Performance evaluation of the fork-join system with Markovian arrival and phase-type service time distribution

In this paper, we examine a fork-join queueing system. Customers enter the system in a MAP (Markovian Arrival Process). Each of the customers entering the system forks into tasks, to be served in independent subsystems. Each subsystem consists of a server and a buffer. The service time of a task by the 𝑘-th server has a PH (Phase type) distribution with an irreducible representation (𝛽𝑘, 𝑆𝑘). For the special case when = 2, the stationary distribution is obtained, and algorithms are presented to compute the stationary distribution, and performance characteristics of the fork-join system. We suggested an approach based on a combination of Machine learning and Monte-Carlo method to investigate the performance characteristics of fork-join system. The results of numerical experiments are presented in this paper.