Stochastic clearing systems

Shaler Stidham

Stochastic Processes and their Applications, 1974, vol. 2, issue 1, 85-113

Abstract: A stochastic clearing system is characterized by a non-decreasing stochastic input process {Y(t), t [greater, double equals] 0}, where Y(t) is the cumulative quantity entering the system in [0, t], and an output mechanism that intermittently and instantaneously clears the system, that is, removes all the quantity currently present. Examples may be found in the theory of queues, inventories, and other stochastic service and storage systems. In this paper we derive an explicit expression for the stationary (in some cases, limiting) distribution of the quantity in the system, under the assumption that the clearing instants are regeneration points and, in particular, first entrance times into sets of the form {y: y>q}. The expression is in terms of the sojourn measure W associated with {Y(t), t [greater, double equals] 0}: W{A} = E{time spent in A by Y(t), 0

Date: 1974
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Citations: View citations in EconPapers (16)

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