Minimal Cost Server Configuration for Meeting Time-Varying Resource Demands in Cloud Centers

We consider the minimal cost server configuration for meeting resource demands over multiple time slots. Specifically, there are some heterogeneous servers. Each server is specified by a cost, certain amounts of several resources, and an active interval, i.e., the time interval that the server is pl...

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Bibliographic Details
Published in:IEEE transactions on parallel and distributed systems Vol. 29; no. 11; pp. 2503 - 2513
Main Authors: Liu, Chubo, Li, Kenli, Li, Keqin
Format: Journal Article
Language:English
Published: New York IEEE 01.11.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation
Approximation algorithms
Bandwidth
Cloud computing
Configurations
Cost engineering
Cost minimization
Knapsack problem
Mathematical analysis
meeting resource demands
Minimization
Optimization
randomized approximation algorithm
Resource management
Rounding
server configuration
Servers
varied Chernoff bound
ISSN:1045-9219, 1558-2183
Online Access:Get full text
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Summary:We consider the minimal cost server configuration for meeting resource demands over multiple time slots. Specifically, there are some heterogeneous servers. Each server is specified by a cost, certain amounts of several resources, and an active interval, i.e., the time interval that the server is planed to work. There are different overall demands for each type of resource over different time slots. A feasible solution is a set of servers such that at any time slot, the resources provided by the selected servers are at least their corresponding demands. Notice that, a selected server can not provide resources for the time slots out of its active interval. The total cost of the solution is the summation of the costs of all selected servers. The goal is to find a feasible solution with minimal total cost. This problem is proved to be NP-hard due to a reduction from the multidimensional knapsack problem (MKP), which is a well-known NP-hard combinational optimization problem. To solve our problem, we present a randomized approximation algorithm called partial rounding algorithm (<inline-formula><tex-math notation="LaTeX">\mathcal {PRA} </tex-math> <inline-graphic xlink:href="liu-ieq1-2836452.gif"/> </inline-formula>), which guarantees <inline-formula><tex-math notation="LaTeX">O\left(\log \left(KT \right) \right)</tex-math> <inline-graphic xlink:href="liu-ieq2-2836452.gif"/> </inline-formula>-approximation, i.e., <inline-formula><tex-math notation="LaTeX">\eta \;\log \left(KT \right)</tex-math> <inline-graphic xlink:href="liu-ieq3-2836452.gif"/> </inline-formula>-approximation, where <inline-formula><tex-math notation="LaTeX">K</tex-math> <inline-graphic xlink:href="liu-ieq4-2836452.gif"/> </inline-formula> is the number of kinds of resources, <inline-formula><tex-math notation="LaTeX">T</tex-math> <inline-graphic xlink:href="liu-ieq5-2836452.gif"/> </inline-formula> is the number of time slots, and <inline-formula><tex-math notation="LaTeX">\eta</tex-math> <inline-graphic xlink:href="liu-ieq6-2836452.gif"/> </inline-formula> is a positive constant. Furthermore, to minimize <inline-formula><tex-math notation="LaTeX">\eta</tex-math> <inline-graphic xlink:href="liu-ieq7-2836452.gif"/> </inline-formula> as much as possible, we propose a varied Chernoff bound and apply it in <inline-formula><tex-math notation="LaTeX">\mathcal {PRA}</tex-math> <inline-graphic xlink:href="liu-ieq8-2836452.gif"/> </inline-formula>. We perform extensive experiments with random inputs and a specific application input. The results show that <inline-formula> <tex-math notation="LaTeX">\mathcal {PRA}</tex-math> <inline-graphic xlink:href="liu-ieq9-2836452.gif"/> </inline-formula> with our varied Chernoff conclusion can find solutions closing to the optimal one.
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ISSN:1045-9219
1558-2183
DOI:10.1109/TPDS.2018.2836452