Queueing Systems

, Volume 35, Issue 1–4, pp 185–200

Optimal control of single-server fluid networks

  • Nicole Bäuerle
  • Ulrich Rieder
Article

Abstract

We consider a stochastic single-server fluid network with both a discounted reward and a cost structure. It can be shown that the optimal policy is a priority index policy. The indices coincide with the optimal indices in a semi-Markovian Klimov problem. Several special cases like single-server reentrant fluid lines are considered. The approach we use is based on sample path arguments and Pontryagins maximum principle.

stochastic fluid model index policy Klimov index largest remaining index algorithm maximum principle sample path argument reentrant fluid lines 

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References

  1. [1]
    F. Avram, Optimal control of fluid limits of queueing networks and stochasticity corrections, in: Mathematics of Stochastic Manufacturing Systems, eds. G.G. Yin and Q. Zhang, Lectures in Applied Mathematics, Vol. 33 (Amer. Math. Soc., Providence, RI, 1997) pp. 1–36.Google Scholar
  2. [2]
    F. Avram, D. Bertsimas and M. Ricard, Fluid models of sequencing problems in open queueing networks: An optimal control approach, in: Stochastic Networks, eds. F.P. Kelly and R.J. Williams (1995) pp. 199–234.Google Scholar
  3. [3]
    H. Chen and A. Mandelbaum, Hierarchical modeling of stochastic networks part 1: Fluid models, in: Stochastic Modeling and Analysis of Manufacturing Systems, ed. D.D. Yao (Springer, New York, 1994) pp. 47–105.Google Scholar
  4. [4]
    H. Chen and D.D. Yao, Dynamic scheduling of a multiclass fluid network, Oper. Res. 41 (1993) 1104–1115.Google Scholar
  5. [5]
    G.P. Klimov, Time-sharing service systems I, Theory Probab. Appl. 19 (1974) 532–551.CrossRefGoogle Scholar
  6. [6]
    S. Meyn, Stability and optimization of queueing networks and their fluid models, in: Mathematics of Stochastic Manufacturing Systems, eds. G.G. Yin and Q. Zhang, Lectures in Applied Mathematics, Vol. 33 (Amer. Math. Soc., Providence, RI, 1997) pp. 175–199.Google Scholar
  7. [7]
    A. Seierstad and K. Sydsæter, Optimal Control Theory with Economic Applications (North-Holland, Amsterdam, 1987).Google Scholar
  8. [8]
    S.P. Sethi and Q. Zhang, Hierarchical Decision Making in Stochastic Manufacturing Systems (Birkhäuser, Boston, 1994).Google Scholar
  9. [9]
    D.W. Tcha and S.R. Pliska, Optimal control of single server queueing networks and multi-class M/G/1 queues with feedback, Oper. Res. 25 (1977) 248–258.CrossRefGoogle Scholar
  10. [10]
    J. Walrand, An Introduction to Queueing Networks (Prentice-Hall, Englewood Cliffs, NJ, 1988).Google Scholar
  11. [11]
    J. Weishaupt, Optimal myopic policies and index policies for stochastic scheduling problems, Math. Methods Oper. Res. 40 (1994) 75–89.CrossRefGoogle Scholar
  12. [12]
    G. Weiss, On optimal draining of reentrant fluid lines, in: Stochastic Networks, eds. F.P. Kelly and R.J. Williams (1995) pp. 91–103.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Nicole Bäuerle
    • 1
  • Ulrich Rieder
    • 1
  1. 1.Department of Mathematics VIIUniversity of UlmUlmGermany

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