Expected antenna utilization and overload

The trade-offs between the number of antennas at Deep Space Network (DSN) Deep-Space Communications Complex and the fraction of continuous coverage provided to a set of hypothetical spacecraft, assuming random placement of the space craft passes during the day. The trade-offs are fairly robust with respect to the randomness assumption. A sample result is that a three-antenna complex provides an average of 82.6 percent utilization of facilities and coverage of nine spacecraft that each have 8-hour passes, whereas perfect phasing of the passes would yield 100 percent utilization and coverage. One key point is that sometimes fewer than three spacecraft are visible, so an antenna is idle, while at other times, there aren't enough antennas, and some spacecraft do without service. This point of view may be useful in helping to size the network or to develop a normalization for a figure of merit of DSN coverage.