In this paper we address the construction of efficient algorithms for the estimation of gradients of general performance measures of Gaussian systems. Exploiting a clever coupling between the normal and the Maxwell distribution, we present a new gradient estimator, and we show that it outperforms both the single-run based infinitesimal perturbation analysis (IPA) estimator and the score functio...

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard perturbative technique, ...

This chapter introduces the network buffer control techniques as a mean to provide QoS. This problem has been extensively studied in the context of wirelined networks; however, the proliferation of wireless networks and the introduction of multimedia applications has significantly changed the characteristics of the traffic mix that flows on the network. The objective of this chapter is to creat...

E quantile sensitivities is important in many optimization applications, from hedging in financial engineering to service-level constraints in inventory control to more general chance constraints in stochastic programming. Recently, Hong (Hong, L. J. 2009. Estimating quantile sensitivities. Oper. Res. 57 118–130) derived a batched infinitesimal perturbation analysis estimator for quantile sensi...

The fluid-flow paradigm is an alternative approach to the traditional queueing paradigm, where workload movement in a network is described in terms of a fluid metaphor rather than the familiar customer metaphor. Stochastic fluid network models can considerably speed up the simulation of complex flow networks, such as high-speed packet-based telecommunications networks, where traditional queuein...

We study the problem of approximating a subgradient of a convex (or concave) discrete function that is evaluated via simulation. This problem arises, for instance, in optimization problems such as finding the minimal cost staff schedule in a call center subject to a service level constraint. There, subgradient information can be used to significantly reduce the search space. The problem of appr...

Quantiles of a random performance serve as important alternatives to the usual expected value. They are used in the financial industry as measures of risk and in the service industry as measures of service quality. To manage the quantile of a performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper, we s...

Communication networks may be abstracted through Stochastic Fluid Models (SFM) with the node dynamics described by switched flow equations as various events take place, thus giving rise to hybrid automaton models with stochastic transitions. The inclusion of feedback mechanisms complicates these dynamics. In a tandem setting, a typical feedback mechanism is the control of a node processing rate...

Recent study for congestion control in high speed networks indicates that the derivative information for the congestion at the common buffer for multiple sources could be useful in achieving efficient and fair allocation of the bandwidth (Kelly 1997, 1998). In this paper we present an algorithm that estimates such derivatives for multiple on-off sources. The algorithm has its root in the infini...

We consider resource contention games in a stochastic hybrid system setting using Stochastic Flow Models (SFM) with multiple classes and class-dependent objectives. We present a general modeling framework for such games, where Infinitesimal Perturbation Analysis (IPA) estimators are derived for the derivatives of various class-dependent objectives. This allows us to study these games from the p...