Approximate mean value analysis-based solution procedures for open queueing networks with population constraints

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 algorithms. We present procedures for single class networks and for multiple 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 networks fit. We show how the new method relates to well-known methods and present some numerical results to indicate its accuracy.