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We consider the problem of promoting sustainability in production forests wherein a given number of strategic entities are authorized to own or manage concession regions. These entities harvest agricultural commodities and sell them in a market. We study optimal price-shaping in a coupled-activity network game model in which the concession owners (agents) engage in two activities: (a) the sustainable activity of producing a commodity that does not interfere with protected forest resources, and (b) the unsustainable activity of infringing into protected regions to expand their agricultural footprint. We characterize two types of policies in a budget-constrained setting: one that maximally suppresses the aggregate unsustainable activity and another that maximizes social welfare while constraining the aggregate unsustainable activity to remain below a predefined tolerance. Our analysis provides novel insights on the agents' equilibrium effort across the two activities and their influence on others due to intra- and cross-activity network effects. We also identify a measure of node centrality that resembles the Bonacich-Katz centrality and helps us determine pricing incentives that lead to welfare improvement while reducing the aggregate unsustainable activity.

Solving large-scale capacity expansion problems (CEPs) is central to cost-effective decarbonization of regional-scale energy systems. To ensure the intended outcomes of CEPs, modeling uncertainty due to weather-dependent variable renewable energy (VRE) supply and energy demand becomes crucially important. However, the resulting stochastic optimization models are often less computationally tractable than their deterministic counterparts. Here, we propose a learning-assisted approximate solution method to tractably solve two-stage stochastic CEPs. Our method identifies low-cost planning decisions by constructing and solving a sequence of tractable temporally aggregated surrogate problems. We adopt a Bayesian optimization approach to searching the space of time series aggregation hyperparameters and compute approximate solutions that minimize costs on a validation set of supply-demand projections. Importantly, we evaluate solved planning outcomes on a held-out set of test projections. We apply our approach to generation and transmission expansion planning for a joint power-gas system spanning New England. We show that our approach yields an estimated cost savings of up to 3.8% in comparison to benchmark time series aggregation approaches.

We study a planner's provision of information to manage workplace occupancy when strategic workers (agents) face risk of infectious disease transmission. The planner implements an information mechanism to signal information about the underlying risk of infection at the workplace. Agents update their belief over the risk parameter using this information and choose to work in-person or remotely. We address the design of the optimal signaling mechanism that best aligns the workplace occupancy with the planner's preference (i.e., maintaining safe capacity limits and operational efficiency at workplace). For various forms of planner preferences, we show numerical and analytical proof that interval-based information mechanisms are optimal. These mechanisms partition the continuous domain of the risk parameter into disjoint intervals and provision information based on interval-specific probability distributions over a finite set of signals. When the planner seeks to achieve an occupancy that lies in one of finitely many pre-specified ranges independent of the underlying risk, we provide an optimal mechanism that uses at most two intervals. On the other hand, when the preference on the occupancy is risk-dependent, we show that an approximately optimal interval-based mechanism can be computed efficiently. We bound the approximation loss for preferences that are expressed through a Lipschitz continuous function of both occupancy and risk parameter. We provide examples that demonstrate the improvement of proposed signaling mechanisms relative to the common benchmarks in information provision. Our findings suggest that information provision over the risk of disease transmission is an effective intervention for maintaining desirable occupancy levels at the workplace.

Building heat electrification is central to economy-wide decarbonization efforts and directly affects energy infrastructure planning through increasing electricity demand and reducing the building sector's use of gas infrastructure that also serves the power sector. Here, we develop a modeling framework to quantify end-use demand for electricity and gas in the buildings sector under various electrification pathways and evaluate their impact on co-optimized bulk power-gas infrastructure investments and operations under deep decarbonization scenarios. Applying the framework to study the U.S. New England region in 2050 across 20 weather scenarios, we find high electrification of the residential sector can increase sectoral peak and total electricity demands by up to 56-158% and 41-59% respectively relative to business-as-usual projections. Employing demand-side measures like building envelope improvements under high electrification, however, can reduce the magnitude and weather sensitivity of peak load as well as induce overall efficiency gains, reducing the combined residential sector energy demand for power and gas by 28-30% relative to the present day. Notably, a combination of high electrification and envelope improvements yields the lowest bulk power-gas system cost outcomes. We also find that inter-annual weather-driven variations in demand result in up to 33% variation in optimal power sector investments, which highlights the importance of capturing weather sensitivity of demand for planning purposes.

We study a market mechanism that sets edge prices to incentivize strategic agents to organize trips that efficiently share limited network capacity. This market allows agents to form groups to share trips, make decisions on departure times and route choices, and make payments to cover edge prices and other costs. We develop a new approach to analyze the existence and computation of market equilibrium, building on theories of combinatorial auctions and dynamic network flows. Our approach tackles the challenges in market equilibrium characterization arising from: (a) integer and network constraints on the dynamic flow of trips in sharing limited edge capacity; (b) heterogeneous and private preferences of strategic agents. We provide sufficient conditions on the network topology and agents' preferences that ensure the existence and polynomial-time computation of market equilibrium. We identify a particular market equilibrium that achieves maximum utilities for all agents, and is equivalent to the outcome of the classical Vickery Clark Grove mechanism. Finally, we extend our results to general networks with multiple populations and apply them to compute dynamic tolls for efficient carpooling in San Francisco Bay Area.

We focus on the problem of uncertainty informed allocation of medical resources (vaccines) to heterogeneous populations for managing epidemic spread. We tackle two related questions: (1) For a compartmental ordinary differential equation (ODE) model of epidemic spread, how can we estimate and integrate parameter uncertainty into resource allocation decisions? (2) How can we computationally handle both nonlinear ODE constraints and parameter uncertainties for a generic stochastic optimization problem for resource allocation? To the best of our knowledge current literature does not fully resolve these questions. Here, we develop a data-driven approach to represent parameter uncertainty accurately and tractably in a novel stochastic optimization problem formulation. We first generate a tractable scenario set by estimating the distribution on ODE model parameters using Bayesian inference with Gaussian processes. Next, we develop a parallelized solution algorithm that accounts for scenario-dependent nonlinear ODE constraints. Our scenario-set generation procedure and solution approach are flexible in that they can handle any compartmental epidemiological ODE model. Our computational experiments on two different non-linear ODE models (SEIR and SEPIHR) indicate that accounting for uncertainty in key epidemiological parameters can improve the efficacy of time-critical allocation decisions by 4-8%. This improvement can be attributed to data-driven and optimal (strategic) nature of vaccine allocations, especially in the early stages of the epidemic when the allocation strategy can crucially impact the long-term trajectory of the disease.

We consider a strategic network monitoring problem involving the operator of a networked system and an attacker. The operator aims to randomize the placement of multiple protected sensors to monitor and protect components that are vulnerable to attacks. We account for the heterogeneity in the components' security levels and formulate a large-scale maximin optimization problem. After analyzing its structure, we propose a three-step approach to approximately solve the problem. First, we solve a generalized covering set problem and run a combinatorial algorithm to compute an approximate solution. Then, we compute approximation bounds by solving a nonlinear set packing problem. To evaluate our solution approach, we implement two classical solution methods based on column generation and multiplicative weights updates, and test them on real-world water distribution and power systems. Our numerical analysis shows that our solution method outperforms the classical methods on large-scale networks, as it efficiently generates solutions that achieve a close to optimal performance and that are simple to implement in practice.

Effective investment planning decisions are crucial to ensure cyber-physical infrastructures satisfy performance requirements over an extended time horizon. Computing these decisions often requires solving Capacity Expansion Problems (CEPs). In the context of regional-scale energy systems, these problems are prohibitively expensive to solve due to large network sizes, heterogeneous node characteristics, and a large number of operational periods. To maintain tractability, traditional approaches aggregate network nodes and/or select a set of representative time periods. Often, these reductions do not capture supply-demand variations that crucially impact CEP costs and constraints, leading to suboptimal decisions. Here, we propose a novel graph convolutional autoencoder approach for spatio-temporal aggregation of a generic CEP with heterogeneous nodes (CEPHN). Our architecture leverages graph pooling to identify nodes with similar characteristics and minimizes a multi-objective loss function. This loss function is tailored to induce desirable spatial and temporal aggregations with regard to tractability and optimality. In particular, the output of the graph pooling provides a spatial aggregation while clustering the low-dimensional encoded representations yields a temporal aggregation. We apply our approach to generation expansion planning of a coupled 88-node power and natural gas system in New England. The resulting aggregation leads to a simpler CEPHN with 6 nodes and a small set of representative days selected from one year. We evaluate aggregation outcomes over a range of hyperparameters governing the loss function and compare resulting upper bounds on the original problem with those obtained using benchmark methods. We show that our approach provides upper bounds that are 33% (resp. 10%) lower those than obtained from benchmark spatial (resp. temporal) aggregation approaches.

In this paper, we study both multi-armed and contextual bandit problems in censored environments. Our goal is to estimate the performance loss due to censorship in the context of classical algorithms designed for uncensored environments. Our main contributions include the introduction of a broad class of censorship models and their analysis in terms of the effective dimension of the problem -- a natural measure of its underlying statistical complexity and main driver of the regret bound. In particular, the effective dimension allows us to maintain the structure of the original problem at first order, while embedding it in a bigger space, and thus naturally leads to results analogous to uncensored settings. Our analysis involves a continuous generalization of the Elliptical Potential Inequality, which we believe is of independent interest. We also discover an interesting property of decision-making under censorship: a transient phase during which initial misspecification of censorship is self-corrected at an extra cost, followed by a stationary phase that reflects the inherent slowdown of learning governed by the effective dimension. Our results are useful for applications of sequential decision-making models where the feedback received depends on strategic uncertainty (e.g., agents' willingness to follow a recommendation) and/or random uncertainty (e.g., loss or delay in arrival of information)., Comment: 45 pages, 5 figures, NeurIPS 2022

The transition to a deeply decarbonized energy system requires coordinated planning of infrastructure investments and operations serving multiple end-uses while considering technology and policy-enabled interactions across sectors. Electricity and natural gas (NG), which are vital vectors of today's energy system, are likely to be coupled in different ways in the future, resulting from increasing electrification, adoption of variable renewable energy (VRE) generation in the power sector and policy factors such as cross-sectoral emissions trading. This paper develops a least-cost investment and operations model for joint planning of electricity and NG infrastructures that considers a wide range of available and emerging technology options across the two vectors, including carbon capture and storage (CCS) equipped power generation, low-carbon drop-in fuels (LCDF) as well as long-duration energy storage (LDES). The model incorporates the main operational constraints of both systems and allows each system to operate under different temporal resolutions consistent with their typical scheduling timescales. We apply the modeling framework to evaluate power-NG system outcomes for the U.S. New England region under different technology, decarbonization goals, and demand scenarios. Under a global emissions constraint, ranging between 80-95\% emissions reduction compared to 1990 levels, the least-cost solution disproportionately relies on using the available emissions budget to serve non-power NG demand and results in the power sector using only 15-43\% of the emissions budget.

A rapid transformation of current electric power and natural gas (NG) infrastructure is imperative to meet the mid-century goal of CO2 emissions reduction requires. This necessitates a long-term planning of the joint power-NG system under representative demand and supply patterns, operational constraints, and policy considerations. Our work is motivated by the computational and practical challenges associated with solving the generation and transmission expansion problem (GTEP) for joint planning of power-NG systems. Specifically, we focus on efficiently extracting a set of representative days from power and NG data in respective networks and using this set to reduce the computational burden required to solve the GTEP. We propose a Graph Autoencoder for Multiple time resolution Energy Systems (GAMES) to capture the spatio-temporal demand patterns in interdependent networks and account for differences in the temporal resolution of available data. The resulting embeddings are used in a clustering algorithm to select representative days. We evaluate the effectiveness of our approach in solving a GTEP formulation calibrated for the joint power-NG system in New England. This formulation accounts for the physical interdependencies between power and NG systems, including the joint emissions constraint. Our results show that the set of representative days obtained from GAMES not only allows us to tractably solve the GTEP formulation, but also achieves a lower cost of implementing the joint planning decisions.

We propose a learning dynamics to model how strategic agents repeatedly play a continuous game while relying on an information platform to learn an unknown payoff-relevant parameter. In each time step, the platform updates a belief estimate of the parameter based on players' strategies and realized payoffs using Bayes's rule. Then, players adopt a generic learning rule to adjust their strategies based on the updated belief. We present results on the convergence of beliefs and strategies and the properties of convergent fixed points of the dynamics. We obtain sufficient and necessary conditions for the existence of globally stable fixed points. We also provide sufficient conditions for the local stability of fixed points. These results provide an approach to analyzing the long-term outcomes that arise from the interplay between Bayesian belief learning and strategy learning in games, and enable us to characterize conditions under which learning leads to a complete information equilibrium., Comment: arXiv admin note: substantial text overlap with arXiv:2109.00719

We study the problem of information provision by a strategic central planner who can publicly signal about an uncertain infectious risk parameter. Signalling leads to an updated public belief over the parameter, and agents then make equilibrium choices on whether to work remotely or in-person. The planner maintains a set of desirable outcomes for each realization of the uncertain parameter and seeks to maximize the probability that agents choose an acceptable outcome for the true parameter. We distinguish between stateless and stateful objectives. In the former, the set of desirable outcomes does not change as a function of the risk parameter, whereas in the latter it does. For stateless objectives, we reduce the problem to maximizing the probability of inducing mean beliefs that lie in intervals computable from the set of desirable outcomes. We derive the optimal signalling mechanism and show that it partitions the parameter domain into at most two intervals with the signals generated according to an interval-specific distribution. For the stateful case, we consider a practically relevant situation in which the planner can enforce in-person work capacity limits that progressively get more stringent as the risk parameter increases. We show that the optimal signalling mechanism for this case can be obtained by solving a linear program. We numerically verify the improvement in achieving desirable outcomes using our information design relative to no information and full information benchmarks.

We consider the security-by-design of a signal-free intersection for connected and autonomous vehicles in the face of strategic jamming attacks. We use a fluid model to characterize macroscopic traffic flow through the intersection, where the saturation rate is derived from a vehicle coordination algorithm. We model jamming attacks as sudden increase in communication latency induced on vehicle-to-infrastructure connectivity; such latency triggers the safety mode for vehicle coordination and thus reduces the intersection saturation rate. A strategic attacker selects the attacking rate, while a system operator selects key design parameters, either the saturation rate or the recovery rate. Both players' actions induce technological costs and jointly determine the mean travel delay. By analyzing the equilibrium of the security game, we study the preferable level of investment in the intersection's nominal discharging capability or recovery capability., Comment: Accepted by 2022 IEEE Conference on Decision and Control(CDC)

This paper introduces a "green" routing game between multiple logistic operators (players), each owning a mixed fleet of internal combustion engine vehicle (ICEV) and electric vehicle (EV) trucks. Each player faces the cost of delayed delivery (due to charging requirements of EVs) and a pollution cost levied on the ICEVs. This cost structure models: 1) limited battery capacity of EVs and their charging requirement; 2) shared nature of charging facilities; 3) pollution cost levied by regulatory agency on the use of ICEVs. We characterize Nash equilibria of this game and derive a condition for its uniqueness. We also use the gradient projection method to compute this equilibrium in a distributed manner. Our equilibrium analysis is useful to analyze the trade-off faced by players in incurring higher delay due to congestion at charging locations when the share of EVs increases versus a higher pollution cost when the share of ICEVs increases. A numerical example suggests that to increase marginal pollution cost can dramatically reduce inefficiency of equilibria., Comment: 8 pages

Modal split prediction in transportation networks has the potential to support network operators in managing traffic congestion and improving transit service reliability. We focus on the problem of hourly prediction of the fraction of travelers choosing one mode of transportation over another using high-dimensional travel time data. We use logistic regression as base model and employ various regularization techniques for variable selection to prevent overfitting and resolve multicollinearity issues. Importantly, we interpret the prediction accuracy results with respect to the inherent variability of modal splits and travelers' aggregate responsiveness to changes in travel time. By visualizing model parameters, we conclude that the subset of segments found important for predictive accuracy changes from hour-to-hour and include segments that are topologically central and/or highly congested. We apply our approach to the San Francisco Bay Area freeway and rapid transit network and demonstrate superior prediction accuracy and interpretability of our method compared to pre-specified variable selection methods.

Aerial images provide important situational awareness for responding to natural disasters such as hurricanes. They are well-suited for providing information for damage estimation and localization (DEL); i.e., characterizing the type and spatial extent of damage following a disaster. Despite recent advances in sensing and unmanned aerial systems technology, much of post-disaster aerial imagery is still taken by handheld DSLR cameras from small, manned, fixed-wing aircraft. However, these handheld cameras lack IMU information, and images are taken opportunistically post-event by operators. As such, DEL from such imagery is still a highly manual and time-consuming process. We propose an approach to both detect damage in aerial images and localize it in world coordinates, with specific focus on detecting and localizing flooding. The approach is based on using structure from motion to relate image coordinates to world coordinates via a projective transformation, using class activation mapping to detect the extent of damage in an image, and applying the projective transformation to localize damage in world coordinates. We evaluate the performance of our approach on post-event data from the 2016 Louisiana floods, and find that our approach achieves a precision of 88%. Given this high precision using limited data, we argue that this approach is currently viable for fast and effective DEL from handheld aerial imagery for disaster response., Comment: Version presented at NeurIPS 2021 AI+HADR workshop

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In this dynamics, a belief estimate of the parameter is repeatedly updated given players' strategies and realized payoffs using Bayes's rule. Players adjust their strategies by accounting for best response strategies given the belief. We show that, with probability 1, beliefs and strategies converge to a fixed point, where the belief consistently estimates the payoff distribution for the strategy, and the strategy is an equilibrium corresponding to the belief. However, learning may not always identify the unknown parameter because the belief estimate relies on the game outcomes that are endogenously generated by players' strategies. We obtain sufficient and necessary conditions, under which learning leads to a globally stable fixed point that is a complete information Nash equilibrium. We also provide sufficient conditions that guarantee local stability of fixed point beliefs and strategies., Comment: arXiv admin note: text overlap with arXiv:2010.09128

This paper presents a modeling approach for probabilistic estimation of hurricane wind-induced damage to infrastructural assets. In our approach, we employ a Nonhomogeneous Poisson Process (NHPP) model for estimating spatially-varying probability distributions of damage as a function of hurricane wind field velocities. Specifically, we consider a physically-based, quadratic NHPP model for failures of overhead assets in electricity distribution systems. The wind field velocities are provided by Forecasts of Hurricanes using Large-Ensemble Outputs (FHLO), a framework for generating probabilistic hurricane forecasts. We use FHLO in conjunction with the NHPP model, such that the hurricane forecast uncertainties represented by FHLO are accounted for in estimating the probability distributions of damage. Furthermore, we evaluate the spatial variability and extent of hurricane damage under key wind field parameters (intensity, size, and asymmetries). By applying our approach to prediction of power outages (loss-of-service) in northwestern Florida due to Hurricane Michael (2018), we demonstrate a statistically significant relationship between outage rate and failure rate. Finally, we formulate parametric models that relate total damage and financial losses to the hurricane parameters of intensity and size. Overall, this paper's findings suggest that our approach is well-suited to jointly account for spatial variability and forecast uncertainty in the damage estimates, and is readily applicable to prediction of system loss-of-service due to the damage., Comment: Submitted to Risk Analysis, 21 pages (main text), 17 figures, includes appendix

Highway capacity is often subject to stochastic perturbations due to the combined effects of weather, traffic mixture, driver behavior, etc. This paper is motivated by the need of a systematic approach to traffic control with performance guarantees in the face of such perturbations. We develop a novel control-theoretic method for designing perturbation-resilient ramp metering. We consider a cell-transmission model with 1) Markovian cell capacities and 2) buffers representing on-ramps and upstream mainline. Using this model, we analyze the stability of on-ramp queues by constructing piecewise Lyapunov functions that consider the nature of nonlinear traffic dynamics. Then, we design ramp controllers that guarantee bounds for throughput and queue sizes. We also formulate the problem of coordinated ramp metering as a bi-level optimization with non-convex inner sub-problems. To address the computational issue in solving this problem, we also consider localized and partially coordinated reformulations. A case study of a 18.1-km highway in Los Angeles, USA indicates a 8.3\% (resp. 9.9\%) reduction of vehicle-hours-traveled obtained by the localized (resp. partially coordinated) control, both outperforming the classical ALINEA and METALINE controllers.

In this paper, we address the existence and computation of competitive equilibrium in the transportation market for autonomous carpooling first proposed by [Ostrovsky and Schwarz, 2019]. At equilibrium, the market organizes carpooled trips over a transportation network in a socially optimal manner and sets the corresponding payments for individual riders and toll prices on edges. The market outcome ensures individual rationality, stability of carpooled trips, budget balance, and market clearing properties under heterogeneous rider preferences. We show that the question of market's existence can be resolved by proving the existence of an integer optimal solution of a linear programming problem. We characterize conditions on the network topology and riders' disutility for carpooling under which a market equilibrium can be computed in polynomial time. This characterization relies on ideas from the theory of combinatorial auctions and minimum cost network flow problem. Finally, we characterize a market equilibrium that achieves strategyproofness and maximizes welfare of individual riders.

Error-Correcting Output Codes (ECOCs) offer a principled approach for combining simple binary classifiers into multiclass classifiers. In this paper, we investigate the problem of designing optimal ECOCs to achieve both nominal and adversarial accuracy using Support Vector Machines (SVMs) and binary deep learning models. In contrast to previous literature, we present an Integer Programming (IP) formulation to design minimal codebooks with desirable error correcting properties. Our work leverages the advances in IP solvers to generate codebooks with optimality guarantees. To achieve tractability, we exploit the underlying graph-theoretic structure of the constraint set in our IP formulation. This enables us to use edge clique covers to substantially reduce the constraint set. Our codebooks achieve a high nominal accuracy relative to standard codebooks (e.g., one-vs-all, one-vs-one, and dense/sparse codes). We also estimate the adversarial accuracy of our ECOC-based classifiers in a white-box setting. Our IP-generated codebooks provide non-trivial robustness to adversarial perturbations even without any adversarial training.

We study learning dynamics induced by strategic agents who repeatedly play a game with an unknown payoff-relevant parameter. In each step, an information system estimates a belief distribution of the parameter based on the players' strategies and realized payoffs using Bayes' rule. Players adjust their strategies by accounting for an equilibrium strategy or a best response strategy based on the updated belief. We prove that beliefs and strategies converge to a fixed point with probability 1. We also provide conditions that guarantee local and global stability of fixed points. Any fixed point belief consistently estimates the payoff distribution given the fixed point strategy profile. However, convergence to a complete information Nash equilibrium is not always guaranteed. We provide a sufficient and necessary condition under which fixed point belief recovers the unknown parameter. We also provide a sufficient condition for convergence to complete information equilibrium even when parameter learning is incomplete.

In recent years, it has become crucial to improve the resilience of electricity distribution networks (DNs) against storm-induced failures. Microgrids enabled by Distributed Energy Resources (DERs) can significantly help speed up re-energization of loads, particularly in the complete absence of bulk power supply. We describe an integrated approach which considers a pre-storm DER allocation problem under the uncertainty of failure scenarios as well as a post-storm dispatch problem in microgrids during the multi-period repair of the failed components. This problem is computationally challenging because the number of scenarios (resp. binary variables) increases exponentially (resp. quadratically) in the network size. Our overall solution approach for solving the resulting two-stage mixed-integer linear program (MILP) involves implementing the sample average approximation (SAA) method and Benders Decomposition. Additionally, we implement a greedy approach to reduce the computational time requirements of the post-storm repair scheduling and dispatch problem. The optimality of the resulting solution is evaluated on a modified IEEE 36-node network., Comment: 6 pages, 5 figures, accepted to 2020 American Control Conference

Platooning of connected and autonomous vehicles (CAVs) has a significant potential for throughput improvement. However, the interaction between CAVs and non-CAVs may limit the practically attainable improvement due to platooning. To better understand and address this limitation, we introduce a new fluid model of mixed-autonomy traffic flow and use this model to analyze and design platoon coordination strategies. We propose tandem-link fluid model that considers randomly arriving platoons sharing highway capacity with non-CAVs. We derive verifiable conditions for stability of the fluid model by analyzing an underlying M/D/1 queuing process and establishing a Foster-Lyapunov drift condition for the fluid model. These stability conditions enable a quantitative analysis of highway throughput under various scenarios. The model is useful for designing platoon coordination strategies that maximize throughput and minimize delay. Such coordination strategies are provably optimal in the fluid model and are practically relevant. We also validate our results using standard macroscopic (cell transmission model, CTM) and microscopic (Simulation for Urban Mobility, SUMO) simulation models.

Traffic navigation services have gained widespread adoption in recent years. The route recommendations generated by these services often leads to severe congestion on urban streets, raising concerns from neighboring residents and city authorities. This paper is motivated by the question: How can a transportation authority design an information structure to induce a preferred equilibrium traffic flow pattern in uncertain network state conditions? We approach this question from a Bayesian persuasion viewpoint. We consider a basic routing game with two parallel routes and an uncertain state that affects the travel cost on one of the routes. The authority sends a noisy signal of the state to a given fraction of travelers. The information structure (i.e., distribution of signals in each state) chosen by the authority creates a heterogeneous information environment for the routing game. The solution concept governing the travelers' route choices is Bayesian Wardrop Equilibrium. We design an information structure to minimize the average traffic spillover -- the amount of equilibrium route flow exceeding a certain threshold -- on one of the routes. We provide an analytical characterization of the optimal information structure for any fraction of travelers receiving the signal. We find that it can achieve the minimum spillover so long as the fraction of travelers receiving the signal is larger than a threshold (smaller than 1).

Traffic Management Centers (TMCs) routinely use traffic cameras to provide situational awareness regarding traffic, road, and weather conditions. Camera footage is quite useful for a variety of diagnostic purposes; yet, most footage is kept for only a few days, if at all. This is largely due to the fact that currently, identification of notable footage is done via manual review by human operators---a laborious and inefficient process. In this article, we propose a semantics-oriented approach to analyzing sequential image data, and demonstrate its application for automatic detection of real-world, anomalous events in weather and traffic conditions. Our approach constructs semantic vector representations of image contents from textual labels which can be easily obtained from off-the-shelf, pretrained image labeling software. These semantic label vectors are used to construct semantic topic signals---time series representations of physical processes---using the Latent Dirichlet Allocation (LDA) topic model. By detecting anomalies in the topic signals, we identify notable footage corresponding to winter storms and anomalous traffic congestion. In validation against real-world events, anomaly detection using semantic topic signals significantly outperforms detection using any individual label signal.

We study learning dynamics induced by myopic travelers who repeatedly play a routing game on a transportation network with an unknown state. The state impacts cost functions of one or more edges of the network. In each stage, travelers choose their routes according to Wardrop equilibrium based on public belief of the state. This belief is broadcast by an information system that observes the edge loads and realized costs on the used edges, and performs a Bayesian update to the prior stage's belief. We show that the sequence of public beliefs and edge load vectors generated by the repeated play converge almost surely. In any rest point, travelers have no incentive to deviate from the chosen routes and accurately learn the true costs on the used edges. However, the costs on edges that are not used may not be accurately learned. Thus, learning can be incomplete in that the edge load vectors at rest point and complete information equilibrium can be different. We present some conditions for complete learning and illustrate situations when such an outcome is not guaranteed.

The tandem fluid queueing model is a useful tool for performance analysis and control design for a variety of transportation systems. In this article, we study the joint impact of stochastic capacity and spillback on the long-time properties of this model. Our analysis focuses on the system of two fluid queueing links in series. The upstream link has a constant capacity (saturation rate) and an infinite buffer size. The downstream link has a stochastic capacity and a finite buffer size. Queue spillback occurs when the the downstream link is full. We derive a necessary condition and a sufficient condition for the total queue length to be bounded on average. The necessary (resp. sufficient) condition leads to an upper (resp. lower) bound for the throughput of the two-link system. Using our results, we analyze the sensitivity of throughput of the two-link system with respect to the frequency and intensity of capacity disruptions, and to the buffer size. In addition, we discuss how our analysis can be extended to feedback-controlled systems and to networks consisting of merges and splits.

We consider an attacker-operator game for monitoring a large-scale network that is comprised on components that differ in their criticality levels. In this zero-sum game, the operator seeks to position a limited number of sensors to monitor the network against an attacker who strategically targets a network component. The operator (resp. attacker) seeks to minimize (resp. maximize) the network loss. To study the properties of mixed-strategy Nash Equilibria of this game, we first study two simple instances: (i) When component sets monitored by individual sensor locations are mutually disjoint; (ii) When only a single sensor is positioned, but with possibly overlapping monitoring component sets. Our analysis reveals new insights on how criticality levels impact the players equilibrium strategies. Next, we extend a previously known approach to obtain an approximate Nash equilibrium for the general case of the game. This approach uses solutions to minimum set cover and maximum set packing problems to construct an approximate Nash equilibrium. Finally, we implement a column generation procedure to improve this solution and numerically evaluate the performance of our approach.

This paper presents a computational approach to evaluate the resilience of electricity Distribution Networks (DNs) to cyber-physical failures. In our model, we consider an attacker who targets multiple DN components to maximize the loss of the DN operator. We consider two types of operator response: (i) Coordinated emergency response; (ii) Uncoordinated autonomous disconnects, which may lead to cascading failures. To evaluate resilience under response (i), we solve a Bilevel Mixed-Integer Second-Order Cone Program which is computationally challenging due to mixed-integer variables in the inner problem and non-convex constraints. Our solution approach is based on the Generalized Benders Decomposition method, which achieves a reasonable tradeoff between computational time and solution accuracy. Our approach involves modifying the Benders cut based on structural insights on power flow over radial DNs. We evaluate DN resilience under response (ii) by sequentially computing autonomous component disconnects due to operating bound violations resulting from the initial attack and the potential cascading failures. Our approach helps estimate the gain in resilience under response (i), relative to (ii).

Advances in microgrids powered by Distributed Energy Resources (DERs) make them an attractive response capability for improving the resilience of electricity distribution networks (DNs). This paper presents an approach to evaluate the value of implementing a timely response using microgrid operations and DER dispatch in the aftermath of a disruption event, involving strategic compromise of multiple DN components. Firstly, we extend the resiliency assessment framework in [1] and develop a sequential (bilevel) model of attacker-operator interactions on a radial DN with one or more microgrids. Particularly, the operator response includes microgrid operations under various islanding configurations (regimes), and single- or multi-master operation of DERs in providing grid-forming services as well as frequency and voltage regulation. Secondly, we introduce a restoration problem in which the operator gradually reconnects the disrupted components over multiple periods to restore the nominal performance of the DN. The first problem, formulated as a bilevel mixed-integer problem, is solved using a Benders decomposition method. The second problem, formulated as a multi-period mixed-integer problem, can be solved using a greedy algorithm. Our results illustrate the benefit of using microgrids in reducing the operator's losses, both immediately after the disruption event and during the restoration process.

This article poses the following problem: Does there exist a probability distribution over subsets of a finite partially ordered set (poset), such that a set of constraints involving marginal probabilities of the poset's elements and maximal chains is satisfied? We present a combinatorial algorithm to positively resolve this question. The algorithm can be implemented in polynomial time in the special case where maximal chain probabilities are affine functions of their elements. This existence problem is relevant for the equilibrium characterization of a generic strategic interdiction game on a capacitated flow network. The game involves a routing entity that sends its flow through the network while facing path transportation costs, and an interdictor who simultaneously interdicts one or more edges while facing edge interdiction costs. Using our existence result on posets and strict complementary slackness in linear programming, we show that the Nash equilibria of this game can be fully described using primal and dual solutions of a minimum-cost circulation problem. Our analysis provides a new characterization of the critical components in the interdiction game. It also leads to a polynomial-time approach for equilibrium computation.

In this brief paper we find computable exponential convergence rates for a large class of stochastically ordered Markov processes. We extend the result of Lund, Meyn, and Tweedie (1996), who found exponential convergence rates for stochastically ordered Markov processes starting from a fixed initial state, by allowing for a random initial condition that is also stochastically ordered. Our bounds are formulated in terms of moment-generating functions of hitting times. To illustrate our result, we find an explicit exponential convergence rate for an M/M/1 queue beginning in equilibrium and then experiencing a change in its arrival or departure rates, a setting which has not been studied to our knowledge., Comment: 13 pages

Electricity distribution networks (DNs) in many regions are increasingly subjected to disruptions caused by tropical storms. Distributed Energy Resources (DERs) can act as temporary supply sources to sustain "microgrids" resulting from disruptions. In this paper, we investigate the problem of suitable DER allocation to facilitate more efficient repair operations and faster recovery. First, we estimate the failure probabilities of DN components (lines) using a stochastic model of line failures which parametrically depends on the location-specific storm wind field. Next, we formulate a two-stage stochastic mixed integer program, which models the distribution utility's decision to allocate DERs in the DN (pre-storm stage); and accounts for multi-period decisions on optimal dispatch and line repair scheduling (post-storm stage). A key feature of this formulation is that it jointly optimizes electricity dispatch within the individual microgrids and the line repair schedules to minimize the sum of the cost of DER allocation and cost due to lost load. To illustrate our approach, we use the sample average approximation method to solve our problem for a small-size DN under different storm intensities and DER/crew constraints., Comment: 7 pages, 4 figures, accepted to 2018 IEEE SmartGridComm Conference

Traffic cameras are commonly deployed monitoring components in road infrastructure networks, providing operators visual information about conditions at critical points in the network. However, human observers are often limited in their ability to process simultaneous information sources. Recent advancements in computer vision, driven by deep learning methods, have enabled general object recognition, unlocking opportunities for camera-based sensing beyond the existing human observer paradigm. In this paper, we present a Natural Language Processing (NLP)-inspired approach, entitled Bag-of-Label-Words (BoLW), for analyzing image data sets using exclusively textual labels. The BoLW model represents the data in a conventional matrix form, enabling data compression and decomposition techniques, while preserving semantic interpretability. We apply the Latent Dirichlet Allocation (LDA) topic model to decompose the label data into a small number of semantic topics. To illustrate our approach, we use freeway camera images collected from the Boston area between December 2017-January 2018. We analyze the cameras' sensitivity to weather events; identify temporal traffic patterns; and analyze the impact of infrequent events, such as the winter holidays and the "bomb cyclone" winter storm. This study demonstrates the flexibility of our approach, which allows us to analyze weather events and freeway traffic using only traffic camera image labels., Comment: To be presented at IEEE-ITSC 2018, Nov 3-7 2018

In this paper, we study the problem of traffic management in highways facing stochastic perturbations. To model the macroscopic traffic flow under perturbations, we use cell-transmission model with Markovian capacities. The decision variables are: (i) the admissible flow through each on-ramp, and (ii) whether individual on-ramps are metered to prioritize the mainline traffic or not. The objective is to maximize the throughput while ensuring that on-ramp queues remain bounded on average. We develop a computational approach to solving this stability-constrained, throughput-maximization problem. We establish a mixed-integer linear program for throughput maximization and construct an algorithm that gives the optimal solution in particular settings. We illustrate the performance benefits of the proposed approach through a computational study on a segment of Interstate 210 in California, USA., Comment: 27 pages

We study a routing game in an environment with multiple heterogeneous information systems and an uncertain state that affects edge costs of a congested network. Each information system sends a noisy signal about the state to its subscribed traveler population. Travelers make route choices based on their private beliefs about the state and other populations' signals. The question then arises, "How does the presence of asymmetric and incomplete information affect the travelers' equilibrium route choices and costs?'' We develop a systematic approach to characterize the equilibrium structure, and determine the effect of population sizes on the relative value of information (i.e. difference in expected traveler costs) between any two populations. This effect can be evaluated using a population-specific size threshold. One population enjoys a strictly positive value of information in comparison to the other if and only if its size is below the corresponding threshold. We also consider the situation when travelers may choose an information system based on its value, and characterize the set of equilibrium adoption rates delineating the sizes of subscribed traveler populations. The resulting routing strategies are such that all travelers face an identical expected cost and no traveler has the incentive to change her subscription.

Infrastructure systems are increasingly facing new security threats due to the vulnerabilities of cyber-physical components that support their operation. In this article, we investigate how the infrastructure operator (defender) should prioritize the investment in securing a set of facilities in order to reduce the impact of a strategic adversary (attacker) who can target a facility to increase the overall usage cost of the system. We adopt a game-theoretic approach to model the defender-attacker interaction and study two models: normal-form game -- where both players move simultaneously; and sequential game -- where attacker moves after observing the defender's strategy. For each model, we provide a complete characterization of how the set of facilities that are secured by the defender in equilibrium vary with the costs of attack and defense. Importantly, our analysis provides a sharp condition relating the cost parameters for which the defender has the first mover advantage. Specifically, we show that to fully deter the attacker from targeting any facility, the defender needs to proactively secure all "vulnerable facilities" at an appropriate level of effort. We illustrate the outcome of the attacker-defender interaction on a simple transportation network. We also suggest a dynamic learning setup to understand how this outcome can affect the ability of imperfectly informed users to make their decisions about using the system in the post-attack stage.

Vehicle-to-Infrastructure (V2I) communications are increasingly supporting highway operations such as electronic toll collection, carpooling, and vehicle platooning. In this paper we study the incentives of strategic misbehavior by individual vehicles who can exploit the security vulnerabilities in V2I communications and negatively impact the highway operations. We consider a V2I-enabled highway segment facing two classes of vehicles (agent populations), each with an authorized access to one server (subset of lanes). Vehicles are strategic in that they can misreport their class (type) to the system operator and get an unauthorized access to the server dedicated to the other class. This misbehavior causes additional congestion externality on the compliant vehicles, and thus, needs to be deterred. We focus on an environment where the operator is able to inspect the vehicles for misbehavior. The inspection is costly and successful detection incurs a fine on the misbehaving vehicle. We formulate a signaling game to study the strategic interaction between the vehicle classes and the operator. Our equilibrium analysis provides conditions on the cost parameters that govern the vehicles' incentive to misbehave or not. We also determine the operator's equilibrium inspection strategy.

This article studies a problem of strategic network inspection, in which a defender (agency) is tasked with detecting the presence of multiple attacks in the network. An inspection strategy entails monitoring the network components, possibly in a randomized manner, using a given number of detectors. We formulate the network inspection problem $(\mathcal{P})$ as a large-scale bilevel optimization problem, in which the defender seeks to determine an inspection strategy with minimum number of detectors that ensures a target expected detection rate under worst-case attacks. We show that optimal solutions of $(\mathcal{P})$ can be obtained from the equilibria of a large-scale zero-sum game. Our equilibrium analysis involves both game-theoretic and combinatorial arguments, and leads to a computationally tractable approach to solve $(\mathcal{P})$. Firstly, we construct an approximate solution by utilizing solutions of minimum set cover (MSC) and maximum set packing (MSP) problems, and evaluate its detection performance. In fact, this construction generalizes some of the known results in network security games. Secondly, we leverage properties of the optimal detection rate to iteratively refine our MSC/MSP-based solution through a column generation procedure. Computational results on benchmark water networks demonstrate the scalability, performance, and operational feasibility of our approach. The results indicate that utilities can achieve a high level of protection in large-scale networks by strategically positioning a small number of detectors.

This note introduces a piecewise-deterministic queueing (PDQ) model to study the stability of traffic queues in parallel-link transportation systems facing stochastic capacity fluctuations. The saturation rate (capacity) of the PDQ model switches between a finite set of modes according to a Markov chain, and link inflows are controlled by a state-feedback policy. A PDQ system is stable only if a lower bound on the time-average link inflows does not exceed the corresponding time-average saturation rate. Furthermore, a PDQ system is stable if the following two conditions hold: the nominal mode's saturation rate is high enough that all queues vanish in this mode, and a bilinear matrix inequality (BMI) involving an underestimate of the discharge rates of the PDQ in individual modes is feasible. The stability conditions can be strengthened for two-mode PDQs. These results can be used for design of routing policies that guarantee stability of traffic queues under stochastic capacity fluctuations., Comment: 20 pages, 3 figures

This article studies the value of information in route choice decisions when a fraction of players have access to high accuracy information about traffic incidents relative to others. To model such environments, we introduce a Bayesian congestion game, in which players have private information about incidents, and each player chooses her route on a network of parallel links. The links are prone to incidents that occur with an ex-ante known probability. The demand is comprised of two player populations: one with access to high accuracy incident information and another with low accuracy information, i.e. the populations differ only by their access to information. The common knowledge includes: (i) the demand and route cost functions, (ii) the fraction of highly-informed players, (iii) the incident probability, and (iv) the marginal type distributions induced by the information structure of the game. We present a full characterization of the Bayesian Wardrop Equilibrium of this game under the assumption that low information players receive no additional information beyond common knowledge. We also compute the cost to individual players and the social cost as a function of the fraction of highly-informed players when they receive perfectly accurate information. Our first result suggests that below a certain threshold of highly-informed players, both populations experience a reduction in individual cost, with the highly-informed players receiving a greater reduction. However, above this threshold, both populations realize the same equilibrium cost. Secondly, there exists another (lower or equal) threshold above which a further increase in the fraction of highly-informed players does not reduce the expected social costs. Thus, once a sufficiently large number of players are highly informed, wider distribution of more accurate information is ineffective at best, and otherwise socially harmful.

This article considers a two-player strategic game for network routing under link disruptions. Player 1 (defender) routes flow through a network to maximize her value of effective flow while facing transportation costs. Player 2 (attacker) simultaneously disrupts one or more links to maximize her value of lost flow but also faces cost of disrupting links. Linear programming duality in zero-sum games and the Max-Flow Min-Cut Theorem are applied to obtain properties that are satisfied in any Nash equilibrium. A characterization of the support of the equilibrium strategies is provided using graph-theoretic arguments. Finally, conditions under which these results extend to budget-constrained environments are also studied. These results extend the classical minimum cost maximum flow problem and the minimum cut problem to a class of security games on flow networks., Comment: The results in this paper only hold under a restrictive assumption on the class of networks (Assumption 1 in page 7). This makes the results inapplicable in practice, and further work is needed

This article focuses on the security assessment of electricity Distribution Networks (DNs) with vulnerable Distributed Energy Resource (DER) nodes. The adversary model is simultaneous compromise of DER nodes by strategic manipulation of generation set-points. The loss to the defender (DN operator) includes loss of voltage regulation and cost of induced load control under supply-demand mismatch caused by the attack. A 3-stage Defender-Attacker-Defender (DAD) game is formulated: in Stage 1, the defender chooses a security strategy to secure a subset of DER nodes; in Stage 2, the attacker compromises a set of vulnerable DERs and injects false generation set-points; in Stage 3, the defender responds by controlling loads and uncompromised DERs. Solving this trilevel optimization problem is hard due to nonlinear power flows and mixed-integer decision variables. To address this challenge, the problem is approximated by a tractable formulation based on linear power flows. The set of critical DER nodes and the set-point manipulations characterizing the optimal attack strategy are computed. An iterative greedy approach to compute attacker-defender strategies for the original nonlinear problem is proposed. These results provide guidelines for optimal security investment and defender response in pre- and post-attack conditions, respectively.