The Nyquist Stability Criterion is generalized to systems where the (open-loop) system has infinite-dimensional input/output spaces and a (possibly) unbounded infinitesimal generator. This is done through use of the perturbation determinant and an extension of the Argument Principle to infinitesimal generators with trace-class resolvent.

We provide algorithms to compute the performance derivatives of Markov chains with respect to changes in their transition matrices and of Markov processes with respect to changes in their infinitesimal generators. Our algorithms are readily applicable to the control and optimization of these Markov systems, since they are based on analyzing a single sample path and do not need explicit specific...

We consider the problem of finding target vectors for which the nonzero duality gap exists in the problem of convex optimization. An infinitesimal approach to the duality gap analysis of convex problems is proposed. The approach is based on finding the order of smallness and the proportionality coefficient of perturbation function of the original optimization problem. We show that in case of du...

This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic building blocks (i.e., the transition probabilities, the distribution and density functions of the even...

In recent years, there has been a surge of research into methods for estimating derivatives of performance measures from sample paths of stochastic systems. In the case of queueing systems, typical performance measures are mean queue lengths, throughputs, etc., and the derivatives estimated are with respect to system parameters, such as parameters of service and interarrival time distributions....

This paper is concerned with the generation of Gaussian invariant states in cascades of open quantum harmonic oscillators governed by linear quantum stochastic differential equations. We carry out infinitesimal perturbation analysis of the covariance matrix for the invariant Gaussian state of such a system and the related purity functional subject to inaccuracies in the energy and coupling matr...

Quantiles are important performance characteristics that have been adopted in many areas for measuring the quality of service. Recently, sensitivity analysis of quantiles has attracted quite some attention. Sensitivity analysis of quantiles is particularly challenging as quantiles cannot be expressed as the expected value of some sample performance function, and it is therefore not evident how ...

We consider coordination among stocking locations through replenishment strategies that explicitly take into account lateral transshipments, i.e., transfer of a product among locations at the same echelon level. Our basic contribution is the incorporation of supply capacity into the traditional transshipment model. Our goal is to analyze the impact on system behavior and on stocking locations’ ...