The Offset Problem

Lenore J. Cowen and Rudolph Mathar

This paper is concerned with the analysis of locally time-synchronized slot systems for broadcast in packet radio networks. Local synchronization has been proposed in practice as less expensive than global synchronization over very wide areas, or over mobile networks. In the case of two locally coordinated stations, under the assumption that the phase shift on the clocks between the two groups is random, it is shown that the probability of no collision is maximized when occupied slots within each group are chosen consecutively, regardless of the number of total slots, or the number of occupied slots in either group.

Click here for the postscript file of the full paper, which will appear in the Journal Combinatorics, Probability and Computing.

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