We propose a new method for the performance evaluation of Open Queueing Net
works with a Population Constraint (represented by a set of tokens). The me
thod is based on the application of Approximate Mean Value Analysis (AMVA)
algorithms. We present procedures for single class networks and for multipl
e class networks, subject to either a common constraint (shared tokens) or
to class-based constraints (dedicated tokens). In fact, the new method is a
unified framework into which all procedures for the different types of net
works fit. We show how the new method relates to well-known methods and pre
sent some numerical results to indicate its accuracy.