  A robotic swarm may encounter traffic congestion when many robots
simultaneously attempt to reach the same area. For solving that efficiently,
robots must execute decentralised traffic control algorithms. In this work, we
propose a measure for evaluating the access efficiency of a common target area
as the number of robots in the swarm rises: the common target area throughput.
We also employ here the target area asymptotic throughput -- that is, the
throughput of a target region with a limited area as the time tends to infinity
-- because it is always finite as the number of robots grows, opposed to the
relation arrival time at the target per number of robots that tends to
infinity. Using this measure, we can analytically compare the effectiveness of
different algorithms. In particular, we propose and formally evaluate three
different theoretical strategies for getting to a circular target area: (i)
forming parallel queues towards the target area, (ii) forming a hexagonal
packing through a corridor going to the target, and (iii) making multiple
curved trajectories towards the boundary of the target area. We calculate the
throughput for a fixed time and the asymptotic throughput for these strategies.
Additionally, we corroborate these results by simulations, showing that when a
strategy has higher throughput, its arrival time per number of robots is lower.
Thus, we conclude that using throughput is well suited for comparing congestion
algorithms for a common target area in robotic swarms even if we do not have
their closed asymptotic equation.
