# A Citywide Location-Allocation Framework for Driver Feedback Signs: Optimizing Safety and Coverage of Vulnerable Road Users

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Discrete Facility Location Problem (DFLP)

#### 2.2. Solution Algorithm

## 3. Methodology

#### 3.1. Framework Overview

#### 3.2. Location Selection Criteria

#### 3.2.1. Traffic Safety

#### 3.2.2. Vulnerable Road Users and Facilities

#### 3.3. Traffic Volume Estimation via Kriging

#### 3.4. Problem Formulation

**Subject to:**

#### 3.5. Optimization via Greedy Algorithm

## 4. Case Study

#### 4.1. Study Area

#### 4.2. Results and Discussions

#### 4.2.1. Interpolation of Missing ADT Values

#### 4.2.2. Mapping of Location Selection Criteria

#### 4.2.3. Citywide DFS Implementation Selection Criteria

#### All-New Scenario

#### Expansion Scenario

## 5. Conclusions, Limitations and Future Research

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- World Health Organization. Global Status Report on Road Safety 2013: Supporting a Decade of Action: Summary; World Health Organizatio: Geneva, Switzerland, 2013. [Google Scholar]
- European Conference of Ministers of Transport; OECD/ECMT Transport Research Centre, Speed Management; OECD Publishing: Pairs, France, 2006.
- Transport Canada. Road Safety in Canada. 2011. Available online: https://www.tc.gc.ca (accessed on 20 November 2019).
- McCoy, P.T.; Bonneson, J.A.; Kollbaum, J.A. Speed reduction effects of speed monitoring displays with radar in work zones on interstate highways. Transp. Res. Rec.
**1995**, 1509, 65–72. [Google Scholar] - Garber, N.J.; Patel, S.T. Effectiveness of Changeable Message Signs in Controlling Vehicle Speeds in Work Zones; Virginia Transportation Research Council: Charlottesville, VA, USA, 1994. [Google Scholar]
- Fontaine, M.D.; Carlson, P.J. Evaluation of speed displays and rumble strips at rural-maintenance work zones. Transp. Res. Rec.
**2001**, 1745, 27–38. [Google Scholar] [CrossRef] [Green Version] - Lee, C.; Lee, S.; Choi, B.; Oh, Y. Effectiveness of speed-monitoring displays in speed reduction in school zones. Transp. Res. Rec.
**2006**, 1973, 27–35. [Google Scholar] [CrossRef] - Rose, E.R.; Ullman, G.L. Evaluation of Dynamic Speed Display Signs (DSDS); Texas Transportation Institute: San Antonio, TX, USA, 2003.
- Wu, M.; El-Basyouny, K.; Kwon, T.J. Before-and-after empirical Bayes evaluation of citywide installation of driver feedback signs. Transp. Res. Rec.
**2020**, 2674, 419–427. [Google Scholar] [CrossRef] - Wu, M.; El-Basyouny, K.; Kwon, T.J. Lessons learned from the large-scale Application of Driver Feedback Signs in an urban city. J. Transp. Saf. Secur.
**2020**, 1–19. [Google Scholar] [CrossRef] - Ullman, G.L.; Rose, E.R. Evaluation of Dynamic Speed Display Signs. Transp. Res. Rec.
**2005**, 1918, 92–97. [Google Scholar] [CrossRef] - Santiago-Chaparro, K.R.; Chitturi, M.; Bill, A.; Noyce, D.A. Spatial Effectiveness of Speed Feedback Signs. Transp. Res. Rec.
**2012**, 2281, 8–15. [Google Scholar] [CrossRef] - Williamson, M.R.; Fries, R.N.; Zhou, H. Long-Term Effectiveness of Radar Speed Display. J. Transp. Technol.
**2016**, 6, 99–105. [Google Scholar] - Effectiveness of Changeable Message Signs in Controlling Vehicle Speeds in Work Zones: Phase II. 1998. Available online: https://trid.trb.org/view/473832 (accessed on 20 November 2019).
- Mattox, J.H.; Sarasua, W.A.; Ogle, J.H.; Eckenrode, R.T.; Dunning, A. Development and Evaluation of Speed-Activated Sign to Reduce Speeds in Work Zones. Transp. Res. Rec.
**2007**, 2015, 3–11. [Google Scholar] [CrossRef] [Green Version] - Kwon, T.J. Development and Evaluation of Models and Algorithms for Locating RWIS Stations. Ph.D. Thesis, University of Waterloo, Waterloo, ON, Canada, 2015. [Google Scholar]
- Hakimi, S.L. Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph. Oper. Res.
**1964**, 12, 450–459. [Google Scholar] [CrossRef] - Hakimi, S.L. Optimum distribution of switching centers in a communication network and some related graph theoretic problems. Oper. Res.
**1965**, 13, 462–475. [Google Scholar] [CrossRef] - ReVelle, C.; Eiselt, H.; Daskin, M. A bibliography for some fundamental problem categories in discrete location science. Eur. J. Oper. Res.
**2008**, 184, 817–848. [Google Scholar] [CrossRef] - Owen, S.H.; Daskin, M.S. Strategic facility location: A review. Eur. J. Oper. Res.
**1998**, 111, 423–447. [Google Scholar] [CrossRef] - Daskin, M.S. Network and Discrete Location: Models, Algorithms, and Applications; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- ReVelle, C.; Toregas, C.; Falkson, L. Applications of the Location Set-covering Problem. Geogr. Anal.
**1976**, 8, 65–76. [Google Scholar] [CrossRef] - Lim, S.; Kuby, M. Heuristic algorithms for siting alternative-fuel stations using the Flow-Refueling Location Model. Eur. J. Oper. Res.
**2010**, 204, 51–61. [Google Scholar] [CrossRef] - Jin, P.J.; Walker, A.; Cebelak, M.; Walton, C.M. Determining Strategic Locations for Environmental Sensor Stations with Weather-Related Crash Data. Transp. Res. Rec.
**2014**, 2440, 34–42. [Google Scholar] [CrossRef] - Church, R.; ReVelle, C. The maximal covering location problem. Pap. Reg. Sci. Assoc.
**1974**, 32, 101–118. [Google Scholar] [CrossRef] - Suzuki, A.; Drezner, Z. The p-center location problem in an area. Locat. Sci.
**1996**, 4, 69–82. [Google Scholar] [CrossRef] - Balinski, M.L. Integer Programming Methods, Uses, Computation. Manag. Sci.
**1965**, 12, 253–313. [Google Scholar] [CrossRef] - Kuby, M.J. Programming Models for Facility Dispersion: The p-Dispersion and Maxisum Dispersion Problems. Geogr. Anal.
**1987**, 19, 315–329. [Google Scholar] [CrossRef] - Dell’Olmo, P.; Ricciardi, N.; Sgalambro, A. A multiperiod maximal covering location model for the optimal location of intersection safety cameras on an urban traffic network. Procedia-Soc. Behav. Sci.
**2014**, 108, 106–117. [Google Scholar] [CrossRef] [Green Version] - Garey, M.R.; Johnson, D.S. Computers and Intractability: A Guide to the Theory of NP-Completeness. In Bulletin (New Series) of the American Mathematical Society; American Mathematical Society: Providence, RI, USA, 1980. [Google Scholar]
- Mahdian, M.; Markakis, E.; Saberi, A.; Vazirani, V. A Greedy Facility Location Algorithm Analyzed Using Dual Fitting. In Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques; Springer: Berlin/Heidelberg, Germany, 2001. [Google Scholar]
- Cormen, T.H.; Leiserson, C.E.; Rivest, R.L.; Stein, C. Introduction to Algorithms; MIT Press: Cambridge, MA, USA, 2001. [Google Scholar]
- Van Laarhoven, P.J.; Aarts, E.H. Simulated annealing. In Simulated Annealing: Theory and Applications; Springer: New York, NY, USA, 1987. [Google Scholar]
- Goldberg, D.E. Computer-Aided Gas Pipeline Operation Using Genetic Algorithms and Rule Learning. Ph.D. Thesis, University of Michigan, Ann Arbor, MI, USA, 1984. [Google Scholar]
- Eberhart, R.C.; Kennedy, J. Particle swarm optimization. In Proceedings of the ICNN’95-International Conference on Neural Networks, Perth, WA, Australia, 27 November–1 December1995; Volume 4, pp. 1942–1948. [Google Scholar]
- Davidović, T.; Ramljak, D.; Šelmić, M.; Teodorović, D. Bee colony optimization for the p-center problem. Comput. Oper. Res.
**2011**, 38, 1367–1376. [Google Scholar] [CrossRef] - Geem, Z.W.; Kim, J.H.; Loganathan, G. A New Heuristic Optimization Algorithm: Harmony Search. Simulation
**2001**, 76, 60–68. [Google Scholar] [CrossRef] - Kim, A.M.; Wang, X.; El-Basyouny, K.; Fu, Q. Operating a mobile photo radar enforcement program: A framework for site selection, resource allocation, scheduling, and evaluation. Case Stud. Transp. Policy
**2016**, 4, 218–229. [Google Scholar] [CrossRef] - Li, M.; Faghri, A.; Fan, R. Determining Ideal Locations for Radar Speed Signs for Maximum Effectiveness: A Review of the Literature; Delaware Center for Transportation: Newark, NJ, USA, 2017. [Google Scholar]
- Constant, A.; Lagarde, E. Protecting Vulnerable Road Users from Injury. PLoS Med.
**2010**, 7, e1000228. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Kim, A.; El-Basyouny, K. Scheduling resources in a mobile photo enforcement program. In Proceedings of the 2017 4th International Conference on Transportation Information and Safety (ICTIS), Banff, AB, Canada, 8–10 August 2017. [Google Scholar]
- Li, Y.; Xie, J.; Kim, A.M.; El-Basyouny, K. Investigating trade-offs between optimal mobile photo enforcement programme plans. J. Multi-Criteria Decis. Anal.
**2019**, 26, 51–61. [Google Scholar] [CrossRef] [Green Version] - Li, R.; El-Basyoung, K.; Kim, A. Before-and-after empirical Bayes evaluation of automated mobile speed enforcement on urban arterial roads. Transp. Res. Rec. J. Transp. Res. Board
**2015**, 2516, 44–52. [Google Scholar] [CrossRef] - Rodegerdts, L.A.; Nevers, B.L.; Robinson, B.; Ringert, J.; Koonce, P.; Bansen, J.; Nguyen, T.; McGill, J.; Stewart, D.; Suggett, J.; et al. Signalized Intersections: Informational Guide; US Department of Transportation: Washington, DC, USA, 2004.
- ESRI ArcGIS. Release 10; Environmental Systems Research Institute: Redlands, CA, USA, 2011.
- Selby, B.; Kockelman, K.M. Spatial Prediction of AADT in Unmeasured Locations by Universal Kriging. 2011. Available online: https://trid.trb.org/view/1092064 (accessed on 20 November 2019).
- Cressie, N. The origins of kriging. Math. Geol.
**1990**, 22, 239–252. [Google Scholar] [CrossRef] - Lichtenstern, A. Kriging Methods in Sptial Statistics. Bachelor’s Thesis, Technical University of Munich, München, Germany, 2013. [Google Scholar]
- Kwon, T.J.; Fu, L. Spatiotemporal variability of road weather conditions and optimal RWIS density—An empirical investigation. Can. J. Civ. Eng.
**2017**, 44, 691–699. [Google Scholar] [CrossRef] [Green Version] - Olea, R.A. A six-step practical approach to semivariogram modelling. Stoch. Environ. Res. Risk Assess.
**2006**, 20, 307–318. [Google Scholar] [CrossRef] - Bird, R.; De Moor, O. From dynamic programming to greedy algorithms. In Formal Program Development; Springer: Berlin/Heidelberg, Germany, 1993. [Google Scholar]
- De Leur, P. Collision Cost Study Update FINAL Report. 2018. Available online: https://drivetolive.ca/wp-content/uploads/2020/07/CollisionCostStudyUpdate_FinalReport.pdf (accessed on 11 December 2020).
- Gouda, M.; El-Basyouny, K. Investigating Distance Halo Effects of Mobile Photo Enforcement on Urban Roads. Transp. Res. Board
**2017**, 2660, 30–38. [Google Scholar] [CrossRef] - City of Edmonton. City Design and Construction Standards. 2019. Available online: https://www.edmonton.ca/ (accessed on 20 November 2019).

**Figure 5.**Historical collisions from 2009 to 2018 in the city of Edmonton [9].

**Table 1.**Overall before-and-after evaluation results from previous works [9].

Collision Severity | Collision Reduction (%) | Standard Error | Statistical Test Ratio | Lower Bound | Upper Bound |
---|---|---|---|---|---|

Property-Damage-Only (PDO) | 34.30 | 4.00 | 8.58 ** | 23.98 | 44.61 |

Severe | 36.74 | 9.70 | 3.79 ** | 11.71 | 61.77 |

Criterion | PDO | Severe | ||
---|---|---|---|---|

Cost | Weight | Cost | Weight | |

Direct Costs | USD 14,065 | 1 | USD 50,025 | 3.56 |

Criterion | Considering Cvg Only (w = 0) | Equally Considering Both (w = 0.5) | Considering Δ_{EPDO} Only (w = 1) |
---|---|---|---|

Collision Reduction (Δ_{EPDO}) | −38.1 | 37.7 | 149.4 |

Coverage of Vulnerable Road Users/Facilities (Cvg) | 69.27 | 64.88 | −32.2 |

Criterion | Considering Cvg Only (w = 0) | Equally Considering Both (w = 0.5) | Considering Δ_{EPDO} Only (w = 1) | |||
---|---|---|---|---|---|---|

Adding 10 | Adding 20 | Adding 10 | Adding 20 | Adding 10 | Adding 20 | |

Collision Reduction (${\Delta}_{EPDO}$) | 4.8 | 7.32 | 13.01 | 18.63 | 30.22 | 51.61 |

Coverage of Vulnerable Road Users/Facilities ($Cvg$) | 14.63 | 29.27 | 13.17 | 27.32 | 3.41 | 8.29 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, M.; Kwon, T.J.; El-Basyouny, K.
A Citywide Location-Allocation Framework for Driver Feedback Signs: Optimizing Safety and Coverage of Vulnerable Road Users. *Sustainability* **2020**, *12*, 10415.
https://doi.org/10.3390/su122410415

**AMA Style**

Wu M, Kwon TJ, El-Basyouny K.
A Citywide Location-Allocation Framework for Driver Feedback Signs: Optimizing Safety and Coverage of Vulnerable Road Users. *Sustainability*. 2020; 12(24):10415.
https://doi.org/10.3390/su122410415

**Chicago/Turabian Style**

Wu, Mingjian, Tae J. Kwon, and Karim El-Basyouny.
2020. "A Citywide Location-Allocation Framework for Driver Feedback Signs: Optimizing Safety and Coverage of Vulnerable Road Users" *Sustainability* 12, no. 24: 10415.
https://doi.org/10.3390/su122410415