A graph-coloring scheme for scheduling cell transmissions and its photonic implementation

The authors present a scheme for scheduling cell-transmissions in an ATM switch capable of atomic multicasts. In an atomic multicast, partial transmissions to subsets of the requested output ports are not allowed. In any transmission slot, a cell at an input port is either successfully (without output contention) transmitted to all requested destinations or it is not transmitted at all. Scheduling is needed because many cells (due to the uncoordinated nature of their arrivals at the switch input ports) can request transmission to the same switch output port at the same time even though the switch may not have the ability to simultaneously satisfy all these requests. The problem is to devise an implementable scheme for scheduling atomic multicast requests such that all requests present at the beginning of a scheduling interval are satisfied in a minimum number of cell transmission slots. However, finding this minimum transmission schedule is equivalent to finding the minimum vertex coloring of a “contention graph” derived from the input requests. Since finding the minimum vertex coloring is an NP-hard problem, it is not feasible to find the minimum schedule. They present a scheduling scheme which uses a heuristic coloring algorithm with a known upper bound on the number of transmission slots used. This scheme can also schedule a mix of request types (unicasts, atomic and non-atomic multicasts). They describe two methods for photonic implementation of the scheduler and also methods to incorporate fairness and priorities