This paper presents an analytical model that can be used to evaluate the blocking probability of each service class in a multi-class optical burst - switching network. The model allows, for the first time, the evaluation of blocking probabilities in optical burst switching (OBS) systems with arbitrary burst -length distributions and arbitrary offsets, including OBS systems in which all classes are different in mean burst length. Such systems do not follow the conservation law and cannot, therefore, be analyzed using previously published OBS models. For an OBS system with two classes, an offset load of 10-3, and a 1 : 5 ratio of high - priority to low - priority traffic, this shows that the model accurately predicts the blocking probability for each class, whereas predictions from previously published models that assume conservation disagree with the simulation results by as much as 75%.