In this paper, the problem of distributed opportunistic channel access in wireless relaying is investigated. A relay network with multiple source-destination pairs and multiple relays is considered. All the source nodes contend through a random access procedure. A winner source node may give up its transmission opportunity if its link quality is poor. In this research, we apply the optimal stopping theory to analyze when a winner node should give up its transmission opportunity. By assuming the winner node has information of channel gains of links from itself to relays and from relays to its destination, the existence and uniqueness of an optimal stopping rule are rigorously proved. It is also found that the optimal stopping rule is a pure-threshold strategy. The case when the winner node does not have information of channel gains of links from relays to its destination is also studied. Two stopping problems exist, one in the main layer (for channel access of source nodes), and the other in the sub-layer (for channel access of relay nodes). An intuitive stopping rule, where the sub-layer and the main layer maximize their throughput respectively, is shown to be a semi-pure-threshold strategy. The intuitive stopping rule turns out to be non-optimal. An optimal stopping rule is then derived theoretically. Our research reveals that multi-user (including multi-source and multi-relay) diversity and time diversity can be fully utilized in a relay network by our proposed strategies.Comment: 20 page
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