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Waveband switching (WBS) in conjunction with multigranular optical cross-connect (MG-OXC) architectures can reduce the cost and complexity of OXCs. In this paper, we study the performance of different MG-OXC architectures under dynamic traffic. In the case with online incremental traffic, we compare two MG-OXC architectures in terms of the blocking probability of new lightpath requests and study the impact of port counts and traffic loads. We develop an online integer linear programming model (On-ILP), which minimizes the number of used ports and the request blocking probability, given a fixed number of wavelengths and MG-OXC architecture. The On-ILP optimizes the routing of new lightpaths so as to maximize lightpath grouping and reduce the port count given that existing traffic cannot be rearranged. We also propose a new efficient heuristic algorithm, called maximum overlap ratio (MOR) to satisfy incremental traffic and compare it with the On-ILP, first-fit, and random-fit algorithms. Our results and analysis indicate that using WBS with MG-OXCs can reduce the size (and, hence, the cost) of switching fabrics compared to using ordinary OXCs. Based on the results and observations in the incremental traffic case, we further study the performance of a particular MG-OXC architecture under fully dynamic or fluctuating traffic. Our simulations show that the proposed heuristic algorithm waveband assignment with path graph, which groups wavelengths to bands and uses wavelength converters efficiently under fluctuating traffic, significantly outperforms other heuristic algorithms.