Analysis of balanced fork-join queueing networks

This paper presents an analysis of closed, balanced, fork-join queueing networks with exponential service time distributions. The fork-join queue is mapped onto two non-parallel networks, namely, a serial-join model and a state-dependent model. Using these models, it is proven that the proportion of the number of jobs in the different subsystems of the fork-join queueing network remains constant, irrespective of the multiprogramming level. This property of balanced fork-join networks is used to compute quick, inexpensive bounds for arbitrary fork-join networks.