## 2 Background and Related Work
\right]\) means that when the current state is stable (\(S\)), the probabilities of the device's state will be low (\(L\)), medium (\(M\)), and high (\(H\)) are 10%, 30%, and 60%, respectively, and when the current state is unstable (\(U\)), the probabilities that the device's state will be low (\(L\)), medium (\(M\)), and high (\(H\)) are 60%, 30%, and 10%, respectively. The parameter \(\pi\) can be used when devices' log information is unavailable, that is, the probabilities that the device is stable (\(S\)) and unstable (\(U\)) in the initial state are 40% and 60%, respectively. For the parameter \(O\), we consider 0 as low (\(L\)), 1 as medium (\(M\)), and 2 as high (\(H\)). In this illustrative example, we do not consider the state transition from low (\(L\)) to high (\(H\)) or high (\(H\)) to low (\(L\)). Table 3 shows the calculated hidden Markov model probabilities for the sequence of SQUUSSUU. As the state sequence proceeds, the hidden Markov model probabilities change, which can be used to predict the device's state for resource consolidation. Performance-aware resource management in cloud computing environments is challenging since it is hard to predict the system's behavior [16], and it is also vital to reduce energy consumption for green cloud computing [17]. In [18], the authors proposed a cloud task mapping strategy for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value** \\ \hline \multirow{3}{*}{\(A\)} & \(S\) \(\mid U\) \\  & \(\frac{S}{H}\) & \(\left[\begin{array}{ccc}0.6&0.4\\ 0.4&0.6\end{array}\right]\) \\  & \(L\) \(\mid M\mid H\) \\ \multirow{3}{*}{\(B\)} & \(\frac{S}{H}\) & \(\left[\begin{array}{ccc}0.1&0.3&0.6\\ 0.6&0.3&0.1\end{array}\right]\) \\  & \(\pi\) & \(\left[\begin{array}{ccc}0.4&0.6\end{array}\right]\) \\ \(O\) & \(\left(2,\,1,\,0,\,1,\,1,\,2,\,1,\,0\right)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters for the illustrative example. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sequence Number** & **Probability of \(S\)** & **Probability of \(U\)** \\ \hline
0 & 0.8947576066 & 0.1052423934 \\
1 & 0.5090529425 & 0.4909470575 \\
2 & 0.1523176942 & 0.8476823058 \\
3 & 0.4439562979 & 0.5560437021 \\
4 & 0.5562550549 & 0.4437449451 \\
5 & 0.8485699873 & 0.1514300127 \\
6 & 0.4997196054 & 0.5002803946 \\
7 & 0.1499719605 & 0.8500280395 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: HMM probabilities (the sequence is SQUUSSUU). heterogeneity and hybrid architectures by considering various system metrics including response time, performance, and energy cost based on evolutionary games on a network equation for the task mapping. In [19], the authors proposed a two-phase queueing mechanism for scheduling cloud tasks by prioritizing the tasks based on constraints and service level agreements. It divides the cloud scheduling strategy into task assignment (by the central cloud server) and task scheduling (by each server in the cloud) phases. To enable the Internet of things for the sensor-based big data analytics environment, the authors of [20] proposed a framework incorporating multiple core techniques (data collection, repository, data processing, analytics algorithms, wireless network, and data visualization) for smart and sustainable cities. To expand resource optimization techniques in the mobile edge cloud system, the authors of [21] proposed a partition technique for the mobile edge cloud clusters based on a graph-based algorithm to consolidate the network traffic in the mobile edge servers. There are a few studies that incorporate an artificial intelligence technique for managing the mobile edge cloud resources. In [22], a deep reinforcement learning mechanism is used to overcome the high deployment and maintenance costs. With the learning technique, it adaptively allocates resources (computing and network) and reduces service time in mobile edge cloud environments. In [23], the authors used the hidden Markov model to detect multi-stage network attacks [24, 25].