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

We present an approximate analytical method to calculate blocking probabilities of linear fragment of wavelength routed networks with multiclass unicast and multicast calls. The 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 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 product-form solution for the equilibrium distribution.