Patrol Planning Research Articles

Time of week intensity estimation from partly interval censored data with applications to police patrol planning

Law enforcement agencies are tasked with crime prevention and crime reduction under limited resources. Having an accurate temporal estimate of the crime rate would be valuable to achieve such a goal. However, estimation is usually complicated by the interval censored nature of crime data. We cast the problem of intensity estimation as a Poisson regression using an EM algorithm to estimate the parameters. Two special penalties are added that provide smoothness over the time of day and day of week. This approach provides accurate intensity estimates and can also uncover day of week clusters that share the same intensity patterns. Both simulated and real crime data gathered from the city of Cincinnati and the city of Dallas are used to demonstrate the effectiveness of the proposed model.

Behavioral Learning in Security Games: Threat of Multi-Step Manipulative Attacks

This paper studies the problem of multi-step manipulative attacks in Stackelberg security games, in which a clever attacker attempts to orchestrate its attacks over multiple time steps to mislead the defender's learning of the attacker's behavior. This attack manipulation eventually influences the defender's patrol strategy towards the attacker's benefit. Previous work along this line of research only focuses on one-shot games in which the defender learns the attacker's behavior and then designs a corresponding strategy only once. Our work, on the other hand, investigates the long-term impact of the attacker's manipulation in which current attack and defense choices of players determine the future learning and patrol planning of the defender. This paper has three key contributions. First, we introduce a new multi-step manipulative attack game model that captures the impact of sequential manipulative attacks carried out by the attacker over the entire time horizon. Second, we propose a new algorithm to compute an optimal manipulative attack plan for the attacker, which tackles the challenge of multiple connected optimization components involved in the computation across multiple time steps. Finally, we present extensive experimental results on the impact of such misleading attacks, showing a significant benefit for the attacker and loss for the defender.

Data-Driven Multimodal Patrol Planning for Anti-poaching

Wildlife poaching is threatening key species that play important roles in the ecosystem. With historical ranger patrol records, it is possible to provide data-driven predictions of poaching threats and plan patrols to combat poaching. However, the patrollers often patrol in a multimodal way, which combines driving and walking. It is a tedious task for the domain experts to manually plan such a patrol and as a result, the planned patrol routes are often far from optimal. In this paper, we propose a data-driven approach for multimodal patrol planning. We first use machine learning models to predict the poaching threats and then use a novel mixed-integer linear programming-based algorithm to plan the patrol route. In a field test focusing on the machine learning prediction result at Jilin Huangnihe National Nature Reserve (HNHR) in December 2019, the rangers found 42 snares, which is significantly higher than the historical record. Our offline experiments show that the resulting multimodal patrol routes can improve the efficiency of patrol and thus they can serve as the basis for future deployment in the field.

Mobile sensors' patrol path planning in unobservable border region

PurposeThe border control becomes challenging when a protected region is large and there is a limited number of border patrols. This research paper proposes a novel heuristic-based patrol path planning scheme in order to efficiently patrol with resource scarcity.Design/methodology/approachThe trespasser influencing score, which is determined from the environmental characteristics and trespassing statistic of the region, is used as a heuristic for measuring a chance of approaching a trespasser. The patrol plan is occasionally updated with a new trespassing statistic during a border operation. The performance of the proposed patrol path planning scheme was evaluated and compared with other patrol path planning schemes by the empirical experiment under different scenarios.FindingsThe result from the experiment indicates that the proposed patrol planning outperforms other patrol path planning schemes in terms of the trespasser detection rate, when more environment-aware trespassers are in the region.Research limitations/implicationsThe experiment was conducted through simulated agents in simulated environment, which were assumed to mimic real behavior and environment.Originality/valueThis research paper contributes a heuristic-based patrol path planning scheme that applies the environmental characteristics and dynamic statistic of the region, as well as a border surveillance problem model that would be useful for mobile sensor planning in a border surveillance application.

Optimal scheduling for police patrol duties

ABSTRACTIn recent years, governmental agencies have issued various types of information about criminal activity. The police department can strengthen crime prevention in high-crime areas by mapping hotspots. However, a shortage of manpower can make it difficult to set up adequate patrol schedules. To overcome this lack of systematic planning, this study utilizes a mathematical programming method to construct both individual and integrated planning models designed to satisfy practical patrol requirements in individual areas and to consider the integration of patrol areas through coordination between police stations, with the objective of minimizing total officer patrol time. To evaluate the performance of both models, a case study is examined and sensitivity analysis is performed based upon real data obtained from a local police department. The results show that the integrated planning model significantly outperforms the individual planning model. These models and results can be useful references for police patrol planning.

Repeated Stackelberg security games: Learning with incomplete state information

Existing applications of Stackelberg Security Games (SSGs) have make use of Reinforcement Learning (RL) approaches to learn and adapt defenders-attackers behavior. The learning process for defenders-attackers is represented by randomized strategies for the defenders applied against adversarial strategies of the attackers, which acquire feedback on their strategies observing the target that was defended-attacked. However, must of the existing SSGs RL models feature strong assumptions including that the defenders and attackers have perfect information about the behavioral model, producing inconsistencies.We address these problems proposing a practical framework for representing real-world security problems by empowering SSGs with a RL approach considering incomplete state information. The players’ behavior and rationality are restricted to a class of partially observed Markov games (POMG). We develop an algorithm that consider randomized strategies for both defenders and attackers and obtain feedback on their partially observed states. We propose adaptive rules for computing the estimated transition matrices and utilities considering the number of unobserved experiences in the game. Furthermore, we study the problems of convergence of the estimated transition matrices and utilities in SSGs. For the realization of the SSG, we propose a new partially observed random walk technique for the randomization in the scheduling of the patrol planning. Results are applied to security games between defenders and attackers, where the noncooperative behaviors are well characterized by the features of the learning process in Stackelberg games.

HAMPP: A Handheld Assistant for Military and Police Patrols for HA/DR Missions

Military and police patrols are an important component of Humanitarian Assistance and Disaster Relief missions. These patrols need to access timely, relevant information about events and conditions along their patrol route, both historical, and ongoing. In the current practice, this information is gathered manually prior to the commencement of the patrol through the use of historical databases, current event repositories, and by conducting a review of records that may be relevant to the area to be patrolled. Being manual, this process is fraught with several problems including high-cost, slow-speed and low-reliability.We are developing HAMPP (Handheld Assistant for Military and Police Patrols) to enhance the effectiveness and security of the patrol units and reduce the cost and time required for patrol planning. HAMPP is designed to assist with gathering detailed information about relevant events along the patrol route and alert the patrol unit when they are in the vicinity of these areas during the patrol. In addition, it performs several other activities which relate to the security of the patrol unit. The goal of this paper is to present our system architecture for a device-independent mobile software system that enables planning of the patrol route and linking of related information to that route, and as the patrol starts, tracking the unit's current location and providing real-time information and alerts about areas of interest along the route of a patrol. Any deviations from the planned route are flagged and alerts sent to the command post.

A Deployed Quantal Response-Based Patrol Planning System for the U.S. Coast Guard

In this paper, we describe the model, theory developed, and deployment of PROTECT, a game-theoretic system that the United States Coast Guard USCG uses to schedule patrols in the Port of Boston. Th...

A Deployed Quantal Response-Based Patrol Planning System for the U.S. Coast Guard

In this paper, we describe the model, theory developed, and deployment of PROTECT, a game-theoretic system that the United States Coast Guard (USCG) uses to schedule patrols in the Port of Boston. The USCG evaluated PROTECT’s deployment in the Port of Boston as a success and is currently evaluating the system in the Port of New York, with the potential for nationwide deployment. PROTECT is premised on an attacker-defender Stackelberg game model; however, its development and implementation required both theoretical contributions and detailed evaluations. We describe the work required in the deployment, which we group into five key innovations. First, we propose a compact representation of the defender’s strategy space by exploiting equivalence and dominance, to make PROTECT efficient enough to solve real-world sized problems. Second, this system does not assume that adversaries are perfectly rational, a typical assumption in previous game-theoretic models for security. Instead, PROTECT relies on a quantal response (QR) model of the adversary’s behavior. We believe this is the first real-world deployment of a QR model. Third, we develop specialized solution algorithms that can solve this problem for real-world instances and give theoretical guarantees. Fourth, our experimental results illustrate that PROTECT’s QR model handles real-world uncertainties more robustly than a perfect-rationality model. Finally, we present (1) a comparison of human-generated and PROTECT security schedules, and (2) results of an evaluation of PROTECT from an analysis by human mock attackers.

Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service

The increasing threat of terrorism makes security at major locations of economic or political importance a major concern. Limited security resources prevent complete security coverage, allowing adversaries to observe and exploit patterns in patrolling or monitoring, and enabling them to plan attacks that avoid existing patrols. The use of randomized security policies that are more difficult for adversaries to predict and exploit can counter their surveillance capabilities. We describe two applications, ARMOR and IRIS, that assist security forces in randomizing their operations. These applications are based on fast algorithms for solving large instances of Bayesian Stackelberg games. Police at the Los Angeles International Airport deploy ARMOR to randomize the placement of checkpoints on roads entering the airport and the routes of canine unit patrols within the airport terminals. The Federal Air Marshal Service has deployed IRIS in a pilot program to randomize the schedules of air marshals on international flights. This paper examines the design choices, information, and evaluation criteria that were critical to developing these applications.

Predictive mapping of season distributions of large mammals using GIS: an application to elephants on Mount Kenya

Summary 1. Knowledge of elephants in forested environments where visibility is poor is often restricted to elephant density estimates derived from counts of elephant dung piles along line transects. Elephant dung piles are a good indicator of elephant habitat use over a period of time (i.e. a season) because they remain visible for several months. Using Mount Kenya (MK) in Kenya as a case study, we demonstrate how those dung pile counts can additionally be used to develop elephant dung pile explanatory models and distribution maps. 2. The dung pile explanatory models are built from a selected number of line‐transect samples per season using generalized linear model analysis, in which the counted dung of each sample is explained by the combined effects of a series of environmental and anthropomorphic parameters. For the significant explanatory parameters in the models, digital map layers are developed and integrated into a geographic information system. Applying the explanatory models, predictive seasonal elephant dung pile distribution maps are developed. 3. Data preparation and analysis are intensive, but the distribution maps derived from explanatory parameters of distribution are a powerful tool for patrol planning and land‐use management and to locate areas of high elephant density and the habitats they move between. This method is useful for sites where physical, environmental, logistical or other constraints render it impossible to spread line transects evenly over the entire study area, assuming that transects are representative samples of the entire habitat.

Patrol planning in the Rotterdam Police Department

A detailed analysis leading to the development of a specialized police department planning section has resulted in an improved patrol operation for Rotterdam, based on Larson's travel time model combined with a three-priority queuing model, and the prospect of improved police dispatching and patrol allocation for other cities in the Netherlands.