Hiba Baroud

Stochastic Measures of Network Resilience: Applications to Waterway Commodity Flows

Given the ubiquitous nature of infrastructure networks in todays society, there is a global need to understand, quantify, and plan for the resilience of these networks to disruptions. This work defines network resilience along dimensions of reliability, vulnerability, survivability, and recoverability, and quantifies network resilience as a function of component and network performance. The treatment of vulnerability and recoverability as random variables leads to stochastic measures of resilience, including time to total system restoration, time to full system service resilience, and time to a specific α% resilience. Ultimately, a means to optimize network resilience strategies is discussed, primarily through an adaption of the Copeland Score for nonparametric stochastic ranking. The measures of resilience and optimization techniques are applied to inland waterway networks, an important mode in the larger multimodal transportation network upon which we rely for the flow of commodities. We provide a case study analyzing and planning for the resilience of commodity flows along the Mississippi River Navigation System to illustrate the usefulness of the proposed metrics.

Proportional hazards models of infrastructure system recovery

As emphasis is being placed on a systems ability to withstand and to recover from a disruptive event, collectively referred to as dynamic resilience, there exists a need to quantify a systems ability to bounce back after a disruptive event. This work applies a statistical technique from biostatistics, the proportional hazards model, to describe (i) the instantaneous rate of recovery of an infrastructure system and (ii) the likelihood that recovery occurs prior to a given point in time. A major benefit of the proportional hazards model is its ability to describe a recovery event as a function of time as well as covariates describing the infrastructure system or disruptive event, among others, which can also vary with time. The proportional hazards approach is illustrated with a publicly available electric power outage data set.

Static and dynamic resource allocation models for recovery of interdependent systems: application to the Deepwater Horizon oil spill

Determining where and when to invest resources during and after a disruption can challenge policy makers and homeland security officials. Two decision models, one static and one dynamic, are proposed to determine the optimal resource allocation to facilitate the recovery of impacted industries after a disruption where the objective is to minimize the production losses due to the disruption. The paper presents necessary conditions for optimality for the static model and develops an algorithm that finds every possible solution that satisfies those necessary conditions. A deterministic branch-and-bound algorithm solves the dynamic model and relies on a convex relaxation of the dynamic optimization problem. Both models are applied to the Deepwater Horizon oil spill, which adversely impacted several industries in the Gulf region, such as fishing, tourism, real estate, and oil and gas. Results demonstrate the importance of allocating enough resources to stop the oil spill and clean up the oil, which reduces the economic loss across all industries. These models can be applied to different homeland security and disaster response situations to help governments and organizations decide among different resource allocation strategies during and after a disruption.

Multi-criteria inoperability analysis of commodity-specific dock disruptions at an inland waterway port

Decision making for managing risks to critical infrastructure systems requires accounting for the widespread impacts of disruptions that render these systems inoperable. This paper integrates a dynamic risk-based interdependency model with a weighted multi-criteria decision analysis technique to evaluate discrete resource allocation alternatives to improve port preparedness. Dock-specific resource allocation provides a more tangible assessment of the effect of preparedness planning on particular commodities that flow through an inland waterway port. Uncertainty is accounted through the use of probability distributions of total expected loss per industry. We analyze a set of discrete allocations options of preparedness plans of a study of the Port of Catoosa in Oklahoma along the Mississippi River Navigation System.

Empirical analysis of Bayesian kernel methods for modeling count data

Bayesian models are used for estimation and forecasting in a wide range of application areas. One extension of such methods is the Bayesian kernel model, which integrate the Bayesian conjugate prior with kernel functions. This paper empirically analyzes the performance of Bayesian kernel models when applied to count data. The analysis is performed with several data sets with different characteristics regarding the numbers of observations and predictors. While the size of the data and number of predictors is changing across data sets, the predictors are all continuous in this study. The Poisson Bayesian kernel model is applied to each data set and compared to the Poisson generalized linear model. The measures of goodness of fit used are the deviance and the log-likelihood functional value, and the computation is done by dividing the data into training and testing sets, for the Bayesian kernel model, a tuning set is used to optimize the parameters of the kernel function. The Bayesian kernel approach tends to outperform classical count data models for smaller data sets with a small number of predictors. The analysis conducted in this paper is an initial step towards the validation of the Poisson Bayesian kernel model. This type of model can be useful in risk analysis applications in which data sources are scarce and can help in analytical and data-driven decision making.

Bayesian Kernel Methods for Critical Infrastructure Resilience Modeling

Integrating Bayesian methods with kernel methods has recently garnered attention, as Bayesian methods make use of previous data in order to estimate posterior probability distributions of the parameter of interest given that it follows a specific prior distribution. As the quantification of resilience has become a vital component of infrastructure risk analysis, the authors use the Beta Bayesian kernel model to estimate resilience metrics used to analyze the recovery process of disrupted critical infrastructure systems. More specifically, stochastic resilience-based component importance measures are assessed using the components characteristics and disruption data. Such estimates would help risk managers determine the overall best recovery strategy of an infrastructure system in case of a disruption impacting multiple components. The model is deployed in an application to an inland waterway transportation network, the Mississippi River Navigation system, for which the recovery of disrupted locks and dams on sections of the river is analyzed by estimating the resilience using the Bayesian kernel model.