## 6 Conclusions  
In this work, we conducted a comprehensive comparison of the deployment of big data processing platforms for three computing paradigms, namely batch processing, stream processing, and function processing in resource-constrained environments, namely edge and fog computing layers, versus cloud-based deployments. For big data processing platforms, we used three off-the-shelf big data platforms, namely Apache Spark for batch processing, Apache Flink for stream processing, and Apache OpenWhisk for function processing. The evaluation results demonstrate that deploying big data processing frameworksin resource-constrained environments by utilizing the collaborative power of local low-cost devices is a viable and promising option for the three investigated processing paradigms. Finally, we discussed our recommendations in regard to building more practical big data frameworks for resource-constrained edge and fog computing environments and provided insights into the performance of applications in each computing layer.  
As part of our future work, we would like to investigate the training of large and complicated deep learning models in edge and fog computing layers by leveraging the local nodes' computational capabilities to collectively contribute to the training processes of resource-intensive deep learning models. Furthermore, the computing continuum across edge, fog, and cloud computing layers could be studied, with a specific focus on observing the implications of big data processing tasks across this continuum. Understanding how big data processing tasks traverse and interact within this multilayered computing architecture is important in terms of optimizing the performance, minimizing the latency, and enhancing the overall efficiency of data processing workflows. This research direction involves the dynamics of data movement, task distribution, and resource utilization as large amounts of data move from edge devices to fog nodes and, ultimately, to cloud infrastructure. Another research direction involves proposing and implementing design changes on each data processing platform, tailored to resource-constrained edge and fog computing environments. In the context of big data solutions, optimizing these platforms for edge and fog environments by carefully considering the constraints of these environments, including their restricted computational capabilities and storage limitations, is crucial due to the unique challenges posed by limited resources and the need for efficient data processing. In addition, we plan to extend the scope of our experiments by incorporating diverse application scenarios. This expansion will ensure a more comprehensive evaluation of big data processing platforms, allowing us to obtain insights into their performance across various use cases and real-world applications.  
Conceptualization, M.A. and T.S.; methodology, M.A. and T.S.; software, T.S.; deployment, T.S.; evaluation and analysis, T.S.; writing--original draft preparation, T.S.; writing--review and editing, M.A.; supervision, M.A.; project administration, T.S.; funding acquisition, M.A. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by JSPS KAKENHI (grant number 22 KF0314).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} EMR & Elastic MapReduce \\ DL & Deep learning \\ IoT & Internet of Things \\ GPU & Graphical processing unit \\ AI & Artificial intelligence \\ MLP & Multilayer perceptron \\ YOLO & You Only Look Once \\ AWS & Amazon Web Services \\ LAN & Local area network \\ VM & Virtual machine \\ CPU & Central processing unit \\ Mem & Memory \\ MLLib & Machine learning library \\ \end{tabular}