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In this paper, we propose a resource allocation scheme to increase the effective capacity subject to the queue-overflow statistical Quality-of-Service (QoS) requirement for a multi-relay cooperative wireless network. Firstly, we consider the block fading channels and derive an algorithm in which each relay is allocated a time slot of optimal length during the cooperation phase, based on the channel statistics. Our analysis indicates that when the QoS requirement is loose, only the relay with the best average channel condition should be selected for cooperation. On the other hand, when the QoS requirement becomes more stringent, more relays should participate in cooperation. The asymptotic case when either the transmit power or the number of relays goes to infinity is discussed, and we shall reveal a tradeoff between the transmit power and the number of relays, given a target effective capacity. By modeling the channel correlation by a two-state Markov model, we will develop two sub-optimal time-slot allocation algorithms which can substantially increase the effective capacity compared with the opportunistic and equal allocation schemes. Our results will show that the channel correlation can sharply decrease the effective capacity and that applying the optimal time-slot allocation result obtained in block fading channels directly to correlated fading channels is no longer optimal.