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OPTIMAL CONTROL OF A TWO-SERVER QUEUEING SYSTEM WITH FAILURES

Published online by Cambridge University Press:  27 June 2014

Erhun Özkan  and
Jeffrey P. Kharoufeh
Erhun Özkan
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA E-mails: [email protected]; [email protected]
Jeffrey P. Kharoufeh
Affiliation:
Department of Industrial Engineering, University of Pittsburgh, 1048 Benedum Hall, 3700 O'Hara Street, Pittsburgh, PA 15261, USA E-mails: [email protected]; [email protected]
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Abstract

We consider the problem of controlling a two-server Markovian queueing system with heterogeneous servers. The servers are differentiated by their service rates and reliability attributes (i.e., the slower server is perfectly reliable, whereas the faster server is subject to random failures). The aim is to dynamically route customers at arrival, service completion, server failure, and server repair epochs to minimize the long-run average number of customers in the system. Using a Markov decision process model, we prove that it is always optimal to route customers to the faster server when it is available, irrespective of its failure and repair rates, if the system is stable. For the slower server, there exists an optimal threshold policy that depends on the queue length and the state of the faster server. Additionally, we analyze a variant of the main model in which there are multiple unreliable servers with identical service rates, but distinct reliability characteristics. For that case it is always optimal to route customers to idle servers, and the optimal policy is insensitive to the servers’ reliability characteristics.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 489 - 527
Copyright
Copyright © Cambridge University Press 2014 

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