The sliding clamps of chromosomal replicases are acted upon by both the clamp loader and DNA polymerase. Several other proteins and polymerases also interact with the clamp. These proteins bind the clamp at the same spot and use it in sequential fashion. First the clamp loader must bind the clamp in order to load it onto DNA, but directly thereafter the clamp loader must clear away from the clamp so it can be used by the replicative DNA polymerase. At the end of replication, the replicase is ejected from the clamp, which presumably allows the clamp to interact with yet other proteins after its use by the replicase. This paper describes how different proteins in the Escherichia coli replicase, DNA polymerase III holoenzyme, coordinate their traffic flow on the clamp. The mechanism by which traffic flow on the beta clamp is directed is based on competition of the proteins for the clamp, where DNA structure modulates the competition. It seems likely that the principles will generalize to a traffic flow of other factors on these circular clamp proteins.