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A new cooperative multiple-access protocol is proposed in which a relay utilizes the empty time slots available in a TDMA frame. In particular, the relay helps the users in the network forwarding their unsuccessfully transmitted packets during the empty time slots. This will better utilize the channel resources that are otherwise wasted, and will introduce on-demand spatial diversity into the network. The proposed cooperation protocol is also different from those proposed in the literature as it does not result in any bandwidth loss. Two different protocols are proposed to implement this new multiple-access scheme, and their stability regions are characterized. The stability regions of the proposed protocols are shown to contain that of TDMA without relaying, hence, relay deployment in wireless networks can increase the network throughput capacity. Moreover, the analysis and numerical results reveal that the proposed cooperative multiple access protocols can simultaneously achieve higher stable throughput and less energy expenditure compared to TDMA without relaying.