  Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their
algorithm is an optimal online algorithm for the online interval coloring
problem. In this paper, for online unit interval coloring, we show that the
number of colors used by the Kierstead-Trotter algorithm is at most $3
\omega(G) - 3$, where $\omega(G)$ is the size of the maximum clique in a given
graph $G$, and it is the best possible.
