Affiliation:
1. Carnegie Mellon University, Pittsburgh, PA, USA
Abstract
Capacity management, whether it involves servers in a data center, or human staff in a call center, or doctors in a hospital, is largely about balancing a resource-delay tradeoff. On the one hand, one would like to turn off servers when not in use (or send home staff that are idle) to save on resources. On the other hand, one wants to avoid the considerable setup time required to turn an off server back on. This paper aims to understand the delay component of this tradeoff, namely, what is the effect of setup time on average delay in a multi-server system?
Surprisingly little is known about the effect of setup times on delay. While there has been some work on studying the M/M/k with Exponentially-distributed setup times, these works provide only iterative methods for computing mean delay, giving little insight as to how delay is affected by k, by load, and by the setup time. Furthermore, setup time in practice is much better modeled by a Deterministic random variable, and, as this paper shows, the effect of a Deterministic setup time is nothing like that of an Exponentially-distributed setup time.
This paper provides the first analysis of the M/M/k with Deterministic setup times. We prove a lower bound on the effect of setup on delay. Our result is a simple algebraic formula which provides insight into how delay scales with the input parameters. For more details, see the full paper.
Funder
Gates Millennium Scholars Program
National GEM Consortium
NSF
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Networks and Communications,Hardware and Architecture,Software
Reference9 articles.
1. Anshul Gandhi Sherwin Doroudi Mor Harchol-Balter and Alan Scheller-Wolf. 2013. Exact analysis of the M/M/k/setup class of Markov chains via Recursive Renewal Reward. In Queueing Syst. 153--166. Anshul Gandhi Sherwin Doroudi Mor Harchol-Balter and Alan Scheller-Wolf. 2013. Exact analysis of the M/M/k/setup class of Markov chains via Recursive Renewal Reward. In Queueing Syst. 153--166.
2. Anshul Gandhi , Varun Gupta , Mor Harchol-Balter , and Michael Kozuch . 2010 a. Optimality Analysis of Energy-Peformance Trade-off for Server Farm Management. In PERFORMANCE 2010 Conference. IFIP WG 7.3 International Symposium on Computer Modeling, Measurement and Evaluation . Namur, Belgium. Anshul Gandhi, Varun Gupta, Mor Harchol-Balter, and Michael Kozuch. 2010a. Optimality Analysis of Energy-Peformance Trade-off for Server Farm Management. In PERFORMANCE 2010 Conference. IFIP WG 7.3 International Symposium on Computer Modeling, Measurement and Evaluation. Namur, Belgium.
3. How Data Center Size Impacts the Effectiveness of Dynamic Power Management. In 49th Annual Allerton Conference on Communication, Control, and Computing;Gandhi Anshul;Urbana-Champaign,2011
4. Server farms with setup costs
5. AutoScale