Minimizing the expected response time of an idled server on a line

We address the problem of where to locate an idle server in a one-dimensional system where the arrival of demands for service has both spatial and temporal uncertainty. In such a system it is reasonable to have an idle server make an anticipatory move in order to better position itself for the next demand. However, moving all the way to its home base, or even moving at all, might delay the service for a demand which arrives during the move. We develop an analytical model to optimize the destination of an anticipatory move based upon the location of the server. Insights into the impact of system parameters as well as empirical examples are given.