Service differentiation is a crucial issue in the next -generation Optical Packet Switched networks. In this paper we examine how bursty traffic influences the performance of a service differentiated Optical Packet Switched network. By using time -continuous Markov chains, we derive explicit results for the packet loss rates in the case of a bursty hyper-exponential arrival process. Results indicate that the performance is degraded as the burstiness of the arrival process increases.