We present an exact analytical model for single-wavelength quality of service (QoS) differentiation in a two-class optical packet switch. In this system, QoS differentiation is achieved by limiting the set of fiber delay lines (FDLs) to the low-priority class, whereas the high-priority class is allowed to access the entire FDL bank. The analytical model is based on multi-regime Markov fluid queues and is extensible to multi-class systems with more than two classes. Markovian arrival process packet arrivals and phase-type distributed packet sizes are considered for the purpose of generality. The proposed analytical model is validated through simulations. The numerical results provide insight into determining appropriate subsets of FDLs allowed for the access of the low-priority class. The results also show that it is possible to direct almost all the packet losses to the low-priority class under moderate loads.