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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.

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.

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., 8 pages

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.

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.

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 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., 27 pages

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 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 paper focuses on the optimal sensor placement problem for the identification of pipe failure locations in large-scale urban water systems. The problem involves selecting the minimum number of sensors such that every pipe failure can be uniquely localized. This problem can be viewed as a minimum test cover (MTC) problem, which is NP-hard. We consider two approaches to obtain approximate solutions to this problem. In the first approach, we transform the MTC problem to a minimum set cover (MSC) problem and use the greedy algorithm that exploits the submodularity property of the MSC problem to compute the solution to the MTC problem. In the second approach, we develop a new augmented greedy algorithm for solving the MTC problem. This approach does not require the transformation of the MTC to MSC. Our augmented greedy algorithm provides in a significant computational improvement while guaranteeing the same approximation ratio as the first approach. We propose several metrics to evaluate the performance of the sensor placement designs. Finally, we present detailed computational experiments for a number of real water distribution networks. Keywords: Fault identification; Minimum test cover; Water networks