Assuming data traffic of fixed-length cells, we propose a frame-oriented scheduling discipline, PFRR (parallel fair round robin), for WDM optical switches by applying pfair (proportionate fairness) scheduling so that deterministic communication performance is guaranteed. Bandwidth reservation for an active session is performed by holding a number of cell slots for the session in a two-dimension frame, which is transferred iteratively over the multiple channels in an optical fiber. To determine the transmission order of cells in a frame, pfair scheduling is used so that the cells belonging to a session are distributed over the frame as uniformly as possible. Through the analysis by network calculus and by network simulator, it is shown that PFRR possesses tight delay bounds and lenient buffer requirements. Also, with a minor modification to PFRR, a new service discipline called MPFRR is proposed that can be used as traffic regulator to support sessions with jitter requirements.