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Time-domain wavelength interleaved networking (TWIN) is an optical mesh network architecture in which each edge node has one (or more) tunable lasers to transmit fixed-length bursts to various destinations and one (or more) burst-mode receivers capable of decoding each burst intended to it. In this architecture, the interior nodes route each burst independently and passively based on the wavelength of the burst. Network scheduling is thus a critical component that arbitrates burst transmissions from sources to destinations so that conflicts are either avoided or minimized, and wavelength division multiplexing (WDM) transport capacity is efficiently utilized. However, in access or metro networks, which lend themselves naturally to the TWIN mesh architecture, centralized network scheduling would be cumbersome. We consider a distributed mechanism that performs scheduling of bursts to further simplify TWIN mesh architectures. In one realization, each source randomly assigns non-overlapping time slots within a frame for its transmissions. In another realization, each destination grants random but non-overlapping time slots to sources for transmissions. In neither scheme is there any coordination across sources and destinations. We present an analytical formulation of these schemes and investigate their performance under two broad types of traffic: dynamic traffic and semi-dynamic traffic. For dynamic traffic, the analytical results show that for offered load close to 100 percent of capacity, there is 63 percent efficiency for the destination-based mechanism and 37 percent efficiency for the source-based mechanism. When end-to-end demands are semi dynamic, we show through simulations that the destination-based random schedules can achieve over 90 percent efficiency even for offered loads close to 100 percent. These results indicate that the proposed distributed schemes, though exceedingly simple, provide acceptable efficiency comparable to that realized by computation-in- ensive centralized schedulers irrespective of propagation delays and applicable to any kind of network traffic.