Analysis of fork/join and related queueing systems

This article introduces a generalization of the classical parallel-server fork-join queueing networks.
We consider open fork-join queueing networks with an arbitrary topology. There are three types of nodes in the queueing networks (service-nodes, fork-nodes, join-nodes). We focus on the infinite server case, in which each service-node is a queueing system with infinite servers. An arriving job is split (at fork-nodes) into a number of independent tasks that are serviced in parallel (at multiple service-nodes). Each task can be split at fork-nodes repetitively. These tasks synchronize (at join-nodes) before they leave the network.
A method, which allows to obtain the sojourn time distribution, was developed.