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In this paper, the optimal scheduling problem for ultrawideband (UWB) networks is formulated as a utility maximization problem, considering heterogeneous traffic characteristics and the fairness constraint, which is an NP-hard problem. The utility function, defined as the user satisfaction level with respect to the allocated bandwidth, takes the link distance as the input parameter that may be noisy due to ranging errors. We solve the stochastic optimization problem by a metaheuristic, called the exclusive-region-based global search algorithm, that can avoid trapping into local optima with reasonable efficiency, complexity, and convergence speed. The concept of exclusive region for concurrent UWB communications is employed to improve algorithm efficiency. Extensive simulations demonstrate that, by appropriately scheduling concurrent transmissions, the total utilities of each traffic class can be significantly improved. In addition, the proposed scheduling algorithm can support heterogeneous applications and guarantee the intraclass and interclass fairness among competing flows.