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Control of arrivals to a stochastic input–output system

Published online by Cambridge University Press:  01 July 2016

Søren Glud Johansen  and
Shaler Stidham Jr
Søren Glud Johansen*
Affiliation:
University of Aarhus
Shaler Stidham Jr*
Affiliation:
North Carolina State University at Raleigh
*
∗Postal address: Department of Operations Research, University of Aarhus, Building 530, Ny Munkegade, 8000 Aarhus C, Denmark.
∗∗Postal address: Department of Industrial Engineering, North Carolina State University, Box 5111, Raleigh, NC 27650, U.S.A.
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Abstract

The problem of controlling input to a stochastic input-output system by accepting or rejecting arriving customers is analyzed as a semi-Markov decision process. Included as special cases are a GI/G/1 model and models with compound input and/or output processes, as well as several previously studied queueing-control models. We establish monotonicity of socially and individually optimal acceptance policies and the more restrictive nature of the former, with random rewards for acceptance and both customer-oriented and system-oriented non-linear waiting costs. Distinctive features of our analysis are (i) that it allows dependent interarrival times and (ii) that the monotonicity proofs do not rely on the standard concavity-preservation arguments.

Keywords

INPUT–OUTPUTSTORAGE SYSTEMGI/G/1 QUEUECONTROL OF QUEUESSEMI-MARKOV DECISION PROCESSDYNAMIC PROGRAMMINGSOCIALLY AND INDIVIDUALLY OPTIMAL POLICIESNON-LINEAR WAITING COSTS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 972 - 999
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research partially supported by NATO Research Grant No. SRG. SS. 5, administered by the NATO Special Programme Panel on System Science.

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