A Study of Petri Nets, Markov Chains and Queueing Theory as Mathematical Modelling Languages Aiming at the Simulation of Enterprise Application Integration Solutions: A First Step

Enterprise Application Integration (EAI) is a research field that seeks to develop methodologies, techniques and tools to design and development integration solutions. The software ecosystem of companies is comprised of several applications, usually obtained from third parties or developed internally and custom-made for their business processes. Interest in EAI has arisen due to the need to integrate different applications composing the software ecosystem to allow business processes to evolve in response to the constant demands of the business market. The main challenge facing companies in this context is that most of their applications are not designed considering integration with other applications. The development of integration solutions is not a simple task. Guaraná technology provides a domain-specific language that allows for the design of conceptual models to represent integration solutions. This paper reports on a study of Petri Nets, Markov Chains and Queueing Theory, aiming to construct simulation models from conceptual models of integration solutions modeled with Guaraná. We map the building blocks Slot and Task of Guaraná to their corresponding elements in the mathematical modelling languages studied.