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The basic principle of waveband switching (WBS) is to group multiple wavelengths together as a band or fiber and switch the group using a single port whenever possible. To support waveband grouping in WBS networks, multi-granular optical cross-connects (MG-OXCs) are introduced to switch the traffic at the fiber, band, and wavelength layers. One important goal in WBS networks is to minimize the number of ports at the MG-OXCs. For WBS networks with dynamic or on-line traffic, both the port consumption and call blocking probability should be considered during the process of accommodating unpredictable traffic demands with limited resources. Call blocking can be caused by port insufficiency as well as wavelength shortage in WBS networks with dynamic traffic. Our study in this work starts with an analysis of a reconfigurable MG-OXC architecture and various cases of port consumption on this architecture. We then analyze the lower/upper bounds for the design parameter of the reconfigurable MG-OXC architecture. Based on the insights obtained from the analysis, we propose a new algorithm, namely, weighted graph-based waveband assignment (WGB), which employs an auxiliary weighted graph technique to make efficient dynamic routing and waveband assignment. The proposed algorithm is simulated in WBS networks with fully dynamic or incremental traffic patterns. Our results show that the proposed scheme can satisfy up to 40% more lightpath requests than the existing scheme, maximum overlap ratio (MOR), before a certain blocking ratio is observed in the network. Our study also shows that with limited resources, WBS can obtain port savings by limiting the design parameter while achieving an allowable blocking probability.