Proofs of conjectures on the competition between observable and unobservable servers.

The impact of information about the quality of service on marketing can be demonstrated by a competition between an observable queue and an unobservable queue. An illustration was given by an earlier paper of Hassin (Manag Sci 42:618–623, 1996), which considers two gas stations located one after the other on a main road. A driver who needs to fill the gas can see the queue length upon arriving at the first station, but not the second one. The driver decides which station to enter based only on this partial information for minimizing the expected waiting time. Via extensive numerical experiments, Hassin showed that the first server enjoys a larger market share, which led him to making a number of challenging conjectures. In this paper, we prove that all the numerical observations and conjectures are true so that the advantage of being the first server is assured. [ABSTRACT FROM AUTHOR]