Long range dependence of point processes, with queueing examples

D.J. Daley and Rein Vesilo

Stochastic Processes and their Applications, 1997, vol. 70, issue 2, 265-282

Abstract: Possible definitions of the long range dependence (LRD) of a stationary point process are discussed. Examples from the standard queueing literature are considered and shown to be amenable to yielding processes with long range count dependence. In particular the effect of the single-server queueing operator, whereby one point process is transformed into another via the mechanism of a simple queue, is examined for possible long range dependence of both the counting and interval properties of the output process. For an infinite server queue, the output is long range count dependent if and only if the input is long range count dependent.

Date: 1997
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