Stochastic processes have been widely employed in order to assess the network layer performance of Optical Packet Switched (OPS) networks. In this paper we consider how the Engset traffic model may be applied to evaluate the blocking probability in asynchronous bufferless OPS networks. We present two types of the Engset traffic model, i.e. the Engset lost calls cleared traffic model and the Engset overflow traffic model. For both traffic models, the time-, call-, and traffic congestion are derived. A numerical study shows that the observed blocking probability is dependent on the choice of traffic model and performance metric.