This paper proposes a new traffic decomposition method
called MNA to solve multi-class queueing networks with
first-come first-serve stations having phase-type (PH) ser-
vice, which generalizes the classic QNA method by Whitt.
MNA not only supports open queueing networks but also
closed networks, which are useful to model concurrency lim-
its in software systems. Using validation models, we show
that under low SCV of service time and inter-arrival time,
the new method is on average more accurate than QNA.
Therefore, MNA can provide better software performance
prediction for quality-of-service management tasks.