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A large-scale service system with packing constraints: minimizing the number of occupied servers

Published: 17 June 2013 Publication History

Abstract

We consider a large-scale service system model proposed in [14], which is motivated by the problem of efficient placement of virtual machines to physical host machines in a network cloud, so that the total number of occupied hosts is minimized. Customers of different types arrive to a system with an infinite number of servers. A server packing configuration is the vector k = {ki}, where ki is the number of type-i customers that the server "contains". Packing constraints are described by a fixed finite set of allowed configurations. Upon arrival, each customer is placed into a server immediately, subject to the packing constraints; the server can be idle or already serving other customers. After service completion, each customer leaves its server and the system. It was shown in [14] that a simple real-time algorithm, called Greedy, is asymptotically optimal in the sense of minimizing ∑k Xk1+α in the stationary regime, as the customer arrival rates grow to infinity. (Here α > 0, and Xk denotes the number of servers with configuration k.) In particular, when parameter α is small, and in the asymptotic regime where customer arrival rates grow to infinity, Greedy solves a problem approximating one of minimizing ∑k Xk, the number of occupied hosts. In this paper we introduce the algorithm called Greedy with sublinear Safety Stocks (GSS), and show that it asymptotically solves the exact problem of minimizing ∑k Xk. An important feature of the algorithm is that sublinear safety stocks of Xk are created automatically - when and where necessary - without having to determine a priori where they are required. Moreover, we also provide a tight characterization of the rate of convergence to optimality under GSS. The GSS algorithm is as simple as Greedy, and uses no more system state information than Greedy does.

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cover image ACM Conferences
SIGMETRICS '13: Proceedings of the ACM SIGMETRICS/international conference on Measurement and modeling of computer systems
June 2013
406 pages
ISBN:9781450319003
DOI:10.1145/2465529
  • cover image ACM SIGMETRICS Performance Evaluation Review
    ACM SIGMETRICS Performance Evaluation Review  Volume 41, Issue 1
    Performance evaluation review
    June 2013
    385 pages
    ISSN:0163-5999
    DOI:10.1145/2494232
    Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 17 June 2013

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Author Tags

  1. fluid scale optimality
  2. infinite-server system
  3. local fluid scaling
  4. markov chain
  5. multi-dimensional bin packing
  6. safety stocks

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SIGMETRICS '13 Paper Acceptance Rate 54 of 196 submissions, 28%;
Overall Acceptance Rate 459 of 2,691 submissions, 17%

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  • (2020)Dynamic Component Placement and Request Scheduling for IoT Big Data StreamingIEEE Internet of Things Journal10.1109/JIOT.2020.29824587:8(7156-7170)Online publication date: Aug-2020
  • (2019)Greener, Energy-Efficient and Sustainable Networks: State-Of-The-Art and New TrendsSensors10.3390/s1922486419:22(4864)Online publication date: 8-Nov-2019
  • (2018)Randomized Algorithms for Scheduling Multi-Resource Jobs in the CloudIEEE/ACM Transactions on Networking10.1109/TNET.2018.286364726:5(2202-2215)Online publication date: 1-Oct-2018
  • (2018)Online VM Auto-Scaling Algorithms for Application Hosting in a CloudIEEE Transactions on Cloud Computing10.1109/TCC.2018.2830793(1-1)Online publication date: 2018
  • (2018)Fully dynamic bin packing revisitedMathematical Programming10.1007/s10107-018-1325-xOnline publication date: 1-Sep-2018
  • (2017)On Non-Preemptive VM Scheduling in the CloudProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/31544931:2(1-29)Online publication date: 19-Dec-2017
  • (2016)Randomized algorithms for scheduling VMs in the cloudIEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications10.1109/INFOCOM.2016.7524536(1-9)Online publication date: Apr-2016
  • (2016)Resource provisioning optimization for service hosting on cloud platform2016 IEEE 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD)10.1109/CSCWD.2016.7566011(340-345)Online publication date: May-2016
  • (2016)A greedy randomized algorithm achieving sublinear optimality gap in a dynamic packing model2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton)10.1109/ALLERTON.2016.7852247(319-326)Online publication date: Sep-2016
  • (2015)Lagrangian-based Online Stochastic Bin PackingACM SIGMETRICS Performance Evaluation Review10.1145/2796314.274589743:1(467-468)Online publication date: 15-Jun-2015
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