In this paper, a WDM metro ring consisting of access nodes with $FT-FR^n$ (Fixed Transmitter - n Fixed Receivers) is considered. A trade-off exists between node throughput and transmission fairness because the access nodes share wavelength channels. In order to eliminate the transmission unfairness and to increase throughput, the p-persistent medium access control (MAC) protocol is proposed: each node uses an empty optical slot to transmit a packet and make it available with the extraction of a transferred packet at the source access node, called source-stripping. The local empty slot can be used to transfer a head-of-line packet in the local buffer with probability p or it is used for the next downstream nodes with 1-p. The proposed MAC protocol provides better node throughput than the non-persistent protocol and exhibits better fairness index than the 1-persistent protocol in WDM ring networks. In addition, numerical analysis shows that the proposed MAC protocol maximizes the node throughput under uniform traffic conditions. For more detailed results, we use the network simulation under Poisson and self-similar traffic. Furthermore, unpredictable traffic constructed by the combination of the former and the latter is also considered. The reasonable probability of the p-persistent protocol for a given architecture can be determined through simulation.