# Markov-Modulated Poisson Process Modeling for Machine-to-Machine Heterogeneous Traffic
## 1 Introduction  
Beyond theoretical mathematics, Markov chains find extensive use in a variety of applied fields, including finance, physics, meteorology, chemistry, statistics, etc. In statistics, Markov chains can be used to analyze states transition simply, rapidly, and accurately. Markov chains can therefore be used to mimic complex distributions and to forecast the likelihood of future events. In health care, the amount of property damage and human casualties these disasters produce might be significantly decreased if they are effectively forecasted. Additionally, there will be a significant rise in the simplicity of using Markov chains due to the transfer matrix's calculation method being highly appropriate for artificial intelligence's computing features. Within the field of artificial intelligence (AI), a Markov chain can be a crucial probabilistic method utilized to comprehend and forecast sequential data. Its capacity to representand analyze dynamic systems makes it relevant and essential for a wide range of AI applications and algorithms. AI techniques incorporate Markov chains to reflect the intrinsically probabilistic aspect of real-world occurrences, like natural language processing (NLP) and reinforcement learning (RL). Indeed, Markov chains are utilized in NLP for speech recognition and text generation. For example, a Markov chain can be used to simulate the prediction of the next word in a sentence, where each state is a word and transitions are the likelihood of one word coming after another [1]. Meanwhile, the environment in RL is frequently represented as a Markov Decision Process (MDP), a kind of Markov chain that consists of decisions and rewards. By forecasting future conditions and rewards, agents acquire decision-making skills [2]. In mathematics, Markov chains can be used to forecast future events. Some sophisticated formulas will be derived and applied. Its applications in other disciplines like engineering, physics, meteorology, and even medicine successfully lessen the harm that different disasters inflict on people's lives and property [3]. People's lives have already made extensive use of Markov chains. Road construction costs are influenced by a wide range of factors; thus, it can be quite helpful to utilize a Markov chain for estimation in order to weed out the less important ones. It can also swiftly obtain data that are relatively more accurate. Markov chains have applications beyond building roads, such as market share research and financial forecasts. In [4], [PERSON] discovered that market share may be accurately predicted using the Markov chain's transfer matrix computation. Markov chains are useful not just in finance and architecture but also in power impulse noise prediction. Markov chains are proven to be highly useful in preventing excessive noise because they may be employed well by artificial intelligence to calculate the probability of excessive power pulses [5]. Future business simulations based on Markov chains may provide a more realistic depiction of the company, lowering the possibility of modeling errors and aiding in the prediction of future events and more precise optimization [6]. In this paper, the main research gap is how to model the heterogeneous M2M traffic. In telecommunication, Machine-to-Machine (M2M) and Human-to-Human (H2H) communications are considered to be game-changing elements [7]. Even though M2M and H2H communications can coexist in different domains (such as industrial automation, medical treatment, electrical power networks, and civil transportation), M2M communications are anticipated to play a vital role as a proxy to limit numerous human interventions through the use of long-term evolution advanced (LTE-A) intelligent systems. Because H2H and M2M patterns are incompatible, coexisting H2H and M2M traffic might present several difficulties for a shared network, decreasing its efficacy.