A Wiener-Hopf integral equation arising in some inference and queueing problems

Abstract

The solution is presented to an integral equation of Wiener-Hopf type which has been recently treated numerically by Hinkley in connexion with the problem of inference about the change-point in a sequence of random variables. The closed form solution given here enables results to be obtained easily in situations where the numerical method fails. A similar integral equation arises in a queueing problem where the difference between inter-arrival and service time of a customer is distributed normally. Explicit expressions are derived for this situation also.