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OPTIMAL CONTROL POLICIES FOR AN M/M/1 QUEUE WITH A REMOVABLE SERVER AND DYNAMIC SERVICE RATES

Published online by Cambridge University Press:  29 July 2019

Pamela Badian-Pessot ,
Mark E. Lewis Open the ORCID record for Mark E. Lewis [Opens in a new window]  and
Douglas G. Down
Pamela Badian-Pessot
Affiliation:
School of Operations Research and Information Engineering, Cornell University, Ithaca, New York, United States E-mails: plb93@cornell.edu; mark.lewis@cornell.edu
Mark E. Lewis
Affiliation:
School of Operations Research and Information Engineering, Cornell University, Ithaca, New York, United States E-mails: plb93@cornell.edu; mark.lewis@cornell.edu
Douglas G. Down
Affiliation:
Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada E-mail: downd@mcmaster.ca
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Abstract

We consider an M/M/1 queue with a removable server that dynamically chooses its service rate from a set of finitely many rates. If the server is off, the system must warm up for a random, exponentially distributed amount of time, before it can begin processing jobs. We show under the average cost criterion, that work conserving policies are optimal. We then demonstrate the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number in system. Finally, we present some numerical experiments to provide insights into the practicality of having both a removable server and service rate control.

Keywords

applied probabilityqueueing theorystochastic dynamic programming
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 2 , April 2021 , pp. 189 - 209
Copyright
Copyright © Cambridge University Press 2019

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