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The Beňes equations for the distribution of excursions for general storage processes. (English) Zbl 0802.60091

Summary: We obtain the Beňes equation for the evolution of the probability distribution of the excursion process associated with the level crossings of a general storage process. We then show that under stationarity and ergodicity assumptions on the process we can recover the well-known rate conservation law. Using the stationary solution we then show that the existence of an invariant solution can be studied in terms of an operator equation and we show how this characterization leads to a very simple explicit computation of the stationary distribution.

MSC:

60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60G17 Sample path properties
90B22 Queues and service in operations research
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