The Role of Information in System Stability with Partially Observable Servers

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dc.contributor.advisor Methodology and Computing in Applied Probability 22(3):949-968 16 Nov 2019
dc.contributor.author Asanjarani, Azam
dc.contributor.author Nazarathy, Yoni
dc.date.accessioned 2021-11-02T03:41:05Z
dc.date.available 2021-11-02T03:41:05Z
dc.date.issued 2019-11-16
dc.identifier.issn 1387-5841
dc.identifier.uri https://hdl.handle.net/2292/57183
dc.description.abstract We present a methodology for analyzing the role of information on system stability. For this we consider a simple discrete-time controlled queueing system, where the controller has a choice of which server to use at each time slot and server performance varies according to a Markov modulated random environment. At the extreme cases of information availability, that is when there is either full information or no information, stability regions and maximally stabilizing policies are trivial. But in the more realistic cases where only the environment state of the selected server is observed, only the service successes are observed or only queue length is observed, finding throughput maximizing control laws is a challenge. To handle these situations, we devise a Partially Observable Markov Decision Process (POMDP) formulation of the problem and illustrate properties of its solution. We further model the system under given decision rules, using Quasi-Birth-and-Death (QBD) structure to find a matrix analytic expression for the stability bound. We use this formulation to illustrate how the stability region grows as the number of controller belief states increases. The example that we consider in this paper is a case of two servers where the environment of each is modulated like a Gilbert-Elliot channel. As simple as this case seems, there appear to be no closed form descriptions of the stability region under the various regimes considered. However, the numerical approximations to the POMDP Bellman equations together with the numerical solutions of the QBDs, both of which are in agreement, hint at a variety of structural results.
dc.publisher Springer Science and Business Media LLC
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm
dc.rights.uri https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html
dc.subject Science & Technology
dc.subject Physical Sciences
dc.subject Statistics & Probability
dc.subject Mathematics
dc.subject System stability
dc.subject POMDP
dc.subject Control
dc.subject Queueing systems
dc.subject Optimal
dc.subject Bellman equations
dc.subject QBD
dc.subject Information
dc.subject Markov models
dc.subject POLICIES
dc.subject math.OC
dc.subject math.OC
dc.subject math.OC
dc.subject math.OC
dc.subject 0102 Applied Mathematics
dc.subject 0103 Numerical and Computational Mathematics
dc.subject 0104 Statistics
dc.title The Role of Information in System Stability with Partially Observable Servers
dc.type Report
dc.identifier.doi 10.1007/s11009-019-09750-4
pubs.begin-page 949
pubs.volume 22
dc.date.updated 2021-10-21T06:44:54Z
dc.rights.holder Copyright: The author en
pubs.author-url http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000541922700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e41486220adb198d0efde5a3b153e7d
pubs.end-page 968
pubs.publication-status Published
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.subtype Working Paper
pubs.elements-id 740841
dc.identifier.eissn 1573-7713


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