Stochastic storage networks: Stationarity and the feedforward case

Stochastic storage networks: Stationarity and the feedforward case

0.00 Avg rating0 Votes
Article ID: iaor19981005
Country: United Kingdom
Volume: 34
Issue: 2
Start Page Number: 498
End Page Number: 508
Publication Date: Jun 1997
Journal: Journal of Applied Probability
Authors:
Abstract:

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Reviews

Required fields are marked *. Your email address will not be published.