The main challenge concerning the design of an optical packet switch is the issue of contention resolution. This paper introduces an optical packet switch architecture, with a two-tiered partially shared buffer using a novel buffer scheduling scheme. The traffic scheduling in the partially shared buffers is done in a hierarchical fashion to ensure the maximum router throughput. We compare the performance of the proposed strategy with single and multiple groups of partially shared buffers, keeping the overall buffer size constant. The performance analysis has been done for a Bernoulli distributed traffic at varying loads. The simulation results indicate a significant improvement in the packet loss probability. A remarkable advantage of the suggested architecture is that it obviates the need for wavelength conversion, thereby achieving a reduction in the infrastructural cost involved in the employment of wavelength converters. The secondary benefits include the elimination of the delay incurred due to searching for the appropriate wavelength and tuning of the wavelength converter. Also, the complexity associated with the accommodation of packets in partially shared buffers is reduced from O(n) to O(1) in comparison to n-groups of partially shared buffers as the search for the least queued partial buffer is replaced by a Boolean decision for every contending packet. Thus, in addition to enhancing the router performance in terms of the packet loss probability, the proposed strategy also augments the router speed.