We focus on all-optical broadcast and select slotted WDM networks. Each network user is equipped with one tunable transmitter and one fixed receiver; full connectivity is achieved by tuning transmitters to all different wavelengths available in the optical spectrum. Tuning latencies are considered to be not negligible with respect to the slot time. A network controller allocates fixed size slots in a TDM/WDM frame according to requests issued by users via signalling procedures. User requests

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... accommodated in the frame incrementally, as soon as they are received by the network controller. Since we aim at an incremental solution, we impose a transparency constraint in the scheduling algorithm: new user requests may be accepted only without affecting existing allocations, otherwise they are refused. We propose a novel scheduling algorithm that may route some flows from source to destination through some intermediate nodes, following a multi-hop approach. A formal definition of an optimal transparent incremental scheduling algorithm is provided as an integer linear programming problem. The optimal incremental scheduling algorithm is NP-hard. Thus, a heuristic quasi-optimal scheduling algorithm is proposed, and its complexity is evaluated. Performance results show that significant benefits can be achieved with respect to traditional single-hop approaches and to other multi-hop approaches. Index Terms-All-optical networks, wavelength division multiplexing.