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Waveband switching (WBS) has attracted attention from the optical networking industry for its practical importance in reducing port count, the associated control complexity, and cost of optical cross-connects (OXCs). However, WBS-related problems of theoretical interest have not been addressed thoroughly by the research community and many issues are still wide open. In particular, WBS is different from wavelength routing and, thus, techniques developed for wavelength-routed networks (including for example, those for traffic grooming) cannot be directly applied to effectively address WBS-related problems. In this paper, we first develop an integer linear programming (ILP) model, which for a given set of lightpath requests, determines the routes and assigns wavelengths to the lightpaths so as to minimize the number of ports needed. Since the optimal WBS problem of minimizing the port count in WBS networks contains an instance of routing and wavelength assignment (RWA), which is NP-complete, we adopt a powerful waveband assignment strategy and develop an efficient heuristic algorithm called balanced path routing with heavy-traffic first waveband assignment (BPHT). Both the ILP and the heuristic algorithm can handle the case with multiple fibers per link. We conduct a comprehensive evaluation of the benefits of WBS through detailed analysis and simulations. For small networks, our results indicate that the performance of the BPHT heuristic is close to that achievable by using the ILP model and, hence verifying its near-optimality. We show that for larger networks, BPHT can perform better than its variation called balanced traffic routing with maximum-hop first waveband assignment and much better than another heuristic based on optimal (but waveband oblivious) RWA that minimizes wavelength resources. We also show that WBS using BPHT is even more beneficial in multifiber networks than in single-fiber networks in terms of reducing the port count. Our analytical and simulation results provide valuable insights into the effect of wavelength band granularity, as well as the tradeoffs between the wavelength-hop and the port count required in WBS networks.