APPLICATION OF BALLOT THEOREMS IN THE THEORY OF QUEUES

Abstract : By using a discrete and a continuous generalization of the classical ballot theorem the author finds the distribution of the supremum for partial sums of some interchangeable random variables taking on integer values and the distribution of the supremum for some stochastic processes having interchangeable increments. The results obtained are applied to some single-server queues in order to find the stochastic law of the fluctuations of the queue size and that of the waiting time. (Author)