Calculating blocking probabilities in linear fragment of wavelength routed networks with multiclass unicast and multicast calls

Abstract

We present an approximate analytical method to calculate the blocking probabilities of a linear fragment in wavelength routed networks with multiclass unicast and multicast calls. A mathematical model accounting for multiclass unicast and multicast calls is introduced. It is shown that the Markov process describing the functioning of a linear fragment is not time-reversible. For the special case of a two-hop linear fragment, we show that it is possible to approximate its functioning by a Markov process defined over the same state space, but with slightly modified transition rates. The constructed Markov process is shown to have a product-form solution for equilibrium distribution