  Multi-packet reception (MPR) has been recognized as a powerful
capacity-enhancement technique for random-access wireless local area networks
(WLANs). As is common with all random access protocols, the wireless channel is
often under-utilized in MPR WLANs. In this paper, we propose a novel
multi-round contention random-access protocol to address this problem. This
work complements the existing random-access methods that are based on
single-round contention. In the proposed scheme, stations are given multiple
chances to contend for the channel until there are a sufficient number of
``winning" stations that can share the MPR channel for data packet
transmission. The key issue here is the identification of the optimal time to
stop the contention process and start data transmission. The solution
corresponds to finding a desired tradeoff between channel utilization and
contention overhead. In this paper, we conduct a rigorous analysis to
characterize the optimal strategy using the theory of optimal stopping. An
interesting result is that the optimal stopping strategy is a simple
threshold-based rule, which stops the contention process as soon as the total
number of winning stations exceeds a certain threshold. Compared with the
conventional single-round contention protocol, the multi-round contention
scheme significantly enhances channel utilization when the MPR capability of
the channel is small to medium. Meanwhile, the scheme automatically falls back
to single-round contention when the MPR capability is very large, in which case
the throughput penalty due to random access is already small even with
single-round contention.
