In Search of Sensitivity in Network Optimization

  • Authors:

  • Mike Chen;Charuhas Pandit;Sean Meyn

  • Affiliations:

  • Department of Electrical and Computer Engineering and the Coordinated Sciences Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA mikechen@uiuc.edu;Department of Electrical and Computer Engineering and the Coordinated Sciences Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA cpandit@students.uiuc.edus-meyn@uiuc.edu

  • Venue:
  • Queueing Systems: Theory and Applications
  • Year:
  • 2003

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Abstract

This paper concerns the following questions regarding policy synthesis in large queueing networks: (i) It is well known that an understanding of variability is important in the determination of safety stocks to prevent unwanted idleness. Is this the only value of high-order statistical information in policy synthesis? (ii) Will a translation of an optimal policy for the deterministic fluid model (in which there is no variability) lead to an allocation which is approximately optimal for the stochastic network? (iii) What are the sources of highest sensitivity in network control? A sensitivity analysis of an associated fluid-model optimal control problem provides an exact dichotomy in (ii). If an optimal policy for the fluid model is ‘maximally non-idling’, then variability plays a small role in control design. If this condition does not hold, then the ‘gap’ between the fluid and stochastic optimal policies is exactly proportional to system variability. Furthermore, under mild assumptions, we find that the optimal policy for the stochastic model is closely approximated by an affine shift of the fluid optimal solution. However, sensitivity of steady-state performance with respect to perturbations in the policy vanishes with increasing variability.