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  4. Control Policies for Queueing Systems with Removable Servers and Energy Considerations

Control Policies for Queueing Systems with Removable Servers and Energy Considerations

File(s)
BadianPessot_cornellgrad_0058F_12106.pdf (870 KB)
Permanent Link(s)
https://doi.org/10.7298/m8rc-c311
https://hdl.handle.net/1813/103075
Collections
Cornell Theses and Dissertations
Author
Badian-Pessot, Pamela Lynne
Abstract

In data centers, response time is typically of paramount concern. Systems are built with excess capacity to handle peak demand. This leads to servers idling for long periods during which time they continue to consume energy. However, it is not necessarily a simple decision to turn servers off. Servers require a warming period when they are turned on. Thus, turning a server off now can lead to long delays in the future and may not even lead to a reduction in energy usage as servers also consume energy while warming. As the financial and economic impact of energy consumption increases, new analysis is needed to identify policies that balance the trade-off between energy usage and delay performance.  We study two queueing models and propose a class of simple and intuitive policies for each. First, 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 that the optimal policy can be characterized by a threshold for turning on the server and the optimal service rate increases monotonically with the number of jobs in the system. Finally, we present numerical experiments to provide insights into the practicality of having both a removable server and service rate control. Next, we consider a parallel queueing system with K removable servers where jobs must be routed to a server upon arrival. We propose a class of policies for the joint routing and server power status control problem called delay-JSQ policies. Delay-JSQ policies turn additional servers on when the queue lengths at all non-empty stations exceed some threshold and route arriving jobs to the shortest non-empty queue. We show that these policies have the same stability region as \textit{join the shortest queue} routing where servers cannot turn off. We show that in the two-server setting, in the heavy traffic limit, delay-JSQ policies are optimal in terms of minimizing the holding cost rate is incurred while also incurring zero warming cost. We conclude with numerical experiments and see that delay-JSQ policies automatically and without knowledge of system parameters, adjust the number of servers to match the current capacity to the current demand

Description
108 pages
Date Issued
2020-08
Committee Chair
Lewis, Mark E.
Committee Member
Pender, Jamol J.
Goldberg, David Alan
Down, Douglas
Degree Discipline
Operations Research and Information Engineering
Degree Name
Ph. D., Operations Research and Information Engineering
Degree Level
Doctor of Philosophy
Type
dissertation or thesis
Link(s) to Catalog Record
https://catalog.library.cornell.edu/catalog/13277744

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