With current optical switches, an entire wavelength is switched from a source node to a single destination node, thereby precluding fractional wavelength allocation. This shortcoming results in (i) requiring at least N(N - 1) wavelengths for complete connectivity of a network with N end nodes; (ii) inability to aggregate/separate traffic in the core nodes; and (iii) a mismatch in connecting subnetworks of different capacities. A recently proposed time-driven optical switch based on a universal time clock (UTC) demonstrates synchronized time frame switching of a given wavelength without processing the frame content. A question that arises then, is how to allocate the time frames of a given wavelength amongst the N destinations so as to meet the required offered load and to minimize the mean delay and buffer size at each source end node. We propose and analyze a fractional wavelength circuit switching scheme based on the uniformity properties of the golden ratio and demonstrate its performance for Poisson and Norros long-range-dependent traffic.