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Aron Laszka, Waseem Abbas, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2018.  Synergistic Security for the Industrial Internet of Things: Integrating Redundancy, Diversity, and Hardening. IEEE International Conference on Industrial Internet (ICII). :153-158.

As the Industrial Internet of Things (IIot) becomes more prevalent in critical application domains, ensuring security and resilience in the face of cyber-attacks is becoming an issue of paramount importance. Cyber-attacks against critical infrastructures, for example, against smart water-distribution and transportation systems, pose serious threats to public health and safety. Owing to the severity of these threats, a variety of security techniques are available. However, no single technique can address the whole spectrum of cyber-attacks that may be launched by a determined and resourceful attacker. In light of this, we consider a multi-pronged approach for designing secure and resilient IIoT systems, which integrates redundancy, diversity, and hardening techniques. We introduce a framework for quantifying cyber-security risks and optimizing IIoT design by determining security investments in redundancy, diversity, and hardening. To demonstrate the applicability of our framework, we present a case study in water-distribution systems. Our numerical evaluation shows that integrating redundancy, diversity, and hardening can lead to reduced security risk at the same cost.

Xenofon Koutsoukos, Gabor Karsai, Aron Laszka, Himanshu Neema, Bradley Potteiger, Peter Volgyesi, Yevgeniy Vorobeychik, Janos Sztipanovits.  2018.  SURE: A Modeling and Simulation Integration Platform for Evaluation of Secure and Resilient Cyber–Physical Systems. Proceedings of the IEEE. 106:93-112.

The exponential growth of information and communication technologies have caused a profound shift in the way humans engineer systems leading to the emergence of closed-loop systems involving strong integration and coordination of physical and cyber components, often referred to as cyber-physical systems (CPSs). Because of these disruptive changes, physical systems can now be attacked through cyberspace and cyberspace can be attacked through physical means. The paper considers security and resilience as system properties emerging from the intersection of system dynamics and the computing architecture. A modeling and simulation integration platform for experimentation and evaluation of resilient CPSs is presented using smart transportation systems as the application domain. Evaluation of resilience is based on attacker-defender games using simulations of sufficient fidelity. The platform integrates 1) realistic models of cyber and physical components and their interactions; 2) cyber attack models that focus on the impact of attacks to CPS behavior and operation; and 3) operational scenarios that can be used for evaluation of cybersecurity risks. Three case studies are presented to demonstrate the advantages of the platform: 1) vulnerability analysis of transportation networks to traffic signal tampering; 2) resilient sensor selection for forecasting traffic flow; and 3) resilient traffic signal control in the presence of denial-of-service attacks.

Amin Ghafouri, Aron Laszka, Xenofon Koutsoukos.  2018.  Application-Aware Anomaly Detection of Sensor Measurements in Cyber-Physical Systems. Sensors. 18:2448.

Detection errors such as false alarms and undetected faults are inevitable in any practical anomaly detection system. These errors can create potentially significant problems in the underlying application. In particular, false alarms can result in performing unnecessary recovery actions while missed detections can result in failing to perform recovery which can lead to severe consequences. In this paper, we present an approach for application-aware anomaly detection (AAAD). Our approach takes an existing anomaly detector and configures it to minimize the impact of detection errors. The configuration of the detectors is chosen so that application performance in the presence of detection errors is as close as possible to the performance that could have been obtained if there were no detection errors. We evaluate our result using a case study of real-time control of traffic signals, and show that the approach outperforms significantly several baseline detectors.

Waseem Abbas, Aron Laszka, Xenofon Koutsoukos.  2018.  Improving Network Connectivity and Robustness Using Trusted Nodes With Application to Resilient Consensus. IEEE Transactions on Control of Network Systems. 5:2036-2048.

To observe and control a networked system, especially in failure-prone circumstances, it is imperative that the underlying network structure be robust against node or link failures. A common approach for increasing network robustness is redundancy: deploying additional nodes and establishing new links between nodes, which could be prohibitively expensive. This paper addresses the problem of improving structural robustness of networks without adding extra links. The main idea is to ensure that a small subset of nodes, referred to as the trusted nodes, remains intact and functions correctly at all times. We extend two fundamental metrics of structural robustness with the notion of trusted nodes, network connectivity, and r-robustness, and then show that by controlling the number and location of trusted nodes, any desired connectivity and robustness can be achieved without adding extra links. We study the complexity of finding trusted nodes and construction of robust networks with trusted nodes. Finally, we present a resilient consensus algorithm with trusted nodes and show that, unlike existing algorithms, resilient consensus is possible in sparse networks containing few trusted nodes.

Amin Ghafouri, Xenofon Koutsoukos, Yevgeniy Vorobeychik, Waseem Abbas, Aron Laszka.  2019.  A game-theoretic approach for selecting optimal time-dependent thresholds for anomaly detection. International Foundation for Autonomous Agents and Multi-Agent Systems Journal. 33

Adversaries may cause significant damage to smart infrastructure using malicious attacks. To detect and mitigate these attacks before they can cause physical damage, operators can deploy anomaly detection systems (ADS), which can alarm operators to suspicious activities. However, detection thresholds of ADS need to be configured properly, as an oversensitive detector raises a prohibitively large number of false alarms, while an undersensitive detector may miss actual attacks. This is an especially challenging problem in dynamical environments, where the impact of attacks may significantly vary over time. Using a game-theoretic approach, we formulate the problem of computing optimal detection thresholds which minimize both the number of false alarms and the probability of missing actual attacks as a two-player Stackelberg security game. We provide an efficient dynamic programming-based algorithm for solving the game, thereby finding optimal detection thresholds. We analyze the performance of the proposed algorithm and show that its running time scales polynomially as the length of the time horizon of interest increases. In addition, we study the problem of finding optimal thresholds in the presence of both random faults and attacks. Finally, we evaluate our result using a case study of contamination attacks in water networks, and show that our optimal thresholds significantly outperform fixed thresholds that do not consider that the environment is dynamical.

Aron Laszka, Gabor Horvath, Mark Felegyhazi, Levente Buttyan.  2014.  FlipThem: Modeling Targeted Attacks with FlipIt for Multiple Resources. 5th Conference on Decision and Game Theory for Security (GameSec).
Recent high-profile targeted attacks showed that even the most secure and secluded networks can be compromised by motivated and resourceful attackers, and that such a system compromise may not be immediately detected by the system owner. Researchers at RSA proposed the FlipIt game to study the impact of such stealthy takeovers. In the basic FlipIt game, an attacker and a defender fight over a single resource; in practice, however, systems typically consist of multiple resources that can be targeted. In this paper, we present FlipThem, a generalization of FlipIt to multiple resources. To formulate the players' goals and study their best strategies, we introduce two control models: in the AND model, the attacker has to compromise all resources in order to take over the entire system, while in the OR model, she has to compromise only one. Our analytical and numerical results provide practical recommendations for defenders.
Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2015.  Optimal Personalized Filtering Against Spear-Phishing Attacks. 29th AAAI Conference on Artificial Intelligence (AAAI).
To penetrate sensitive computer networks, attackers can use spear phishing to sidestep technical security mechanisms by exploiting the privileges of careless users. In order to maximize their success probability, attackers have to target the users that constitute the weakest links of the system. The optimal selection of these target users takes into account both the damage that can be caused by a user and the probability of a malicious e-mail being delivered to and opened by a user. Since attackers select their targets in a strategic way, the optimal mitigation of these attacks requires the defender to also personalize the e-mail filters by taking into account the users' properties. In this paper, we assume that a learned classifier is given and propose strategic per-user filtering thresholds for mitigating spear-phishing attacks. We formulate the problem of filtering targeted and non-targeted malicious e-mails as a Stackelberg security game. We characterize the optimal filtering strategies and show how to compute them in practice. Finally, we evaluate our results using two real-world datasets and demonstrate that the proposed thresholds lead to lower losses than non-strategic thresholds.
Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2015.  Integrity Assurance in Resource-Bounded Systems through Stochastic Message Authentication. 2nd Annual Symposium and Bootcamp on the Science of Security (HotSoS).
Assuring communication integrity is a central problem in security. However, overhead costs associated with cryptographic primitives used towards this end introduce significant practical implementation challenges for resource-bounded systems, such as cyber-physical systems. For example, many control systems are built on legacy components which are computationally limited but have strict timing constraints. If integrity protection is a binary decision, it may simply be infeasible to introduce into such systems; without it, however, an adversary can forge malicious messages, which can cause significant physical or financial harm. We propose a formal game-theoretic framework for optimal stochastic message authentication, providing provable integrity guarantees for resource-bounded systems based on an existing MAC scheme. We use our framework to investigate attacker deterrence, as well as optimal design of stochastic message authentication schemes when deterrence is impossible. Finally, we provide experimental results on the computational performance of our framework in practice.
George Rontidis, Emmanouil Panaousis, Aron Laszka, Tasos Dagiuklas, Pasquale Malacaria, Tansu Alpcan.  2015.  A Game-Theoretic Approach for Minimizing Security Risks in the Internet-of-Things. 1st IEEE International Workshop on Security and Privacy for Internet of Things and Cyber-Physical Systems, in conjunction with IEEE ICC 2015 (IoT/CPS-Security).
In the Internet-of-Things (IoT), users might share part of their data with different IoT prosumers, which offer applications or services. Within this open environment, the existence of an adversary introduces security risks. These can be related, for instance, to the theft of user data, and they vary depending on the security controls that each IoT prosumer has put in place. To minimize such risks, users might seek an "optimal" set of prosumers. However, assuming the adversary has the same information as the users about the existing security measures, he can then devise which prosumers will be preferable (e.g., with the highest security levels) and attack them more intensively. This paper proposes a decision-support approach that minimizes security risks in the above scenario. We propose a non-cooperative, two-player game entitled Prosumers Selection Game (PSG). The Nash Equilibria of PSG determine subsets of prosumers that optimize users' payoffs. We refer to any game solution as the Nash Prosumers Selection (NPS), which is a vector of probabilities over subsets of prosumers. We show that when using NPS, a user faces the least expected damages. Additionally, we show that according to NPS every prosumer, even the least secure one, is selected with some non-zero probability. We have also performed simulations to compare NPS against two different heuristic selection algorithms. The former is proven to be approximately 38% more effective in terms of security-risk mitigation.
Aron Laszka, Jens Grossklags.  2015.  Should Cyber-Insurance Providers Invest in Software Security? 20th European Symposium on Research in Computer Security (ESORICS).
Insurance is based on the diversifiability of individual risks: if an insurance provider maintains a large portfolio of customers, the probability of an event involving a large portion of the customers is negligible. However, in the case of cyber-insurance, not all risks are diversifiable due to software monocultures. If a vulnerability is discovered in a widely used software product, it can be used to compromise a multitude of targets until it is eventually patched, leading to a catastrophic event for the insurance provider. To lower their exposure to non-diversifiable risks, insurance providers may try to influence the security of widely used software products in their customer population, for example, through vulnerability reward programs. We explore the proposal that insurance providers should take a proactive role in improving software security, and provide evidence that this approach is viable for a monopolistic provider. We develop a model which captures the supply and demand sides of insurance, provide computational complexity results on the provider's investment decisions, and propose different heuristic investment strategies. We demonstrate that investments can reduce non-diversifiable risks and can lead to a more profitable cyber-insurance market. Finally, we detail the relative merits of the different heuristic strategies with numerical results.
Waseem Abbas, Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2015.  Scheduling Intrusion Detection Systems in Resource-Bounded Cyber-Physical Systems. 1st ACM Workshop on Cyber-Physical Systems Security and Privacy, in conjunction with ACM CCS 2015 (CPS-SPC).

In order to be resilient to attacks, a cyber-physical system (CPS) must be able to detect attacks before they can cause significant damage. To achieve this, intrusion detection systems (IDS) may be deployed, which can detect attacks and alert human operators, who can then intervene. However, the resource-constrained nature of many CPS poses a challenge, since reliable IDS can be computationally expensive. Consequently, computational nodes may not be able to perform intrusion detection continuously, which means that we have to devise a schedule for performing intrusion detection. While a uniformly random schedule may be optimal in a purely cyber system, an optimal schedule for protecting CPS must also take into account the physical properties of the system, since the set of adversarial actions and their consequences depend on the physical systems. Here, in the context of water distribution networks, we study IDS scheduling problems in two settings and under the constraints on the available battery supplies. In the first problem, the objective is to design, for a given duration of time, scheduling schemes for IDS so that the probability of detecting an attack is maximized within that duration. We propose efficient heuristic algorithms for this general problem and evaluate them on various networks. In the second problem, our objective is to design scheduling schemes for IDS so that the overall lifetime of the network is maximized while ensuring that an intruder attack is always detected. Various strategies to deal with this problem are presented and evaluated for various networks.

Nika Haghtalab, Aron Laszka, Ariel Procaccia, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2015.  Monitoring Stealthy Diffusion. 15th IEEE International Conference on Data Mining (ICDM).
Starting with the seminal work by Kempe et al., a broad variety of problems, such as targeted marketing and the spread of viruses and malware, have been modeled as selecting a subset of nodes to maximize diffusion through a network. In cyber-security applications, however, a key consideration largely ignored in this literature is stealth. In particular, an attacker often has a specific target in mind, but succeeds only if the target is reached (e.g., by malware) before the malicious payload is detected and corresponding countermeasures deployed. The dual side of this problem is deployment of a limited number of monitoring units, such as cyber-forensics specialists, so as to limit the likelihood of such targeted and stealthy diffusion processes reaching their intended targets. We investigate the problem of optimal monitoring of targeted stealthy diffusion processes, and show that a number of natural variants of this problem are NP-hard to approximate. On the positive side, we show that if stealthy diffusion starts from randomly selected nodes, the defender's objective is submodular, and a fast greedy algorithm has provable approximation guarantees. In addition, we present approximation algorithms for the setting in which an attacker optimally responds to the placement of monitoring nodes by adaptively selecting the starting nodes for the diffusion process. Our experimental results show that the proposed algorithms are highly effective and scalable.
Benjamin Johnson, Aron Laszka, Jens Grossklags.  2015.  Games of Timing for Security in Dynamic Environments. 6th Conference on Decision and Game Theory for Security (GameSec).
Increasing concern about insider threats, cyber-espionage, and other types of attacks which involve a high degree of stealthiness has renewed the desire to better understand the timing of actions to audit, clean, or otherwise mitigate such attacks. However, to the best of our knowledge, the modern literature on games shares a common limitation: the assumption that the cost and effectiveness of the players' actions are time-independent. In practice, however, the cost and success probability of attacks typically vary with time, and adversaries may only attack when an opportunity is present (e.g., when a vulnerability has been discovered). In this paper, we propose and study a model which captures dynamic environments. More specifically, we study the problem faced by a defender who has deployed a new service or resource, which must be protected against cyber-attacks. We assume that adversaries discover vulnerabilities according to a given vulnerability-discovery process which is modeled as an arbitrary function of time. Attackers and defenders know that each found vulnerability has a basic lifetime, i.e., the likelihood that a vulnerability is still exploitable at a later date is subject to the efforts by ethical hackers who may rediscover the vulnerability and render it useless for attackers. At the same time, the defender may invest in mitigation efforts to lower the impact of an exploited vulnerability. Attackers therefore face the dilemma to either exploit a vulnerability immediately, or wait for the defender to let its guard down. The latter choice leaves the risk to come away empty-handed. We develop two versions of our model, i.e., a continuous-time and a discrete-time model, and conduct an analytic and numeric analysis to take first steps towards actionable guidelines for sound security investments in dynamic contested environments.
Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2015.  Resilient Observation Selection in Adversarial Settings. 54th IEEE Conference on Decision and Control (CDC).

Monitoring large areas using sensors is fundamental in a number of applications, including electric power grid, traffic networks, and sensor-based pollution control systems. However, the number of sensors that can be deployed is often limited by financial or technological constraints. This problem is further complicated by the presence of strategic adversaries, who may disable some of the deployed sensors in order to impair the operator's ability to make predictions. Assuming that the operator employs a Gaussian-process-based regression model, we formulate the problem of attack-resilient sensor placement as the problem of selecting a subset from a set of possible observations, with the goal of minimizing the uncertainty of predictions. We show that both finding an optimal resilient subset and finding an optimal attack against a given subset are NP-hard problems. Since both the design and the attack problems are computationally complex, we propose efficient heuristic algorithms for solving them and present theoretical approximability results. Finally, we show that the proposed algorithms perform exceptionally well in practice using numerical results based on real-world datasets.

Aron Laszka, Jian Lou, Yevgeniy Vorobeychik.  2016.  Multi-Defender Strategic Filtering Against Spear-Phishing Attacks. 30th AAAI Conference on Artificial Intelligence (AAAI).
Spear-phishing attacks pose a serious threat to sensitive computer systems, since they sidestep technical security mechanisms by exploiting the carelessness of authorized users. A common way to mitigate such attacks is to use e-mail filters which block e-mails with a maliciousness score above a chosen threshold. Optimal choice of such a threshold involves a tradeoff between the risk from delivered malicious emails and the cost of blocking benign traffic. A further complicating factor is the strategic nature of an attacker, who may selectively target users offering the best value in terms of likelihood of success and resulting access privileges. Previous work on strategic threshold-selection considered a single organization choosing thresholds for all users. In reality, many organizations are potential targets of such attacks, and their incentives need not be well aligned. We therefore consider the problem of strategic threshold-selection by a collection of independent self-interested users. We characterize both Stackelberg multi-defender equilibria, corresponding to short-term strategic dynamics, as well as Nash equilibria of the simultaneous game between all users and the attacker, modeling long-term dynamics, and exhibit a polynomial-time algorithm for computing short-term (Stackelberg) equilibria. We find that while Stackelberg multi-defender equilibrium need not exist, Nash equilibrium always exists, and remarkably, both equilibria are unique and socially optimal.
Aron Laszka, Bradley Potteiger, Yevgeniy Vorobeychik, Saurabh Amin, Xenofon Koutsoukos.  2016.  Vulnerability of Transportation Networks to Traffic-Signal Tampering. 7th ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS).

Traffic signals were originally standalone hardware devices running on fixed schedules, but by now, they have evolved into complex networked systems. As a consequence, traffic signals have become susceptible to attacks through wireless interfaces or even remote attacks through the Internet. Indeed, recent studies have shown that many traffic lights deployed in practice have easily exploitable vulnerabilities, which allow an attacker to tamper with the configuration of the signal. Due to hardware-based failsafes, these vulnerabilities cannot be used to cause accidents. However, they may be used to cause disastrous traffic congestions. Building on Daganzo's well-known traffic model, we introduce an approach for evaluating vulnerabilities of transportation networks, identifying traffic signals that have the greatest impact on congestion and which, therefore, make natural targets for attacks. While we prove that finding an attack that maximally impacts congestion is NP-hard, we also exhibit a polynomial-time heuristic algorithm for computing approximately optimal attacks. We then use numerical experiments to show that our algorithm is extremely efficient in practice. Finally, we also evaluate our approach using the SUMO traffic simulator with a real-world transportation network, demonstrating vulnerabilities of this network. These simulation results extend the numerical experiments by showing that our algorithm is extremely efficient in a microsimulation model as well.

Aron Laszka, Waseem Abbas, Shankar Sastry, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2016.  Optimal Thresholds for Intrusion Detection Systems. 3rd Annual Symposium and Bootcamp on the Science of Security (HotSoS).

In recent years, we have seen a number of successful attacks against high-profile targets, some of which have even caused severe physical damage. These examples have shown us that resourceful and determined attackers can penetrate virtually any system, even those that are secured by the "air-gap." Consequently, in order to minimize the impact of stealthy attacks, defenders have to focus not only on strengthening the first lines of defense but also on deploying effective intrusion-detection systems. Intrusion-detection systems can play a key role in protecting sensitive computer systems since they give defenders a chance to detect and mitigate attacks before they could cause substantial losses. However, an over-sensitive intrusion-detection system, which produces a large number of false alarms, imposes prohibitively high operational costs on a defender since alarms need to be manually investigated. Thus, defenders have to strike the right balance between maximizing security and minimizing costs. Optimizing the sensitivity of intrusion detection systems is especially challenging in the case when multiple interdependent computer systems have to be defended against a strategic attacker, who can target computer systems in order to maximize losses and minimize the probability of detection. We model this scenario as an attacker-defender security game and study the problem of finding optimal intrusion detection thresholds.

Aron Laszka, Mingyi Zhao, Jens Grossklags.  2016.  Banishing Misaligned Incentives for Validating Reports in Bug-Bounty Platforms. 21st European Symposium on Research in Computer Security (ESORICS).
Bug-bounty programs have the potential to harvest the efforts and diverse knowledge of thousands of white hat hackers. As a consequence, they are becoming increasingly popular as a key part of the security culture of organizations. However, bug-bounty programs can be riddled with myriads of invalid vulnerability-report submissions, which are partially the result of misaligned incentives between white hats and organizations. To further improve the effectiveness of bug-bounty programs, we introduce a theoretical model for evaluating approaches for reducing the number of invalid reports. We develop an economic framework and investigate the strengths and weaknesses of existing canonical approaches for effectively incentivizing higher validation efforts by white hats. Finally, we introduce a novel approach, which may improve effi- ciency by enabling different white hats to exert validation effort at their individually optimal levels.
Mingyi Zhao, Aron Laszka, Thomas Maillart, Jens Grossklags.  2016.  Crowdsourced Security Vulnerability Discovery: Modeling and Organizing Bug-Bounty Programs. HCOMP Workshop on Mathematical Foundations of Human Computation.
(No abstract.)
Amin Ghafouri, Waseem Abbas, Aron Laszka, Yevgeniy Vorobeychik, Xenofon Koutsoukos.  2016.  Optimal Thresholds for Anomaly-Based Intrusion Detection in Dynamical Environments. 2016 Conference on Decision and Game Theory for Security (GameSec 2016).

In recent years, we have seen a number of successful attacks against high-profile targets, some of which have even caused severe physical damage. These examples have shown us that resourceful and determined attackers can penetrate virtually any system, even those that are secured by the "air-gap." Consequently, in order to minimize the impact of stealthy attacks, defenders have to focus not only on strengthening the first lines of defense but also on deploying effective intrusion-detection systems. Intrusion-detection systems can play a key role in protecting sensitive computer systems since they give defenders a chance to detect and mitigate attacks before they could cause substantial losses. However, an over-sensitive intrusion-detection system, which produces a large number of false alarms, imposes prohibitively high operational costs on a defender since alarms need to be manually investigated. Thus, defenders have to strike the right balance between maximizing security and minimizing costs. Optimizing the sensitivity of intrusion detection systems is especially challenging in the case when multiple inter-dependent computer systems have to be defended against a strategic attacker, who can target computer systems in order to maximize losses and minimize the probability of detection. We model this scenario as an attacker-defender security game and study the problem of finding optimal intrusion detection thresholds.

Aron Laszka, Galina A. Schwartz.  2016.  Becoming Cybercriminals: Incentives in Networks with Interdependent Security. 7th Conference on Decision and Game Theory for Security (GameSec).
We study users’ incentives to become cybercriminals when network security is interdependent. We present a game-theoretic model in which each player (i.e., network user) decides his type, honest or malicious. Honest users represent law-abiding network users, while malicious users represent cybercriminals. After deciding on their types, the users make their security choices. We will follow [29], where breach probabilities for large-scale networks are obtained from a standard interdependent security (IDS) setup. In large-scale IDS networks, the breach probability of each player becomes a function of two variables: the player’s own security action and network security, which is an aggregate characteristic of the network; network security is computed from the security actions of the individual nodes that comprise the network. This allows us to quantify user security choices in networks with IDS even when users have only very limited, aggregate information about security choices of other users of the network.
Aron Laszka, Waseem Abbas, Xenofon Koutsoukos.  2017.  Scheduling Battery-Powered Sensor Networks for Minimizing Detection Delays. IEEE Communication Letters.
Sensor networks monitoring spatially-distributed physical systems often comprise battery-powered sensor devices. To extend lifetime, battery power may be conserved using sleep scheduling: activating and deactivating some of the sensors from time to time. Scheduling sensors with the goal of maximizing average coverage, that is the average fraction of time for which each monitoring target is covered by some active sensor has been studied extensively. However, many applications also require time-critical monitoring in the sense that one has to minimize the average delay until an unpredictable change or event at a monitoring target is detected. In this paper, we study the problem of sleep scheduling sensors to minimize the average delay in detecting such time-critical events in the context of monitoring physical systems that can be modeled using graphs, such as water distribution networks. We provide a game-theoretic solution that computes schedules with near optimal average delays. We illustrate that schedules that optimize average coverage may result in large average detection delays, whereas schedules minimizing average detection delays using our proposed scheme also result in near optimal average coverage.