## Optimization of the Size of Thread Pool in Runtime Systems to Enterprise Application Integration: A Mathematical Modelling Approach

ABSTRACT Companies seek technological alternatives that provide competitiveness for their business processes. One of them is integration platforms, software tools that build integration solutions, which allow the different applications that make up the software ecosystem to work synchronously and that new applications or functionality be incorporated with the least impact in the existing ones. The runtime system is the component of the integration platform responsible for managing the computational resources that run the integration solution. Among these resources are the processing units, called threads, or sets of those threads, called thread pools. The performance of the runtime systems is directly related to the number of threads available to run the integration solution, but scaling the number of threads that provide a shorter response time is a challenge for software engineers. If this quantity is undersized, it may cause a delay in the execution; if it is overestimated, it could cause a waste of computational resources. This article presents a mathematical model, defined by differential equations, that establishes the optimum number of threads, which maximizes the expected performance gain by minimizing the execution time of the integration solution. In addition, it presents the mathematical model application, which assists the analysis of the expected gain in different architecture scenarios and quantity of threads.