A self-correcting point process
1979; Elsevier BV; Volume: 8; Issue: 3 Linguagem: Inglês
10.1016/0304-4149(79)90008-5
ISSN1879-209X
Autores Tópico(s)Markov Chains and Monte Carlo Methods
ResumoSuppose a point process is attempting to operate as closely as possible to a deterministic rate ρ, in the sense of aiming to produce ρt 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-ρt, 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→∞ the mean number of points occuring in (0, t] is ρt+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.
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