In probability theory, the Lindley equation, Lindley recursion or Lindley process[1] is a discrete-time stochastic process An where n takes integer values and:
An + 1 = max(0, An + Bn).
Processes of this form can be used to describe the waiting time of customers in a queue or evolution of a queue length over time. The idea was first proposed in the discussion following Kendall's 1951 paper.[2][3]
^Asmussen, Søren (2003). Applied probability and queues. Springer. p. 23. doi:10.1007/0-387-21525-5_1. ISBN 0-387-00211-1.
^Kingman, J. F. C. (2009). "The first Erlang century—and the next". Queueing Systems. 63: 3–4. doi:10.1007/s11134-009-9147-4.
^Kendall, D. G. (1951). "Some problems in the theory of queues". Journal of the Royal Statistical Society, Series B. 13: 151–185. JSTOR 2984059. MR 0047944.
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