A make-to-stock mountain-type inventory model

We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate α ( x ) that is a function of the current buffer level  x ; in states 1 and...

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Bibliographic Details
Published in:Annals of operations research 2015-08, Vol.231 (1), p.65-77
Main Authors: Boxma, Onno J., Parlar, Mahmut, Perry, David
Format: Article
Language:English
Subjects:
Analysis
Buffers
Business and Management
Combinatorics
Computational fluid dynamics
Fluid flow
Fluids
Inventory control
Markov analysis
Markov processes
Operations research
Operations Research/Decision Theory
Queueing theory
Queues
Queuing
Studies
Theory of Computation
Workloads
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Summary:We consider the buffer content of a fluid queue or storage process. The buffer content varies in a way that depends on the state of an underlying three-state Markov process. In state 0 the buffer content increases at a rate α ( x ) that is a function of the current buffer level  x ; in states 1 and 2 it decreases linearly, with different speeds. We study the steady-state buffer content, by using level crossing theory and by exploiting relations between the fluid queue and queues with instantaneous input and/or output.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-013-1370-z