On the Uniform-Traffic Capacity of Single-Hop Interconnections Employing Shared Directional Multichannels

A shared directional multichannel (SDM) consists of a set of inputs and a set of outputs to which we connect transmitters and receivers, respectively. A signal placed at any given input reaches a subset of the outputs, and a channel is specified by the sets of outputs that are reachable from each input. A message is received successfully at an output of the channel if and only if it is addressed to the receiver connected to that output and no other signals reach that output at the same time. Constructive lower bounds as well as some upper bounds on the uniform-traffic capacity of SDM-based single-hop interconnections between a set of multitransmitter source stations and a set of multireceiver destination stations are derived. (Every source station is connected to every destination station through the channel.) A bidirectional interconnection among a set of stations would be obtained by representing each station as one source station and one destination station. Both randomized transmissions and deterministic scheduling are considered. It is shown that with randomized transmissions, SDM's that can be described as a collection of buses can perform as well as any other ones. With deterministic scheduling, however, the use of certain non-bus-oriented SDM's yields a much higher interconnection capacity.