The effects of destructive interference and wasted transmissions on the uniform-traffic capacity of non-bus-oriented single-hop interconnections

The uniform-traffic capacity of switchless, non-busoriented, fiber-optic single-hop interconnections among N stations, each equipped with a small number of transmitters and receivers, can be as high as Θ(log₂ N)* concurrent transmissions on a single wavelength with round-robin scheduling in a time-slotted system. However, their capacity with the slotted ALOHA access scheme does not increase with N. (The capacity of bus-oriented interconnections, in contrast, varies across time-slotted access schemes by, at most, a factor of e.) This paper quantifies the contribution of several factors to capacity. Merely avoiding destructive interference with ongoing receptions contributes, at most, a factor of e over slotted ALOHA, the same as in bus-oriented interconnections. For an interconnection among two-transmitter, single-receiver stations, whose capacity is log₂ N with global scheduling and 2/e with slotted ALOHA, also avoiding transmissions to blocked receivers increases capacity to, at most, log₂ log₂ N. These results suggest that the added complexity of non-bus-oriented SHI's may be warranted only if they are operated in ways that permit the selection of "good" combinations of (source, destination) pairs for concurrent transmission, and further research should focus on those.