Queuing Systems in Which the Discipline is “Last-Come, First-Served”

Abstract

In this paper we compare the waiting-time distributions under different queue disciplines of customers in a single-server queuing system with Poisson input and general (independent) service time. To make the comparison it is necessary to know the distribution of the unexpended service time at a moment of arrival, and the distribution of busy periods. These are discussed and it is shown that the variance of the waiting-time distribution when the queue discipline is “last-come, first-served” is greater (whatever the service-time distribution) than the corresponding variance when the queue discipline is “first-come, first-served.” The same comparison is also discussed (and is shown to be simpler) for the system with general independent input and negative exponential distribution of service times.