In current optical switches, an entire wavelength is switched from a source node to a single destination node, thereby precluding fractional wavelength allocation. This limitation results in two major problems: (i) N(N -1) wavelengths are required to fully connect a network with N edge nodes; and (ii) traffic arriving at the core switch from multiple optical links cannot be groomed in the optical domain. Whereas wavelength switching is feasible at a very fine time granularity, forwarding decisions are based on frame processing which is infeasible in the optical domain. However, the newly proposed time-driven optical switch based on a universal time clock (UTC) facilitates frame switching of a given wavelength without requiring frame content processing. In a previous paper , we presented and analysed a deterministic frame scheduler with optimal delays, based on the uniformity properties of the golden ratio (GR). The scheduler of  resolves the N(N -1) problem; however it leaves the traffic grooming open. In this study, we extend our GR scheduler to cope with the problem of traffic grooming. We further propose a model to analyse its performance and simulate it with Poissonian frame arrival processes. Surprisingly, the simulation demonstrates that our restricted GR scheduler performs as well as the strict GR and the idealized schedulers.