Server Allocation Algorithms for Tiered Systems

  • Kamalika Chaudhuri
  • Anshul Kothari
  • Rudi Pendavingh
  • Ram Swaminathan
  • Robert Tarjan
  • Yunhong Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3595)


Many web-based systems have a tiered application architecture, in which a request needs to transverse all the tiers before finishing its processing. One of the most important QoS metrics for these applications is the expected response time for the user. Since the expected response time in any tier depends upon the number of servers allocated to this tier, and a request’s total response time is the sum of the response times at all the tiers, many different configurations (number of servers allocated to each tier) can satisfy the expected response time requirement. Naturally, one would like to find the configuration to minimize the total system cost while satisfying the total response time requirement. This is modeled as a non-linear optimization problem using an open-queuing network model of response time, which we call the server allocation problem for tiered systems (SAPTS).

In this paper we study the computational complexity of SAPTS and design efficient algorithms to solve it. For a variable number of tiers, we show that the decision problem of SAPTS is NP-complete. Then we design a simple two-approximation algorithm and a fully polynomial time approximation scheme (FPTAS). If the number of tiers is a constant, we show that SAPTS is polynomial-time solvable. Furthermore, we design a fast polynomial-time exact algorithm to solve for the important two-tier case. Most of our results extend to the general case where each tier has an arbitrary response time function.


Knapsack Problem Polynomial Time Approximation Scheme Fully Polynomial Time Approximation Scheme Total Response Time Tier System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Appleby, K., Fakhouri, S., Fong, L., Goldszmidt, G., Kalantar, M.: Océano – SLAbased management of a computing utility. In: Proc. 7th IFIP/IEEE Intl. Symp. on Integrated Network Management (May 2001)Google Scholar
  2. 2.
    Brin, S., Page, L.: The anatomy of a large-scale hypertextual web search engine. Computer Networks and ISDN Systems 30, 107–117 (1998)CrossRefGoogle Scholar
  3. 3.
    Chandra, A., Hirschberg, D., Wong, C.: Approximate algorithms for some generalized knapsack problems. Theoretical Computer Science 3, 293–304 (1976)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Frederickson, G.N., Johnson, D.B.: The complexity of selection and ranking in x+y and matrices with sorted columns. Journal of Computer and System Sciences 24(2), 197–208 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Garg, P.K., Hao, M., Santos, C., Tang, H.-K., Zhang, A.: Web transaction analysis and optimization (TAO). In: Proceedings of the 3rd Workshop on Software and Performance, pp. 286–293 (2002)Google Scholar
  6. 6.
    Gens, G., Levner, E.: Approximation algorithms for certain universal problems in scheduling theory. Soviet J. of Computers & System Sciences 6, 31–36 (1978)Google Scholar
  7. 7.
    Grőtschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  8. 8.
    Hochbaum, D.S.: A nonlinear knapsack problem. Operations Research Letters (17), 103–110 (1995)Google Scholar
  9. 9.
    Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Heidelberg (2004)CrossRefzbMATHGoogle Scholar
  10. 10.
    Kleinrock, L.: Queueing Systems. Computer Applications, vol. II. Wiley, Chichester (1976)zbMATHGoogle Scholar
  11. 11.
    Lenstra, H.W.: Integer linear programming with a fixed number of variables. Mathematics of Operations Research 8, 538–548 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Menasce, D.A., Almeida, V.A.: Capacity Planning for Web PerformanceGoogle Scholar
  13. 13.
    Zhang, A., et al.: Optimal server resource allocation using an open queueing network model of response time. Technical Report HPL-2002-301, HP Labs (2002)Google Scholar
  14. 14.
    Zhu, X., Singhal, S.: Optimal resource assignment in internet data centers. In: Proc. 9th MASCOTS, Cincinnati, OH, August 15-18, 2001, pp. 61–69 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kamalika Chaudhuri
    • 1
  • Anshul Kothari
    • 2
  • Rudi Pendavingh
    • 3
  • Ram Swaminathan
    • 4
  • Robert Tarjan
    • 4
  • Yunhong Zhou
    • 4
  1. 1.Computer Science DivisionUniversity of CaliforniaBerkeleyUSA
  2. 2.Computer Science DepartUniversity of CaliforniaSanta BarbaraUSA
  3. 3.Depart. of Math. and CS.TU EindhovenEindhovenThe Netherlands
  4. 4.HP LabsPalo AltoUSA

Personalised recommendations