Queueing analysis of scheduling policies in copy networks ofspace-based multicast packet switches

Space-based multicast switches use copy networks to generate the copies requested by the input packets. In this paper our interest is in the multicast switch proposed by Lee (1988). The order in which the copy requests of the input ports are served is determined by the copy scheduling policy and this plays a major part in defining the performance characteristics of a multicast switch. In any slot, the sum of the number of copies requested by the active inputs of the copy network may exceed the number of output ports and some of the copy requests may need to be dropped or buffered. We first propose an exact model to calculate the overflow probabilities in an unbuffered Lee's copy network. Our exact results improve upon the Chernoff bounds on the overflow probability given by Lee by a factor of more than 10. Next, we consider buffered inputs and propose queueing models for the copy network for three scheduling policies: cyclic service of the input ports with and without fanout splitting of copy requests and acyclic service without fanout splitting. These queueing models obtain the average delay experienced by the copy requests. We also obtain the sustainable throughput of a copy network, the maximum load that can be applied to all the input ports without causing an unstable queue at any of the inputs, for the scheduling policies mentioned above