Optimizing Edge Device Routing in Edge Computing: Harnessing the Synergy of Distributed Processing and Correlation Analysis

Edge computing, characterized by its decentralized architecture, demands sophisticated techniques to optimize the allocation of computational tasks across diverse edge devices. This paper presents a potential approach for enhancing edge device routing through the synergistic integration of distributed processing and correlation analysis. The utilization of distributed processing enables decentralized task allocation, ensuring efficient resource utilization and load balancing. Concurrently, correlation analysis techniques are employed to uncover intricate relationships and dependencies among tasks and devices. By harnessing these correlations, the system makes intelligent, context-aware routing decisions, anticipating task requirements and predicting network conditions. This innovative integration empowers edge computing environments with adaptive load balancing, predictive optimization, and scalability. The proposed method significantly reduces the time required for selecting an edge device to process data packets, achieving nearly 50% reduction in comparison to two randomly selected methods. The proposed methodology not only ensures the efficient allocation of tasks but also lays the foundation for resilient and responsive edge computing ecosystems, transforming the landscape of edge-enabled applications and services.


INTRODUCTION
In the era of edge computing, where data is generated and processed closer to the source, the efficient allocation of computational tasks among edge devices is fundamental to the system's performance, responsiveness, and overall user experience [1].However, the dynamic and heterogeneous nature of edge environments poses significant challenges to traditional routing algorithms.Addressing these challenges demands innovative approaches that not only optimize task allocation but also anticipate changing demands and network conditions.This paper explores a potential methodology aimed at revolutionizing edge device routing by integrating two potent technologies: distributed processing and correlation analysis.Distributed processing allows for the decentralized allocation of computational tasks, promoting load balancing and efficient resource utilization [2].Simultaneously, correlation analysis techniques delve into the intricate relationships and dependencies among tasks and devices, unveiling patterns crucial for making intelligent, context-aware routing decisions.The synergy between distributed processing and correlation analysis forms the core of our research, enabling the development of adaptive, responsive, and intelligent edge computing systems.By unleashing the power of these technologies, this study aims to enhance the efficiency of edge device routing, paving the way for the evolution of resilient and highly responsive edge computing ecosystems.This paper delves into the theoretical foundations, the innovative methodology employed, and the transformative implications of integrating distributed processing and correlation analysis in the realm of edge computing optimization.Through comprehensive analysis and empirical validation, this research contributes to the advancement of edge computing architectures, offering new horizons for the development of intelligent and adaptive edge-enabled applications and services.In the context we present, we envision an edge computing environment comprising n edge devices, each equipped with specific information, including coordinate location, computing capacity per second, historical processing results, and stability levels.In this intricate setting, our proposed solution, outlined in this article, unfolds in two pivotal steps.In the first step, when a user sends a request, we leverage the available data on computing capacity and the distances of edge devices to identify a subset of potential devices capable of handling the given request.This selection process involves evaluating the computing capabilities and proximity of each edge device to determine its suitability for the task at hand.The subsequent step involves the construction of a graph and the application of correlation analysis techniques among the edge devices.This analytical process aims to establish relationships between devices based on historical processing results and stability levels.The outcome of this step is the identification of a refined subset-a subset characterized by a higher likelihood of possessing the requisite data processing capabilities.This final subset represents edge devices with the optimal combination of historical performance, stability, and processing capacities, ensuring the efficient and effective execution of user requests within the edge computing environment.We first review related issues and challenges in edge computing, distributed computing processing techniques, and correlation analysis techniques in a multipoint graph in Section II.Section III explains and elaborates upon presenting our proposed solution to the edge device routing problem using a combination of distributed processing technology and correlation analysis techniques.Section IV gives the experiments and comparisons with other algorithms with different data sets

RELATED WORKS 2.1 Edge Computing and Its Routing Challenges
Edge computing has emerged as a transformative paradigm in the world of computing, enabling data processing and analysis closer to the source of data generation [1].This approach significantly reduces latency, enhances real-time decision-making, and conserves bandwidth by processing data locally on edge devices rather than relying on centralized cloud servers.Despite its numerous advantages, edge computing presents unique challenges, particularly in the domain of edge device routing.We can synthesize the challenges in edge device routing: 2.1.1Limited Resources.Edge devices, such as sensors, IoT devices, and mobile devices, typically have limited computational power, memory, and battery life.Efficiently utilizing these scarce resources while ensuring optimal routing decisions becomes a critical concern.

Low Latency
Requirements.Many edge applications, especially those related to IoT and real-time data analysis, demand ultralow latency [2].Traditional routing algorithms might not suffice in meeting these stringent latency requirements, necessitating the development of specialized routing strategies tailored for low-latency scenarios.

Distributed Processing Techniques in Edge Computing
Distributed processing techniques play a crucial role in addressing the challenges posed by edge computing environments.These techniques enable the efficient utilization of computational resources across multiple edge devices, allowing for parallel processing, load balancing, fault tolerance, and scalability.Here are several key distributed computing processing techniques commonly used in edge computing:

Correlation Analysis
Correlation analysis in a multipoint graph involves examining the relationships between multiple variables or points within a graph.
In the context of a multipoint graph, which typically represents complex relationships between various data points, correlation analysis can provide valuable insights into the interdependencies and patterns among these points [6].Here, we analyze techniques used for correlation analysis in a multipoint graph: Pearson Correlation Coefficient The Pearson correlation coefficient measures the linear relationship between two variables.In the context of a multipoint graph, you can calculate the Pearson correlation coefficient between pairs of connected nodes to quantify the strength and direction of their correlation.

Optimizing Multiple Targets
Optimizing multiple targets often involves dealing with a multiobjective optimization problem [7].In mathematical terms, a multiobjective optimization problem can be defined as follows: Minimize or Maximize   () for i = 1, 2, ..., m, where  is the number of objectives, subject to constraints   () and ℎ  ().Here,  represents the vector of decision variables that you can adjust to optimize the objectives.  () represents the ℎ objective function that you want to minimize or maximize.  () and ℎ  () represent inequality and equality constraints, respectively.Weighted Sum Method: Convert multiple objectives into a single objective function by taking a weighted sum of the objectives.For minimization, this would look like: Here,   are weights representing the importance of each objective.This method assumes that you can assign appropriate weights to balance the trade-offs between objectives.

THE APPROACH: INTEGRATING DISTRIBUTED PROCESSING AND CORRELATION ANALYSIS
The situation we're addressing is as follows Fig. 1: within an edge computing environment, there are numerous edge devices, each equipped with basic information such as its computational power and geographical coordinates.When there are  users sending requests to the edge computing system, we have access to both the coordinates of these users (requests) and the amount of computational resources each request demands.The challenge here lies in achieving load balancing: distributing these  requests across  available devices in a way that maximizes the likelihood of successful processing at the edge devices.It's important to note that this task becomes more intricate when each request requires a different amount of computational resources, considering the varying processing capabilities of the edge devices.Additionally, we introduce another crucial factor into the optimization process: the distance between where the request originates and the respective edge device.This additional condition further complicates the task, making the optimization process multifaceted and requiring careful consideration of both computational demands and geographical proximity.In this stage, we define the criteria for an A request to be handled by a specific edge device B. The first requirement, Issue 1, is a prerequisite -the processing capacity of the edge device must meet or exceed the computational demands of the request.Issue 2 introduces an optimization factor: proximity and stability.Devices closer to the request location take precedence, ensuring efficient processing.Additionally, priority is given to devices with greater stability, enhancing the reliability of the processing task.These conditions not only ensure optimal resource utilization but also improve the overall efficiency and reliability of the edge computing system.
As depicted in Fig. 2, our model comprises a collection of n edge devices.For each request, we identify a subset of potential processing candidates among m edge devices that meet the prerequisite criteria.Here, m is less than n, and this subset is referred to as the candidate set.The subsequent step involves optimization, where we determine the most suitable edge device to handle the request, ensuring the highest probability of successful processing.

Figure 2: The candidate edge devices
To make this decision, we delve into the analysis of relationships among nodes within the candidate set.This analysis leverages historical usage data and the successful processing rates of edge devices.The formula for calculating the Pearson correlation coefficient between two variables  and  with  data points can be expressed as: : Where:   and   are the individual data points of variables  and  respectively, X and Ȳ are the means (average) of the variables  and  respectively, represents summation, and √ represents square root.
Simultaneously, we can compute the distance from the request to the edge devices to assess latency.This evaluation is performed using the following formula: This calculation provides crucial insights into the network's responsiveness, enabling us to optimize request allocation based on both processing efficiency and minimal latency, ensuring a swift and efficient edge computing system.Therefore, as shown in Fig. 3, we work with two distinct sets of data.The first set, denoted as {}{}, signifies the correlation between devices.In this context, correlation reflects the stability of the device; devices with low correlation values exhibit higher stability in comparison to others.This metric stands as a key criterion for optimal selection.The second set, represented as  {}, embodies distances between devices.Devices with shorter distances take precedence, indicating higher priority in the processing queue.

EXPERIMENTAL RESULTS
We utilize a dataset comprising 95,562 edge devices deployed across an edge computing area, Fig. 4 presents data regarding the processing history of edge devices.This information includes crucial parameters such as ID, coordinates (, ), processing capacity of the edge device in range [1,200], and the success rate of data processing, all of which require our attention In our experimentation, we follow a specific procedure: First, we begin by assuming the existence of a request, denoted as A. This request involves a certain number of calculations, represented as C, and is associated with specific coordinates (, ).We select the coordinate value of point A to serve as the central reference point for the edge devices.Our next step involves calculating the distance from the request A to the edge devices.This distance measurement is a crucial aspect of our experiment.Subsequently, we utilize processing time as a metric to assess the outcomes.To quantify our results, we employ the following formula: In Fig. 5, we conduct a comparative analysis involving two random selection methods and the proposed method.To determine the average time required for selecting an optimal edge device capable of processing the packet, we conduct 50,000 experiments for each packet capacity parameter-10, 50, 100, and 150 units.Subsequently, we calculate the average values for these experiments to facilitate a comprehensive comparison.The experimental results, as presented in Table 1, reveal that for packets with small capacity, the time to successfully transfer the packet to the edge device for processing appears to exhibit insignificant differences among the compared methods.In contrast, for larger data packages, the proposed method demonstrates significantly superior results, with a reduction in time of nearly 50%.

CONCLUSION
Our demo experiments provide compelling evidence of the effectiveness of our solution.We have demonstrated that our approach leads to significantly improved processing efficiency compared to randomly allocated methods and setups that do not employ correlation analysis techniques.These results underscore the practical benefits of our approach, highlighting its superior performance in optimizing processing time.In the future, we plan to delve deeper into the computing capabilities of individual devices.By doing so, we aim to enhance the optimization of routing solutions specifically tailored for edge devices.

Figure 1 :
Figure 1: The scenario of edge computing

Figure 3 :
Figure 3: The Optimize edge device

Figure 4 :
Figure 4: The structure of the dataset

Figure 5 :
Figure 5: The methods [4].1 Distributed Data Processing.Distributed data processing techniques involve distributing and processing large datasets across multiple edge devices.By dividing data processing tasks among devices, these techniques reduce the data transfer overhead and improve overall processing efficiency[4].Data processing frameworks like Apache Hadoop and Apache Spark are commonly used in edge environments to implement distributed data processing.Task offloading involves transferring computational tasks from resource-constrained devices to more capable edge devices or cloud servers.Offloading decisions are made based on factors such as device capabilities, task requirements, and network conditions.By offloading tasks strategically, edge devices can conserve energy, reduce processing time, and improve overall system efficiency.

Table 1 :
The experimental results