We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 07 May 2024
Introduction
In this chapter, we supplement the problem of minimizing the flow time with multiple fixedspeed servers considered in Chapter 13 by allowing the flexibility for each server to have a tuneable speed. This setup is typically referred to as speed scaling in the literature. Increasing server speed decreases the flow time but comes at a cost of increased energy consumption, which is typically accounted for by defining a speed based power cost function P(s) that is an increasing function of speed s.
A variety of problems can now be formulated, such as minimizing flow time subject to a constraint on the total energy cost, or minimizing a linear combination of flow time and total energy cost, etc. The most popular problem studied in literature is the linear combination of flow time and total energy cost, generally referred to as the flow time plus energy problem.
In this chapter, we consider the flow time plus energy problem and begin with the single server case. With a single server, SRPT remains an optimal scheduling algorithm, and the only non-trivial decision is the speed choice. We will show that an algorithm that chooses speed such that the power consumption at each time instant is equal to the number of incomplete jobs in the system plus one is 3-competitive, independent of the power cost function P.
Next, we consider the more challenging speed scaling problem when there are multiple identical servers, i.e., with the same power cost function P. We consider the multi-server version of the SRPT algorithm for scheduling, and the following speed choice: the total power consumption across all servers at any time instant is equal to the number of incomplete jobs in the system, and all servers process their jobs at the same speed. We show that this algorithm is constant competitive, where the constant depends only on the cost function P. Recall from Chapter 13 that the competitive ratio of the SRPT algorithm with fixed speed servers to minimize the flow time is, where n is the number of jobs and m is the number of servers, and wmax and wmin are the maximum and minimum job sizes.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
