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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 Σk 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 Σk 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 Σk 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.

Original languageEnglish (US)
Title of host publicationSIGMETRICS 2013 - Proceedings of the 2013 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems
Pages41-52
Number of pages12
Edition1 SPEC. ISS.
DOIs
StatePublished - Jul 22 2013
Externally publishedYes
Event2013 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2013 - Pittsburgh, PA, United States
Duration: Jun 17 2013Jun 21 2013

Publication series

NamePerformance Evaluation Review
Number1 SPEC. ISS.
Volume41
ISSN (Print)0163-5999

Other

Other2013 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, SIGMETRICS 2013
CountryUnited States
CityPittsburgh, PA
Period6/17/136/21/13

Keywords

  • Fluid scale optimality
  • Infinite-server system
  • Local fluid scaling
  • Markov chain
  • Multi-dimensional bin packing
  • Safety stocks

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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  • Cite this

    Stolyar, A. L., & Zhong, Y. (2013). A large-scale service system with packing constraints: Minimizing the number of occupied servers. In SIGMETRICS 2013 - Proceedings of the 2013 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems (1 SPEC. ISS. ed., pp. 41-52). (Performance Evaluation Review; Vol. 41, No. 1 SPEC. ISS.). https://doi.org/10.1145/2494232.2465547