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A MultiCode-CDMA network that is capable of providing quality-of-service guarantees will find widespread application in future wireless multimedia networks. However, providing delay guarantees to time-sensitive traffic in such a network is challenging because its transmission capacity is variable even in the absence of any channel impairment. We propose and evaluate the performance of a novel transmission scheduling scheme that is capable of providing such a delay guarantee in a MultiCode-CDMA network. The proposed scheme drops packets to ensure that delays for all transmitted packets are within the guaranteed target bounds, but packets are dropped in a controlled manner such that the average dropping ratios of a set of time-sensitive flows can be proportionally differentiated according to the assigned weighting factors or shares. We provide extensive simulation results to show the effectiveness of the proposed scheme as well as to study the effects of various parameters on its performance. In particular, we show that it can simultaneously guarantee a delay upper bound and a proportionally differentiated dropping ratio in a fading wireless channel for different traffic loads, peak transmission rates, and weighting factors of individual flows.