REJECTION RULES IN THE M G 1 QUEUE

We consider a M/G/1 queue modified such that an arriving customer may be totally or partially rejected depending on a r.v. (the barricade) d escribing his impatience and on the state of the system. Three main va riants of this scheme are studied. The steady-state distribution is ex pressed in terms of Volterra equations and the relation to storage pro cesses, dams and queues with state-dependent Poisson arrival rate is d iscussed. For exponential service times, we further find the busy peri od Laplace transform in the case of a deterministic barricade, whereas for exponential barricade it is shown by a coupling argument that the busy period can be identified with a first passage time in an associa ted birth-death process.