In an optical burst switching (OBS) network, the blocking time, representing the time interval during which the channel is occupied for a given class of incoming burst, is a key metric for performance evaluation and traffic shaping. In this paper, we study a horizon-based single-channel multi-class OBS node, for which the multiple traffic classes are differentiated using different offset time of each class. By assuming Poisson burst arrivals and phase-type distributed burst lengths and using the theory of Multi-layer stochastic fluid model, we obtain the Erlangian approximation for the finite time probability of the blocking time for a given class of burst in an OBS node. We further propose an explicit algorithm and procedure to calculate the Erlangian approximation. Numerical results are provided to illustrate the accuracy and the speed of convergence of the proposed method.
