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