In this paper, we present a distributed medium access control (MAC) protocol and a network architecture suitable for optical intra-rack data center networks (DCNs). The intra-rack communication is performed using passive optical components, over four data wavelength division multiplexing (WDM) channels of either 40 or 100 Gbps each, keeping low power consumption. On the other hand, the inter-rack communication is performed over a separate network through upper layer routers. In this study, we focus only on the intra-rack communication. We introduce an intra-rack DCN (IR-DCN) architecture that works in the optical domain, and two IR-DCN configurations with different total nominal capacity: 160 and 400 Gbps, respectively. Also, we propose a synchronous pre-transmission coordination fair access intra-rack MAC (intra-MAC) protocol taking into account the traffic characteristics and priority classes within existing DCNs. The proposed intra-MAC protocol totally eliminates packet collisions, achieving high performance. Particularly, it reaches high bandwidth utilization even under heavy loads: 90% and 87.5% for the two IR-DCN configurations of 160 and 400 Gbps total capacity, respectively. Also, it achieves low mean end-to-end (e2e) packet delay, lower than 0.25 and 0.12 ms, respectively, providing a reliable solution for time-sensitive DCN traffic. Specifically, simulation results demonstrate that the highest priority traffic experiences e2e delay lower than 1.9 and 1.1 µs, respectively, which is sufficient for the service of the strictest delay requirements of time-sensitive cloud applications. The intra-MAC protocol is decentralized, without the need for a network controller, providing high flexibility. Our IR-DCN proposal is studied in comparison to other currently dominant intra-rack/cluster DCNs, and it achieves from 6% to 57% higher throughput and from 20% to 99% lower e2e delay at high loads. Comparatively, it is on average 80% and 68% more energy and cost efficient, respectively.