Felisa J. Vázquez-Abad

Gradient estimation for discrete-event systems by measure-valued differentiation

In simulation of complex stochastic systems, such as Discrete-Event Systems (DES), statistical distributions are used to model the underlying randomness in the system. A sensitivity analysis of the simulation output with respect to parameters of the input distributions, such as the mean and the variance, is therefore of great value. The focus of this article is to provide a practical guide for robust sensitivity, respectively, gradient estimation that can be easily implemented along the simulation of a DES. We study the Measure-Valued Differentiation (MVD) approach to sensitivity estimation. Specifically, we will exploit the “modular” structure of the MVD approach, by firstly providing measure-valued derivatives for input distributions that are of importance in practice, and subsequently, by showing that if an input distribution possesses a measure-valued derivative, then so does the overall Markov kernel modeling the system transitions. This simplifies the complexity of applying MVD drastically: one only has to study the measure-valued derivative of the input distribution, a measure-valued derivative of the associated Markov kernel is then given through a simple formula in canonical form. The derivative representations of the underlying simple distributions derived in this article can be stored in a computer library. Combined with the generic MVD estimator, this yields an automated gradient estimation procedure. The challenge in automating MVD so that it can be included into a simulation package is the verification of the integrability condition to guarantee that the estimators are unbiased. The key contribution of the article is that we establish a general condition for unbiasedness which is easily checked in applications. Gradient estimators obtained by MVD are typically phantom estimators and we discuss the numerical efficiency of phantom estimators with the example of waiting times in the G/G/1 queue.

Stochastic Model for Cognitive Radio Networks under Jamming Attacks and Honeypot-Based Prevention

Limited and dynamically available resources and no right to protection from interference in the open access dynamic spectrum access model bring forth a serious challenge of sustenance among the secondary networks and make them more susceptible to various spectrum etiquette attacks. Among these, the most common are jamming-based denial of service DoS attacks, which result in packet loss. The concept of a honeypot node or honeynode has been explored for wireless networks and has shown to be effective in attracting attacks, thus deterring the jammers from productive nodes. Yet a single dedicated honeynode, on account of its permanent idleness, is wasteful of an entire node as resource. In this paper, we seek to resolve this dilemma by dynamically selecting the honeynode for each transmission period, and we explore various methods of doing so. To begin with, we develop the first comprehensive queuing model for CRNs, which pose unique modeling challenges due to their periodic sensing and transmission cycles. We then build a simulation of CRNs under attack from jammers, introduce a series of strategies for honeynode assignment to combat these attacks, and assess the performance of each strategy. We find that the predictions of our mathematical model track closely with the results of our simulation experiments.

Gradient-based simulation optimization under probability constraints

We study optimization problems subject to possible fatal failures. The probability of failure should not exceed a given confidence level. The distribution of the failure event is assumed unknown, but it can be generated via simulation or observation of historical data. Gradient-based simulation-optimization methods pose the difficulty of the estimation of the gradient of the probability constraint under no knowledge of the distribution. In this work we provide two single-path estimators with bias: a convolution method and a finite difference, and we provide a full analysis of convergence of the Arrow-Hurwicz algorithm, which we use as our solver for optimization. Convergence results are used to tune the parameters of the numerical algorithms in order to achieve best convergence rates, and numerical results are included via an example of application in finance.

CR-Honeynet: A Learning & Decoy Based Sustenance Mechanism against Jamming Attack in CRN

Cognitive Radio Network (CRN) enables secondary users to borrow unused spectrum from the proprietary users in a dynamic and opportunistic manner. However, dynamic and open access nature of available spectrum brings a serious challenge of sustenance amongst CRNs which makes them vulnerable to various spectrum etiquette attacks. Jamming-based denial of service (DoS) attack poses serious threats to legitimate communications and packet delivery. A rational attacker targets certain transmission characteristics to find the highest impacting communication of CRN and causes maximum disruption. In this paper, inspired by the honey pot concept in cyber crime, we propose a honey net based defense mechanism, which aims to deter the attacker from jamming legitimate communications. The honey net passively learns the attackers strategy from the past history of attacks and actively adapts pre-emptive decoy mechanisms to prevent attacks on legitimate communications. Simulation results show that the with help of honey net mechanism, CRN successfully avoids jamming attacks and thereby improves system performance in terms of packet delivery ratio.

A Perturbation Analysis Approach to Phantom Estimators for Waiting Times in the G/G/1 Queue

We study gradient estimation for waiting times in the G/G/1 queue. We propose a new estimator based on a synthesis of perturbation analysis and weak differentiation. More specifically, we combine the perturbation propagation rules from perturbation analysis with perturbation generation rules from weak differentiation. This leads to an on-line phantom estimator. Numerical experiments show that this estimator has smaller work normalized variance than IPA.

Performance analysis of CR-honeynet to prevent jamming attack through stochastic modeling

Abstract Cognitive Radio Network (CRN) has to stall its packet transmission periodically to sense the spectrum for Primary User’s (PU’s) transmission. The limited and dynamically available spectrum and fixed periodic schedule of transmission interruption makes it harder to model the performance of a CRNs. Again, an open and dynamic spectrum access model brings forth a serious challenge of sustenance among the CRN and makes them more susceptible to jamming-based denial of service (DoS) attacks. Inspired by honeypot in the network security, we propose a honeynet based defense mechanism called CR-honeynet. CR-honeynet aims to avoid attacks on legitimate communications by dedicating a Secondary User (SU) as a honeynode, to deter the attacker from attacking legitimate SUs and attack the honeynode instead. Dedicating an SU as honeynode, on account of its permanent idleness, is wasteful of an entire node as a resource. We seek to resolve the dilemma by dynamically selecting the honeynode for each transmission period. The contribution of the current paper is two-fold. Initially, we develop the first comprehensive queuing model for CRNs, which pose unique modeling challenges, due to their fixed periodic sensing and transmission cycles. In the second step, we introduce a series of strategies for honeynode selection to combat these attacks while keeping the CRN’s performance optimal for different traffic scenarios. We build a simulation of a CRN under jamming attack and analyze its performance with different honeynode selection strategies. We find that the predictions, of our mathematical model, track closely with the results of our simulation experiments.

Change-point monitoring for online stochastic approximations

We consider stochastic approximations in a quickly changing non-stationary environment. We assume the parameters of the system are subject to sudden discontinuous changes, which we refer to as regime-switching. We are interested in problems characterized by frequent significant jumps with no a priori knowledge about the regimes. Our approach is based on constant step size stochastic approximation. While larger step sizes have the advantage of fast adaptation, smaller step sizes provide more precise estimates of the target value once the process is close to stationary. We propose to use a small constant step size combined with change-point monitoring, and to reset the process at a value closer to the new target when a change is detected. Stochastic approximation and change-point monitoring complement each other by achieving high precision as well as cutting down the convergence time. We give a theoretical characterization and discuss the tradeoff between precision and fast adaptation. We also introduce a new monitoring scheme, the regression-based hypothesis test, which performs comparably well to Page-Hinkleys test and the CUSUM of residuals. The novelty of our approach is (a) the combination of change-point monitoring to stochastic approximation in a regime-switching environment and (b) the introduction of a new monitoring scheme. We provide an asymptotic analysis of this method and we show weak convergence to a limiting switching ODE for the non-reset method, and to a hybrid DE for a reset method that we propose.

A game-theoretic and stochastic survivability mechanism against induced attacks in Cognitive Radio Networks ☆

Abstract Cognitive Radio Networks (CRNs) are envisioned to provide a solution to the scarcity of the available frequency spectrum. It allows unlicensed secondary users (SUs) to use spectrum bands that are not occupied by licensed primary users (PUs) in an opportunistic manner. This dynamic manner of spectrum access gives rise to vulnerabilities that are unique to CRNs. In the battle over the available spectrum, SUs do not have any means of identifying whether disruption sensed on a band is intentional or unintentional. This problem is further intensified in the case of heterogeneous spectrum, where different bands provide different utilities. A smart malicious agent can use this vulnerability to temporarily disrupt transmissions on certain bands and induce their unavailability on SUs. The motivation for such disruption-induced attacks can be either monopolism, i.e. to capture as much spectrum as possible and make other SUs starve, or denial of service by intentional disruption of other SUs’ communications. This paper proposes an adaptive strategy for robust dynamic spectrum access in the event of induced attacks. Assuming rational players, and considering the notion of channel utility, the optimal strategy is established by modeling such scenarios as zero-sum games that lead to Nash equilibrium. Thereafter, the case of non-stationary channel utilities is investigated, where utilities are subject to abrupt changes due to fluctuations in channel characteristics, as well as arrival and departure of PUs. Through concurrent estimation, learning, and optimal play, it is shown that the proposed mechanism performs robustly even in such dynamic environments. Comparison of the proposed mechanism to other reasonable benchmark strategies in simulation confirms that this mechanism significantly enhances the performance of CRNs.

Ghost simulation model for discrete event systems, an application to a local bus service

In this paper we present a simulation model for large networks that increases the efficiency compared to a discrete event simulation model. These networks have two different time scales: a fast one and a slow one. The main idea is to replace some of the faster point processes by a “fluid” (called the ghost processes) thus accelerating the execution of the simulation. Using local modularity for the code, there is no need to keep a list of events. Clocks are not necessarily synchronized. When a local clock advances due to a slower event, retrospective calculations recover the fine detail lost in the fluid model. Mathematically, the model is a special case of the Filtered Monte Carlo method. Efficiency improvement results not only from the speed of execution, but also from variance reduction. We provide proofs of unbiasedness. Throughout the paper we use a case scenario of an airport car park.

Gradient estimation for quantiles of stationary waiting times

Abstract Quantiles of customer based performance characteristics 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 standard gradient estimation methods can be applied. While sensitivity analysis of quantiles of waiting times for static or fixed time horizon problems is well understood, quantile estimation for stationary waiting times remains an open question. This paper will close this gap and will provide a framework for gradient estimation for quantiles of stationary waiting times.