining a good balance between accuracy and simulation performance is the aim of aggregated traffic models, for example, the Simulink simulator [18; 19]. For instance, in [11], we looked at how H2H and M2M traffic interact in crowded areas and during emergencies. Based on the suggested design in [20], we also performed several simulations in which a single LTE-A network with average arrival rates (\(\lambda_{1}\); \(\lambda_{2}\)) and service rates (\(\mu_{1}\); \(\mu_{2}\)) for M2M and H2H traffic is assumed. The simulation findings showed that a prioritized LTE-A system could handle more M2M and H2H traffic demands in less time. According to the simulation results, a prioritized LTE-A system for both M2M and H2H traffic may manage more requests in dense area scenarios by lowering the completion rate of lower-priority traffic and preserving higher-priority traffic without degradation. In contrast, during an emergency, higher-priority traffic is prioritized over lower-priority traffic, leading to a higher completion rate and the total elimination of low-priority traffic. Because it allows H2H and M2M traffic to continue operating simultaneously and uninterrupted, the non-priority traffic approach offers an advantage over other options under these circumstances. In this paper, to simplify our work, we use equal priority for M2M and H2H traffic, while keeping the door opened to discuss applying various priorities over different traffic in our coming research. As stated in [21], the 3 GPP offers two models: Model 1 represents non-synchronized M2M communication, whereas Model 2 represents synchronized M2M traffic, as shown in Figure 1.  
1. Model 1 of the 3 GPP can be thought of as a regular scenario in which M2M devices access the network in a consistent manner over a period of time (i.e., a non-synchronized way). 2. Model 2 of the 3 GPP can be viewed as a disaster scenario in which a large number of M2M devices connect to the network in a highly synchronized fashion (e.g., after a power outage). In [20], the authors propose the Coupled Markov-Modulated Poisson Process (CMMPP) framework, which combines the benefits of both modeling paradigms (source traffic modeling and aggregated traffic modeling). It demonstrates the viability of M2M source traffic modeling with only linearly increasing complexity. CMMPPs improve the accuracy and flexibility of aggregated M2M traffic models at the cost of moderate computational complexity, as proposed by the aforementioned 3 GPP model in [21].