In Search of Sensitivity in Network Optimization

This paper concerns policy synthesis in large queuing networks. The results provide answers to the following questions: (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 use 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? If so, what is the ‘regret’? (iii) Where are the highest sources of 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. However, sensitivity of steady state performance with respect to perturbations in the policy vanishes with increasing variability.