Semi-stationary clearing processes
A clearing process describes the net quantity in a service system (e.g. a batch service queue or dam) which receives an exogenous random input over time. and has an output mechanism that intermittently clears random quantities from the system. A semistationary clearing process is strictly stationary over its random clearing epochs. We describe the asymptotic distribution of such processes and show how it arises in limits of certain functionals of these processes. An asymptotic distribution is different from a limiting distribution, but it has some similar properties. We then identify some clearing processes whose asymptotic distribution is uniform. This is true for modulo c clearing with a stationary input if the Palm probability is used rather than the usual probability. Our results on this give a partial answer to an anomaly in the classical economic lot size inventory model. We also present a functional central limit law and law of the iterated logorithm for clearing processes, as well as a result on the convergence of a sequence of such processes.
Year of publication: |
1978
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Authors: | Serfozo, Richard ; Stidham, Shaler |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 6.1978, 2, p. 165-178
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Publisher: |
Elsevier |
Saved in:
Online Resource
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