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Medium access control (MAC) represents a vital part of any wireless network and directly affects important quality-of-service (QoS) measures such as the end-to-end delay or data throughput. In this study, we evaluate the delay performance and robustness of a distributed adaptive MAC scheme for power-controlled wireless networks with shared communication channels. The scheme was proposed in our previous work and enables multiple network links (transmitter-receiver pairs) to transmit simultaneously over the shared channels with a guaranteed predefined signal-to-interference and noise ratio (SINR) at each receiver in order to achieve reliable data transfers. Moreover, in this scheme, links are admitted on the basis of theoretically optimum decisions and iterative interference measurements are the only algorithmic input. Our simulations show that, as a result of an exponential convergence rate, interference measurements in at most four power-update cycles are on average required to make optimum MAC decisions with probability one in networks with low and medium reuse of shared channels. Typically ten to twenty cycles are required in networks with higher channel congestion. Furthermore, if network links engage in collective MAC decision making by sharing information on measured co-channel interference, the overall robustness of the scheme to the effects of erroneous power control or channel impairments increases with the fraction of the participating links.