A self-correcting point process

Valerie Isham and Mark Westcott

Stochastic Processes and their Applications, 1979, vol. 8, issue 3, 335-347

Abstract: Suppose a point process is attempting to operate as closely as possible to a deterministic rate [rho], in the sense of aiming to produce [rho]t points during the interval (0,t] for all t. This can be modelled by making the instantaneous rate of t of the process a suitable function of n-[rho]t, n being the number of points in [0, t]. This paper studies such a self-correcting point process in two cases: when the point process is Markovian and the rate function is very general, and when the point process is arbitrary and the rate function is exponential. In each case it is shown that as t-->[infinity] the mean number of points occuring in (0, t] is [rho]t+O(1) while the variance is bounded further, in the Markov case all the absolute central moments are bounded. An application to the outputs of stationary D/M/s queues is given.

Keywords: Comparison; method; controlled; variability; count-conditional; intensity; Markov; birth; process; point; process; self-correcting (search for similar items in EconPapers)
Date: 1979
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Citations: View citations in EconPapers (7)

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