Queueing Systems

, 63:3

The first Erlang century—and the next

Article

DOI: 10.1007/s11134-009-9147-4

Cite this article as:
Kingman, J.F.C. Queueing Syst (2009) 63: 3. doi:10.1007/s11134-009-9147-4

Abstract

The history of queueing theory, particularly over the first sixty years after Erlang’s 1909 paper, is summarised and assessed, with particular reference to the influence of Pollaczek and Kendall. The interactions between the world of telephone traffic and that of applied probability and operational research are a significant factor. The history is followed by speculation about the directions in which the theory might now develop, in response to new problems and new possibilities. It is suggested that classical unsolved problems like the queue M/G/k might be revisited, and that non-renewal inputs might be handled by martingale techniques.

History of queueing theoryMulti-server queuesTeletrafficPoisson arrivalsMartingales

Mathematics Subject Classification (2000)

60K25

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.BristolUK