Queueing network is important in modeling, analysis,
and performance evaluation of manufacturing, computer
and communication, and transportation and logistics systems. There are two
classes of networks that are known to be "solvable", i.e., networks of
quasi-reversible nodes (e.g., Kelly, Whittle, Walrand, etc.), and networks
of reversible nodes (e.g., Kingman, Pollett, etc). This talk addresses the
following question: are there any other networks that have analytically
tractable solution and, if yes, how to solve them? We answer these
questions by developing a necessary and sufficient condition for a
network to have a product form stationary distribution, and present a
computational procedure to solve it.