# System Criticality of Road Network Areas for Emergency Management Services—Spatial Assessment Using a Tessellation Approach

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Short State of the Art

## 3. Spatial Assessment and Tessellation Method

#### 3.1. Tessellation and Route Calculation

^{2}was chosen since it seems to keep a reasonable balance between calculation time and the grade of detail necessary for an adequate criticality assessment. This was evaluated by conducting test runs on a smaller scale with different tile sizes, and then comparing the results and calculation times. However, it would be far more useful to be able to define the optimal size of the tiles by some sort of metric depending on the characteristics of the study region, like the density of the road network and the size of the area. Overall, it can be said that smaller tiles lead to a large increase in the calculation time since more routes and iterations have to be calculated, while bigger ones provide less detailed results.

_{n}). The UOT is always specific to a condition, like the blockage of a single tile or no blockages at all.

#### 3.2. Route Weighting

_{B}= Specific criticality value of tile B.; R

_{(a,B)}= Calculated travel time for the routes to centroid a under the condition that tile B is blocked; W

_{a}= Weighting Factor for the destination of the route a.

_{B}value being calculated without a response time for the blocked tile itself. Therefore, the value of C

_{B}could become smaller as the unblocked overall response time, if tile B is a tile with a high weight. To compensate for this error, the response time (likewise from two fire stations) to the blocked tile itself (without blockage) is added to C

_{B}.

_{B}. Therefore, the isolated tiles and the blocked tile itself do not influence the criticality value.

_{B}= Specific criticality value of tile B.; ${\mathrm{R}}_{\mathrm{a},\mathrm{B}}$ = Calculated travel time for the routes to centroid a under the condition that tile B is blocked; W

_{B}= Weighting Factor for the destination of route B; ${\mathrm{R}}_{\mathrm{b}}$ = Calculated travel time for the routes to centroid a without blockage; Tnr = Tiles not reachable n = all Tiles. ${\mathrm{R}}_{\mathrm{a},\mathrm{B}}$ = Calculated travel time for the routes to centroid a under the condition that no tile is blocked.

#### 3.3. Model Structure

**Ground Level**(light blue) represents the basic platform for further model construction. Here, the input parameters are added to the model and further parameters are calculated from the resulting data. In the

**Main Calculation Level**(light grey) [$\sum}_{\mathrm{a}}^{\mathrm{n}}({\mathrm{R}}_{\mathrm{a},\mathrm{B}}\text{}\ast \text{}{\mathrm{w}}_{\mathrm{a}})]$ most of the calculation effort takes place. At this level, the network dataset layer is built, and the fire brigade locations are set as facilities serving as origins for further network analysis. As incidents, the centroids of each tile are assigned. For the improvement of the processing capacity, the iteration of blockages is shifted to its sub level, the

**Iteration Sub Level**(dark grey). This prevents the network dataset layer from being rebuilt for each blockage iteration. The previous processes of the two levels are processed in combination with the Closest Facility Algorithm. During the blockage iteration, the weighting of the tiles takes place by assigning the number of deployments per year and tile. Thus, the number of routes that are followed between the fire brigade locations and the destination centroids is determined. In the

**Final Calculation Level**(light grey) [${\mathrm{R}}_{\mathrm{B}}\text{}\ast \text{}{\mathrm{w}}_{\mathrm{B}}+\text{}{\displaystyle \sum}_{\mathrm{x}\in \mathrm{Tnr}}^{\mathrm{n}}({\mathrm{R}}_{\mathrm{x},\mathrm{B}}\text{}\ast \text{}{\mathrm{w}}_{\mathrm{x}}$)] the travel times of the compensation calculation, i.e., without blockages, are calculated and the number of routes is calculated analogously to the number of deployments. For the result, the response times of routes that took place under the condition of the blockage of the same tile, as well as the missing response to that blocked tile compensation calculation, are summed up. Afterwards the number of tiles, that are completely cut off by each blockage is determined, and the unblocked drive time to these tiles is added to compensate for this problem. At last, the overall travel time without any blockades is subtracted from the calculated travel times with blocked tiles [$-\left({\displaystyle \sum}_{\mathrm{a}}^{\mathrm{n}}({\mathrm{R}}_{\mathrm{a}}\text{}\ast \text{}{\mathrm{w}}_{\mathrm{a}}\right)]$.

## 4. Road Network Criticality Assessment for Cologne, Germany; Data Used and Model Adaptation

^{2}[41,42], as well as a road network with a length of 2865 km [41]. The fire and ambulance services were responding to over 250,000 calls in 2018 [43]. For the usage of the model, some input data are required this includes a digital road network, the location of the facilities, driving speeds for the emergency vehicles on different road classes and the locations of the incidents (see Table 2).

^{2}tile indicates a major scenario and also the emergency vehicles underlay the special rights of way privileges. Step-by-step explanations on how to do routing calculation and how to work with network dataset in ArcGIS can be found on the homepage of ArcMap or under the link https://desktop.arcgis.com/en/arcmap/latest/extensions/network-analyst/a-quick-tour-of-network-analyst.htm.

## 5. Result for the Case Study of Cologne

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

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**Figure 1.**Route without blockage: Response time 8.6 min (

**a**) and Route blocked with lower impact: Response time 9.3 min (

**b**) (Legend: green = route; grey = road network, red = blocked tile).

**Figure 2.**Route blocked with higher impact: Response time 11.8 min (Legend: green = route; grey = road network, red = blocked tile).

**Figure 3.**(

**a**): Closest Facility calculation with one facility per tile. (

**b**): Same setting with two facilities per tile. (Legend: Red = Facilities; Grey = Road network; Colour = Calculated routes).

**Figure 4.**On the

**left**: Number of deployed rescue vehicles; On the

**right**: Presentation of deployment data.

**Figure 6.**Result of the road network criticality assessment of Cologne (Legend: Green to red = Rising criticality value; violet = fire stations; white to black dots = Rising number of generated “non-reachable” tiles (1–17); black = road network).

**Figure 8.**(

**a**): A nearly empty tile gets a rather high criticality value, because it cuts an important segment. (

**b**): A tile is considered unreachable, because the segment closest to the centre of the tile belongs to an isolated subnet.

**Table 1.**Impact of the number of tiles and facilities on the number of iterations and route calculations.

Number of Tiles | Number of Iterations | Number of Route Calculations in Each Iteration with One Starting Facility | Total Number of Route Calculations Because of Model Iterations with One Starting Facility | Total Number of Route Calculations in Each Iteration with Two Starting Facilities | Total Number of Route Calculations Because of Model Iterations with Two Starting Facility |
---|---|---|---|---|---|

5 | 5 | 5 | 25 | 10 | 50 |

10 | 10 | 10 | 100 | 20 | 200 |

20 | 20 | 20 | 400 | 40 | 800 |

Data | Data Type | Data Source | Application Field |
---|---|---|---|

Road network | Polyline Shapefile | OpenStreetMap | Network dataset for Closest Facility routing calculation |

Fire and Rescue Stations location | Polypoint Shapefile | Fire Department Cologne | Network dataset for Closest Facility routing calculation |

Emergency vehicles driving speed | Table | Fire Department Cologne | Calculation of driving time for the road network/network dataset |

Annual incident locations | Polypoint Shapefile | Fire Department Cologne | Weighting of driving time |

Driving Speeds for the Fire Department of Cologne | Occurrence in Network | |
---|---|---|

5 km/h | Path, pedestrian, track_grade3 | >1% |

34.7 km/h | Residential, living street, service, unclassified, | 72% |

40.5 km/h | Track_grade1, track_grade2, track | 6% |

45.9 km/h | Secondary, tertiary | 16% |

50.4 km/h | primary | >1% |

62.9 km/h | trunk | 1% |

85.5 km/h | motorway | 3% |

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**MDPI and ACS Style**

Rohr, A.; Priesmeier, P.; Tzavella, K.; Fekete, A.
System Criticality of Road Network Areas for Emergency Management Services—Spatial Assessment Using a Tessellation Approach. *Infrastructures* **2020**, *5*, 99.
https://doi.org/10.3390/infrastructures5110099

**AMA Style**

Rohr A, Priesmeier P, Tzavella K, Fekete A.
System Criticality of Road Network Areas for Emergency Management Services—Spatial Assessment Using a Tessellation Approach. *Infrastructures*. 2020; 5(11):99.
https://doi.org/10.3390/infrastructures5110099

**Chicago/Turabian Style**

Rohr, Adrian, Peter Priesmeier, Katerina Tzavella, and Alexander Fekete.
2020. "System Criticality of Road Network Areas for Emergency Management Services—Spatial Assessment Using a Tessellation Approach" *Infrastructures* 5, no. 11: 99.
https://doi.org/10.3390/infrastructures5110099