\epsilon, \frac{1}{7} - 5 \epsilon, \frac{1}{7} - 4 \epsilon, \frac{1}{7} - 3 \epsilon, \frac{1}{7} - 2 \epsilon, \frac{1}{7} - \epsilon, \frac{1}{7} + 21 \epsilon \}$, where $0 < \epsilon << 1$. OSA would maximize the probability of success in every minislot and hence, would consider the thresholds in the following sequence (if we restrict to integer thresholds) $15, 13, 11, 9, 7, 5$ and $3$. The average number of minislots required to resolve contention with OSA/MPA is $\frac{1}{7} (1 + 2 + \cdots + 6 + 6) \approx \frac{27}{7} \approx 4$. In general, if there are $k$ channel states, then the average number of slots required to resolve contention is approximately $\frac{k}{2}$.

Consider the following alternative strategy in resolving contention. In the first minislot, we consider the threshold value $9$ to resolve contention. If a collision occurs in the first minislot, then the next threshold would be $13$ for the second minislot and in the event of an idle first minislot, the next threshold would be set to $7$ for the second minislot. Similarly, if there is collision in the first two minislots, then, the threshold would be set to $15$ for the third minislot and so on. If there 