Systems in stochastic equilibrium
Systems in stochastic equilibrium
The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
Queueing Systems: Theory and Applications
Mathematics of Operations Research
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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.