Lambda-Systolic Routing in a Wavelength-Division Multiplexed All-Optical Butterfly

In this paper we present an all-optical network architecture and a routing protocol for it. A 2r-dimensional coloured optical butterfly (COBF) network consists of P = $2^{2r}$ processors, N = $r2^{2r+1}$ routing nodes, and E = $r2^{2r+2}$ edges. The routing machinery is divided in an r-dimensional front-end and 2r = $\sqrt{P}$ r-dimensional back-ends. Processors are deployed at the level 0 (identical to level 2r) nodes of the network. Routing is based on the use of $\sqrt{P}$ wavelength-multiplexed optical signals, a cyclic control bit sequence, and scheduled sendings of packets. The routing protocol ensures that no electro-optical conversion is needed in the intermediate routing nodes and all the packets injected into the routing machinery will reach their target without collisions. We then present an analysis of the routing algorithm with a batch type routing problem. According to our experiments, a work-optimal routing of an h-relation is achieved with a reasonable size of h ÎΩ(P).