A Hypercube Queuing Model Approach to the Police Units Allocation Problem

Nilson Felipe Matos Mendes, André Gustavo dos Santos

Abstract

Providing security requires efficient police services. Considering this, we deal in this paper with the police units allocation problem. To describe the problem a probabilistic model based on Hypercube Queuing Model is proposed. Considering an action radius and constraints for minimal coverage and mandatory closeness, the model aims to allocate police units on several points of an urban area to minimize the expected distance traveled by these units when they are answering calls for service. A VND heuristic is used to solve the model, and we analyse the improvement of using a Tabu Serach method instead of a random initialization. We experiment the methods in scenarios with different parameters values to verify the robustness and suitability of the proposed model. The results presented a high influence of service time on solutions quality, some difficulties in getting feasible solutions.

References

  1. Araz, C., Selim, H., and Ozkarahan, I. (2007). A fuzzy multi-objective covering-based vehicle location model for emergency services. Computers & Operations Research, 34(3):705 - 726. Logistics of Health Care Management Part Special Issue: Logistics of Health Care Management.
  2. Chaiken, J. M. and Dormont, P. (1976). A patrol car allocation model. Technical report, DTIC Document.
  3. Chawathe, S. S. (2007). Organizing hot-spot police patrol routes. In Intelligence and Security Informatics, 2007 IEEE, pages 79-86. IEEE.
  4. Chen, X. (2013). Police patrol optimization with security level functions. Systems, Man, and Cybernetics: Systems, IEEE Transactions on, 43(5):1042-1051.
  5. Chiyoshi, F., Iannoni, A. P., and Morabito, R. (2011). A tutorial on hypercube queueing models and some practical applications in emergency service systems. Pesquisa Operacional, 31(2):271-299.
  6. Church, R. and ReVelle, C. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32(1):101-118.
  7. Cihan, A., Zhang, Y., and Hoover, L. (2012). Police response time to in-progress burglary a multilevel analysis. Police Quarterly, 15(3):308-327.
  8. Coupe, R. T. and Blake, L. (2005). The effects of patrol workloads and response strength on arrests at burglary emergencies. Journal of Criminal Justice, 33(3):239- 255.
  9. Curtin, K. M., Hayslett-McCall, K., and Qiu, F. (2010). Determining optimal police patrol areas with maximal covering and backup covering location models. Networks and Spatial Economics, 10(1):125-145.
  10. D'Amico, S. J., Wang, S.-J., Batta, R., and Rump, C. M. (2002a). A simulated annealing approach to police district design. Computers & Operations Research, 29(6):667-684.
  11. D'Amico, S. J., Wang, S.-J., Batta, R., and Rump, C. M. (2002b). A simulated annealing approach to police district design. Computers & Operations Research, 29(6):667 - 684. Location Analysis.
  12. Dell'Olmo, P., Ricciardi, N., and Sgalambro, A. (2014). A multiperiod maximal covering location model for the optimal location of intersection safety cameras on an urban traffic network. Procedia - Social and Behavioral Sciences, 108(0):106 - 117. Operational Research for Development, Sustainability and Local Economies.
  13. Fórum Nacional de Seguranc¸a P ública (2013). 8o anuário de seguranc¸a p ública. Technical report.
  14. Glover, F. and Kochenberger, G. A. (2003). Handbook of metaheuristics. Springer Science & Business Media.
  15. Green, L. V. and Kolesar, P. J. (2004). Anniversary article: Improving emergency responsiveness with management science. Management Science, 50(8):1001- 1014.
  16. Jarvis, J. P. (1985). Approximating the equilibrium behavior of multi-server loss systems. Management Science, 31(2):235-239.
  17. Keskin, B. B., Li, S. R., Steil, D., and Spiller, S. (2012). Analysis of an integrated maximum covering and patrol routing problem. Transportation Research Part E: Logistics and Transportation Review, 48(1):215 - 232. Select Papers from the 19th International Symposium on Transportation and Traffic Theory.
  18. Larson, R. C. (1974). A hypercube queuing model for facility location and redistricting in urban emergency services. Computers & Operations Research, 1(1):67- 95.
  19. Larson, R. C. (1975). Approximating the performance of urban emergency service systems. Operations Research, 23(5):845-868.
  20. Larson, R. C. and Rich, T. F. (1987). Travel-time analysis of new york city police patrol cars. Interfaces, 17(2):15- 20.
  21. Li, L., Jiang, Z., Duan, N., Dong, W., Hu, K., and Sun, W. (2011). Police patrol service optimization based on the spatial pattern of hotspots. In Service Operations, Logistics, and Informatics (SOLI), 2011 IEEE International Conference on, pages 45-50.
  22. Lin, K. Y., Atkinson, M. P., Chung, T. H., and Glazebrook, K. D. (2013). A graph patrol problem with random attack times. Operations Research, 61(3):694-710.
  23. Maltz, M. D. (1996). From poisson to the present: Applying operations research to problems of crime and justice. Journal of Quantitative Criminology, 12(1):3-61.
  24. Mendes, N. F. M. and dos Santos, A. G. (2015). A tabu search based heuristic for police units positioning. In 2015 Latin American Computing Conference, CLEI 2015, Arequipa, Peru, October 19-23, 2015, pages 1- 11.
  25. Mendes, N. F. M., Santos, A. G., and Gonc¸alves, L. B. (2014). Métodos para o problema de posicionamento de unidades policiais. In Anais do XVLI Simpósio Brasileiro de Pesquisa Operacional, XLVI SBPO, pages 639-650.
  26. Mladenovic, N. and Hansen, P. (1997). Variable neighborhood search. Computers & Operations Research, 24(11):1097-1100.
  27. Perrucci, A. (2011). Algoritmi esatti per la ricerca di strategie ottime nel problema di pattugliamento con singolo pattugliatore.
  28. Rajagopalan, H. K. and Saydam, C. (2009). A minimum expected response model: Formulation, heuristic solution, and application. Socio-Economic Planning Sciences, 43(4):253-262.
  29. Ruan, S., Meirina, C., Yu, F., Pattipati, K. R., and Popp, R. L. (2005). Patrolling in a stochastic environment. Technical report, DTIC Document.
  30. Saladin, B. A. (1982). Goal programming applied to police patrol allocation. Journal of Operations Management, 2(4):239 - 249.
  31. Simpson, N. and Hancock, P. (2009). Fifty years of operational research and emergency response. Journal of the Operational Research Society, pages S126-S139.
  32. Smith, R. D. (1961). Computer applications in police manpower distribution. Field Service Division, International Association of Chiefs of Police.
  33. Talbi, E.-G. (2009). Metaheuristics: from design to implementation, volume 74. John Wiley & Sons.
  34. Telep, C. W. and Weisburd, D. (2012). What is known about the effectiveness of police practices in reducing crime and disorder? Police Quarterly, page 1098611112447611.
  35. Vasconcelos, D. d. (2008). Gapatrol - uma abordagem evolutiva para otimizac¸a˜o de rotas de patrulha policial via calibrac¸a˜o de simulac¸a˜o multiagens.
  36. Waiselfisz, J. J. (2013). Mapa da vio leˆncia 2013. homicídio e juventude no brasil. Technical report, Centro Brasileiro de Estudos Latino Americanos.
  37. Weisburd, D. and Eck, J. E. (2004). What can police do to reduce crime, disorder, and fear? The Annals of the American Academy of Political and Social Science, 593(1):42-65.
  38. Zhang, Y. and Brown, D. (2013). Police patrol districting method and simulation evaluation using agent-based model & gis. Security Informatics, 2:1-13.
  39. Zhang, Y. and Brown, D. (2014a). Simulation optimization of police patrol district design using an adjusted simulated annealing approach. In Proceedings of the Symposium on Theory of Modeling & Simulation - DEVS Integrative, DEVS 7814, pages 18:1-18:8, San Diego, CA, USA. Society for Computer Simulation International.
  40. Zhang, Y. and Brown, D. (2014b). Simulation optimization of police patrol districting plans using response surfaces. Simulation, 90(6):687-705.
  41. Zhang, Y., Huddleston, S. H., Brown, D. E., and Learmonth, G. P. (2013). A comparison of evaluation methods for police patrol district designs. In Proceedings of the 2013 Winter Simulation Conference: Simulation: Making Decisions in a Complex World, pages 2532- 2543. IEEE Press.
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Paper Citation


in Harvard Style

Mendes N. and dos Santos A. (2016). A Hypercube Queuing Model Approach to the Police Units Allocation Problem . In Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS, ISBN 978-989-758-187-8, pages 70-81. DOI: 10.5220/0005837800700081


in Bibtex Style

@conference{iceis16,
author={Nilson Felipe Matos Mendes and André Gustavo dos Santos},
title={A Hypercube Queuing Model Approach to the Police Units Allocation Problem},
booktitle={Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS,},
year={2016},
pages={70-81},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005837800700081},
isbn={978-989-758-187-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 18th International Conference on Enterprise Information Systems - Volume 2: ICEIS,
TI - A Hypercube Queuing Model Approach to the Police Units Allocation Problem
SN - 978-989-758-187-8
AU - Mendes N.
AU - dos Santos A.
PY - 2016
SP - 70
EP - 81
DO - 10.5220/0005837800700081