Formalism of Stochastic Queueing Network using Stochastic Petri Nets

Queueing process is an essential behavior of common software systems. It would have critical impact on the requirements, including credibility, accuracy, timeliness and cost. Especially in the real-time system, a queueing network system provides a high level comprehensive model to help analyze and adjust the performance of the availability of incoming customer and service resources. In this paper, we intend to focus on the formalism of stochastic queues and the construction of them into a comprehensive queueing network system, as to cope with the random behaviors of the arrival time and service time. A stochastic Petri net is considered and illustrated to represent the target stochastic queueing network and a simple Markovian graph is generated to represent the probability distribution of the behavioral model.