Some Problems in the Theory of Queues

Abstract

Summary The paper opens with a general review of some points in congestion theory, and continues with a simplified account of the Pollaczek-Khintchine “equilibrium” theory for the single-counter queue fed by an input of the Poisson type and associated with a general service-time distribution. It is pointed out that although the stochastic process describing the fluctuations in queue-size is not (in general) Markovian, it is possible to work instead with an enumerable Markov chain if attention is directed to the epochs at which individual customers depart (these epochs forming a sequence of regeneration points).