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This study addresses the problem of resource allocation for a multi-class time-slotted optical overlapped code-division multiple access network. A delay-constraint fair resource allocation (DC-FRA) scheme is considered with the quality of service requirements on both physical layer signal-to-interference ratio and network layer average packet delay. A cross-layer approach in allocating the transmission power and rate for every class of users in the network is considered. The performances of the S-ALOHA, R-ALOHA and R3T medium access control protocols have been investigated in the DC-FRA scheme. It is shown that the R-ALOHA protocol has the highest throughput and the minimum average packet delay. On the other hand, although the DC-FRA allocates the largest bandwidth under the R-ALOHA protocol, it forces the users to transmit with relatively higher power in comparison with the power required for the S-ALOHA and the R3T protocols. In addition, the packets exhibit much smaller delay when using the DC-FRA, especially at low and moderate throughput for the three protocols.