Bounds of the overflow priority classification for blocking probability approximation in OBS networks

It has been demonstrated that the overflow priority classification approximation (OPCA) is an accurate method for blocking probability evaluation for various networks and systems, including optical burst switched networks with deflection routing. OPCA is a hierarchical algorithm that requires fixed-point iterations in each layer of its hierarchy. This may imply a long running time. We prove here that the OPCA iterations alternately produce upper and lower bounds that consistently become closer to each other as more fixed-point iterations in each layer are used, and we demonstrate numerically that only a small number of iterations per layer are required for the bounds to be sufficiently close to each other. This behavior is demonstrated for various system parameters including offered load, number of channels per trunk, and maximum allowable number of deflections.