Encyclopedia of Algorithms

2008 Edition
| Editors: Ming-Yang Kao

Flow Time Minimization

2001; Becchetti, Leonardi, Marchetti-Spaccamela, Pruhs
  • Luca Becchetti
  • Stefano Leonardi
  • Alberto Marchetti-Spaccamela
  • Kirk Pruhs
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30162-4_146

Keywords and Synonyms

Flow time: response time            

Problem Definition

Shortest-job-first heuristics arise in sequencing problems, when the goal is minimizing the perceived latency of users of a multiuser or multitasking system. In this problem, the algorithm has to schedule a set of jobs on a pool of m identical machines. Each job has a release date and a processing time, and the goal is to minimize the average time spent by jobs in the system. This is normally considered a suitable measure of the quality of service provided by a system to interactive users. This optimization problem can be more formally described as follows:


A set of m identical machines and a set of n jobs \( { 1, 2,\ldots , n } \)

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Recommended Reading

  1. 1.
    Becchetti, L., Leonardi, S.: Nonclairvoyant scheduling to minimize the total flow time on single and parallel machines. J. ACM 51(4), 517–539 (2004)MathSciNetGoogle Scholar
  2. 2.
    Crovella, M.E., Frangioso, R., Harchal‐Balter, M.: Connection scheduling in web servers. In: Proceedings of the 2nd USENIX Symposium on Internet Technologies and Systems (USITS-99), 1999 pp. 243–254Google Scholar
  3. 3.
    Kalyanasundaram, B., Pruhs, K.: Minimizing flow time nonclairvoyantly. J. ACM 50(4), 551–567 (2003)MathSciNetGoogle Scholar
  4. 4.
    Kalyanasundaram, B., Pruhs, K.: Speed is as powerful as clairvoyance. J. ACM 47(4), 617–643 (2000)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Kellerer, H., Tautenhahn, T., Woeginger, G.J.: Approximability and nonapproximability results for minimizing total flow time on a single machine. In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing (STOC '96), 1996, pp. 418–426Google Scholar
  6. 6.
    Leonardi, S., Raz, D.: Approximating total flow time on parallel machines. In: Proceedings of the Annual ACM Symposium on the Theory of Computing STOC, 1997, pp. 110–119Google Scholar
  7. 7.
    Motwani, R., Phillips, S., Torng, E.: Nonclairvoyant scheduling. Theor. Comput. Sci. 130(1), 17–47 (1994)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Nutt, G.: Operating System Projects Using Windows NT. Addison‐Wesley, Reading (1999)Google Scholar
  9. 9.
    Schrage, L.: A proof of the optimality of the shortest remaining processing time discipline. Oper. Res. 16(1), 687–690 (1968)zbMATHGoogle Scholar
  10. 10.
    Smith, D.R.: A new proof of the optimality of the shortest remaining processing time discipline. Oper. Res. 26(1), 197–199 (1976)Google Scholar
  11. 11.
    Tanenbaum, A.S.: Modern Operating Systems. Prentice-Hall, Englewood Cliffs (1992)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Luca Becchetti
    • 1
  • Stefano Leonardi
    • 1
  • Alberto Marchetti-Spaccamela
    • 1
  • Kirk Pruhs
    • 2
  1. 1.Department of Information and Computer SystemsUniversity of RomeRomeItaly
  2. 2.Computer ScienceUniversity of PittsburghPittsburghUSA