How do cops patrol

Due to the randomness of the districting algorithm, some combinations of parameter settings cannot generate compact districting plans. Furthermore, we cannot use simulation to evaluate too many districting plans due to the evaluation complexity of the problem, especially at the beginning phase of the experiment. More plans can be evaluated if more computational resources can be used.

Based on result from statistical analysis, the center of the concentric circles, the radius of the outer circle are significant to average response time. For workload variation, the significant districting parameters are number of seeds on each circle, the center of the concentric circles and the number of iterations of balancing the CFS probabilities of districts.

For the intermediate measurements, the variation of CFS probabilities is more important for both response variables. Its linear relationship to both responses can be seen in Figure 5.

It can be seen that lower variation of cumulative CFS probabilities among districts leads to better performances for both responses. So, in the next iteration of ranking randomly generated plans, more weight can be given to standard deviation of CFS probabilities.

Then, the relationship between responses and each districting parameter was analyzed individually and they were adjusted in the steepest decent direction to responses and another batch of thousands of plans was generated. The weights for two intermediate measurements became [0. For each of the selected districting plans we ran the simulation for ticks simulation time units and 50 minutes of actual time.

Under parallel running in current computing resources 13 batches on 3 PCs , the actual evaluation time for a districting plan can be reduced to 5 minutes. This length of time ensured the convergence of the simulation to a steady state, which can be seen in Figure 6.

While we put more effort into analysis of the performance metrics, average response time and workload, we also wanted to visualize the simulation. This allowed us and our police colleagues to visually assess and validate the behavior of the simulation. We showed the simulation to members of the police and they confirmed its behavior was consistent with that of their patrols. A static view of the simulation is shown in Figure 7. The current districting plan was also evaluated by the simulation system.

The simulation results show both performance measurements can be improved. The average response time of current districting plan was The standard deviation of workload proportion among 8 districts was reduced from 0. Due to the NP-completeness of the graph-partition problem, there are too many possibilities of districting plans. We cannot use exact method to evaluate each of them. The evaluated districting plans in this case study are only a small proportion of the whole solution set and the solutions provided are preliminary.

The global optimality cannot be guaranteed. We only find some significant districting parameters and intermediate measurements that may lead to better plans. More rigorous experimental design and statistical analysis can be conducted to further study the relationship between these factors and responses.

With more powerful computational resources, more districting plans can be further generated and evaluated. It is possible to make improvements on both response variables. Because we have a multiple objective problem i. Further no single plan was best in both average response time and workload variation. To provide a multiple objective solution we used Pareto analysis. This analysis shows the positioning of each of the alternative districting plans with respect to each other on the two dimensional plot of both metrics.

Using this plot we can trace the Pareto frontier which is the set of non-dominated districting plans. These plans are not dominated because no other plan is better than them in at least one of the performance metrics. Figure 8 shows the Pareto frontier of average response time and workload standard deviation for the Charlottesville case study.

This figure shows that 2 out of districting plans are on the Pareto frontier. They are No. Under any weighting of response time and workload variation, one of the two districting plans dominates the others. So, they are the best 2 districting plans. The police department can choose one of them based on their needs and some practical considerations. The actual physical compositions of districting plan No. Clearly, the boundaries based on the grid network violate these boundaries.

However, some existing geographical units such as police beats and census block groups consider these boundaries.

So, replacing the grid boundaries needs to consulting with police departments. If patrol boundaries must be drawn based on police beats or census blocks, conversion can be made between grid network and these units.

Example can be seen in Figure If not necessary, the grid boundaries can be replaced by the nearest roads. In this way, the performance of the districting plan may be close the optimal solution based on grid network.

In this paper, we reviewed the characteristics of the police patrol district design problem from the perspective of past and current work. We also showed the complexity of the problem from both computational and evaluation perspectives.

First, an algorithm for automatically generating police patrol districting plans was developed by growing them incrementally using small atomic geographic units as the building blocks.

The second step is to screen these plans to obtain a smaller number of promising plans that can undergo more detailed and rigorous evaluation. Our last step is the perform evaluation using an agent-based simulation that provides high fidelity measures of performance. The case study presented in this paper shows the use of our police patrol districting approach for the Charlottesville Police Department.

Compared with the current patrol district boundaries, the solution generated from our patrol districting approach shows improvement on both average response time and variation of the workload through the detailed simulation study. While our simulation provides high fidelity it does not affectively capture changes over the course of an entire year. The changes include significant changes in weather and traffic patterns. To make our simulation in its current form work for an entire year would require run lengths of several months.

Hence we must develop improvements, either through sub-sampling, meta-modeling or other data reduction strategies. We also need to improve the screening method to ensure that we do not inadvertently remove an alternative that may prove superior in our more intensive simulation based evaluation. Rosenshine M: Contributions to a theory of patrol scheduling. Q — , 99— Article Google Scholar.

Interfaces , 4— Upper Saddle River: Prentice Hall; Google Scholar. Res , 29 6 — Soc , 60 51 — Cincinnati: Anderson; Mitchell PS: Optimal selection of police patrol beats. Law , 63 4 — Econ , — AAAly: Police briefing stations: a location problem. AIIE Trans. Altman M: The computational complexity of automated redistricting: Is automation the answer?

Rutgers Comput. Law J , 81— Algorithms , 3 2 — Data Min, Ninth IEEE. Int Conf , — Chapter Google Scholar. School of Geography, University of Leeds; Download references.

You can also search for this author in PubMed Google Scholar. Correspondence to Yue Zhang. YZ implemented the simulation system, developed the districting algorithm in this paper, tested them, and drafted the manuscript. DB provided theoretical guidance in the whole procedure and revised the manuscript.

Both authors read and approved the final manuscript. WMV 9 MB. Reprints and Permissions. Zhang, Y. Secur Inform 2, 7 Download citation.

Received : 18 October Accepted : 01 February Published : 02 March Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Skip to main content.

Search all SpringerOpen articles Search. Download PDF. Abstract Abstract Police patrols play an important role in public safety. Introduction Police patrols play an important role in public service by responding to incidents, deterring and preventing crimes. Police patrol district design As noted previously the design of police patrol districts can significantly impact the effectiveness of police operations. Performance measurements and related problems There are two common performance measures used for police district design: the average response time and the variation of workload [ 4 ].

Operations research and GIS methods According to [ 9 ], the first OR application was to use p-Median clustering as in [ 8 ] to minimize the total weighted travel distance to service the expected calls. Problem complexity Computational complexity A convenient formulation for the police district design problem is as the aggregation of smaller geographic units into larger units that form the districts. Approach to police patrol districting The approach we have developed for the police districting problem begins by generating alternative districting plans.

Generation of alternative districting plans The generation of districting plans is based on atomic geographical units. Figure 1. Seeds selection of police districting for Charlottesville. Full size image. Figure 2. Random growth vs. Compact growth. Case study and preliminary result To illustrate the use of our approach to police patrol districting we used data from the Charlottesville, VA, USA police department.

Figure 3. Locations of historical CFS incidents. Police Law Enforcement Police Patrol. Sites Covered. Shots Fired Assembly Video. Detrick: RML: 0. Contact Information. Police Patrol Page Content. The police are to ensure the mission of NIH is not impeded, and to guard against personal attacks, loss of assets, criminal activity, and acts of terrorism. The Division of Police consists of ninety-six officers, seventy-three of which are assigned as Patrol Officers.

This unit is made up of Supervisors, Managers, K-9 Officers and patrol officers. Patrol Officers provide safety to the stated NIH locations and communities continuously all day, every day. Patrol officers are responsible for the prevention of crime, enforcement of all laws, the arrest and prosecution of criminals and the protection of life and property. The patrol division is also responsible for traffic and crowd control at all the major parades and events in the Town.

In addition to daily patrol functions, the officers must also frequently attend court for misdemeanor and felony cases.

Town parks are heavily patrolled by the district officers to reduce the problems officers normally encounter each summer season. The goal is to reduce the problems of disorderly youths, criminal mischief, fights, drug activities and bike thefts to make our parks safe for family activities throughout the summer.