Abstract:
A conflict between $k$ packets numbered by $1,\dots,k$. is considered. Our problem is to find the optimal conflict resolution strategy minimizing the average time to the instant when the packet 1 begins its successful transmission or maximizing the probability that this time is not greater than $x$. It is assumed that the strategy knows the multiplicity of the initial conflict $k$ as well as the multiplicities of conflicts occurring before the time when the packet 1 achieves success. We find the optimal strategies for the cases $k=2$ and $k=3$. The problem is still open for $k\geq 4$.
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