# Graph-Based Spatial Data Processing and Analysis for More Efficient Road Lighting Design

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Motivation

- road maps, which provide vital information about road connections, their categories and traffic parameters, but lack the actual shape of roads, pavements, etc.,
- geodetic/CAD maps, which contain very precise data regarding the shapes of objects (e.g., road kerbs), but do not usually add semantic meaning to them (e.g., there is no “street” object, only the area between the kerbs),
- utility infrastructure data, which includes information about power lines (which can be used to estimate the location of lamp poles) as well as gas or water lines (which are useful when placing newly-installed lamps),
- sensor data archives, which may provide vital information about traffic intensity—a crucial parameter for lighting class selection—but do not actually link it to streets; also, vehicle flow simulation may be required to estimate such data for places with no sensors,
- infrastructure inventory data, which provides information about lamp types and pole/arm geometries and may include geographic locations of lamps, but often only contains aggregate data about lamps illuminating a given street.

## 3. State of the Art

#### 3.1. The Process of Lighting Design

- analysing the project area street by streets,
- defining the lighting segments’ characteristics, including:
- lighting requirements, e.g., the lighting class,
- geometric/geographic parameters, e.g., road width, lamp spacing, etc.

- determining the desired lamp configuration,
- performing the photometric calculations,
- altering the configuration if the requirements are not met.

#### 3.2. Related Research

## 4. Methods

#### 4.1. The Semantic Environment Graph

**Definition**

**1.**

- ${V}_{\Omega}$ is the set of nodes,
- ${E}_{\Omega}$ is the set of edges,
- $la{b}_{\Omega}^{V}:{V}_{\Omega}\to {\Sigma}_{\Omega}$ is the node labelling function,
- $la{b}_{\Omega}^{E}:{E}_{\Omega}\to {\Gamma}_{\Omega}$ is the edge labelling function,
- ${\Sigma}_{\Omega}=\{T,S,F,C,O\}$ is the set of node labels, where:
- -
- T represents streets,
- -
- S represents road lighting segments located on streets,
- -
- F represents freeform lighting segments, which are not located on streets (e.g., to represent a parking lot),
- -
- P represents pedestrian crossings, located on road segments,
- -
- O represents other objects, such as buildings, points of interest, etc.

- ${\Gamma}_{\Omega}=\{on\left(x\right),on(x,y),distance\left(x\right)\}$ is the set of edge labels, where:
- -
- $on$ denotes that a point object (e.g., pedestrian crossing) is located at a given line object (e.g., road segment),
- -
- $part\_of$ denotes that a line object is part of another line object,
- -
- $spatial\_rel$ denotes that there is a spatial relationship between two objects,
- -
- $eq$ denotes that an object is equivalent to another object.

- $at{t}_{\Omega}^{V}:{V}_{\Omega}\times {\Sigma}_{\Omega}\to {2}^{{A}_{\Omega}^{V}}$ is a node attributing function, such that for $x\in {V}_{\Omega},l\in {\Sigma}_{\Omega},a\in {A}_{\Omega}^{V}$$at{t}_{\Omega}^{V}(x,l)\left(a\right)$ is a value of the attribute a,
- $at{t}_{\Omega}^{E}:{E}_{\Omega}\times {\Gamma}_{\Omega}\to {2}^{{A}_{\Omega}^{E}}$ is an edge attributing function, such that for $x\in {E}_{\Omega},l\phantom{\rule{3.33333pt}{0ex}}\in {\Gamma}_{\Omega},a\in {A}_{\Omega}^{E}$$at{t}_{\Omega}^{E}(x,l)\left(a\right)$ is a value of the attribute a,
- ${A}_{\Omega}^{V}$ is the set of node attributes, where:
- -
- $type$ denotes the type of an object (e.g., the type of building for O nodes),
- -
- $geometry$ denotes the shape of an object and its geographic location; this can be expressed e.g., as a Well-Known Text (WKT) string,
- -
- $name$ is the name of an object, e.g., the street name or segment label,
- -
- $lighting\_class$ is the lighting class assigned to a road or freeform segment,

- ${A}_{\Omega}^{E}$ is the set of edge attributes, where:
- -
- $position$ denotes the metre within a line object on which a given point is located,
- -
- $from$ and $to$ mark the metres within a line object where another line object begins and ends,
- -
- $distance$ denotes the distance (in metres) between two objects,
- -
- $intersects$ (yes, no) indicates that two objects spatially intersect.

#### 4.2. The Dual Nature of Geographic Data

#### 4.3. Graph Generation Using a Formal Grammar

**Definition**

**2.**

- ${\Sigma}_{\Omega}$ is the set of node labels,
- ${\Delta}_{\Omega}\subset {\Sigma}_{\Omega}$, is the set of terminal node labels,
- ${\Gamma}_{\Omega}$ is the set of edge labels,
- ${\Phi}_{\Omega}$ is the set of transformation rules,
- ${S}_{\Omega}$ is the starting graph,
- ${\Pi}_{\Omega}$ is the validation graph grammar condition, that verifies the current state of the graph.

- the $lhs$ graph is removed from G creating ${G}^{\prime}$;
- the $lhs$ graph is added to ${G}^{\prime}$ (but at this moment these graphs are separated);
- all edges in G that contain one of the nodes belonging to ${V}_{lhs}\cap {V}_{rhs}$ and the second to ${V}_{G}\backslash {V}_{l}hs$ are restored in ${G}^{\prime}\cup rhs$;
- all edges in G that contains removed nodes (${V}_{lhs}\backslash {V}_{rhs}$) are removed.

#### 4.4. A Practical Example

- ${S}_{1}$, occupying the initial 100 m of the street length, with lighting class M4,
- ${S}_{2}$, occupying the following 200 metres, with lighting class M3,
- ${S}_{3}$, occupying the final 200 m, with lighting class M4.

- x and y denote the location of a lighting segment within the street,
- z denotes the location of a crossing within a segment,
- w denotes the desired width of the lighting segment to be created in the location of the pedestrian crossing.

- segments ${S}^{\prime}$ and ${S}^{\u2034}$ shall inherit class from segment S in $lhs$,
- segment ${S}^{\u2033}$ will be assigned class C comparable to an M class two levels higher than that of S.

- segments ${S}_{21}$ and ${S}_{23}$ will inherit class M3 from segment ${S}_{2}$,
- segment ${S}_{22}$ will be assigned class C1.

## 5. Proposed Solution

#### 5.1. Inclusion of Selection Criteria as Defined by Standards

#### 5.1.1. Design Speed or Speed Limit

#### 5.1.2. Traffic Volume

#### 5.1.3. Traffic Composition

#### 5.1.4. Junction Density

#### 5.1.5. Ambient Luminosity

#### 5.1.6. Navigational Task

#### 5.1.7. Separation of Carriageway

#### 5.1.8. Parked Vehicles

#### 5.2. Automatic Processing of Geographic Data

#### 5.3. Interaction with Users

## 6. Results

#### 6.1. Comparison of Different Approaches to Design in a Case Study in KrakóW

- A professional lighting designer analysed the area of the project, extracted the different lighting situations, and assigned them to streets in the area. Then, a photometric design was prepared using typical design software.
- A human designer used a dedicated web application to define lighting segments for an automatic photometric design tool, PhoCa [24]. Since the calculations were then carried out without user interaction, the increasing number of segments no longer posed the risk of making the calculations infeasible. However, manual definition of the lit areas was still prone to inconsistencies and human error.

- more precise distribution of lighting segments may, in many cases, improve the energy efficiency of the installation, as the less precise approaches usually assume a worst-case scenario (e.g., a higher lighting class is used for an entire road even if only one part of it actually requires that),
- the lighting parameters better reflect the reality, providing more light where needed (e.g., for pedestrian crossings), and reducing the intensity where it is not required (which may effect in reduced light pollution).

#### 6.2. Results for Various European Cities

## 7. Future Work

- coverage—data for some areas may be lacking, and therefore may require appropriate estimation (interpolation, prediction) algorithms be used; this process requires a formal model to allow that, but does not require actual definition of new concepts,
- conceptual—where new concepts (and their relation to other elements) may become required to make design decisions; an example here could be the age structure of pedestrians crossing the street at a given location—given lack of such data, one may estimate it by analysing the types of surrounding buildings.

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Flowchart presenting the stages and components of a lighting design or modernisation process; steps marked with yellow colour are supported by the proposed system. (

**a**) Traditional lighting design process, with rough (simplified) data used for photometric calculations, (

**b**) Precise process, using exact data for the calculations.

**Table 1.**Coverage of OpenStreetMap speed limit data for roads in the Małopolskie Voivodeship, as of August 2018.

Type Label | Total Number | Coverage | Average Value [km/h] |
---|---|---|---|

Motorway | 495 | 100% | 135.27 |

Trunk road | 144 | 85% | 115.53 |

Primary road | 4479 | 84% | 64.77 |

Secondary road | 4123 | 60% | 57.53 |

Tertiary road | 10,238 | 40% | 52.42 |

Residential street | 40,773 | 11% | 38.51 |

Service road | 52,080 | 2% | 30.81 |

Unclassified | 6982 | 7% | 49.04 |

Approach | No. of Segments |
---|---|

Human designer, traditional tool | 99 |

Human designer, PhoCa automated tool | 637 |

Proposed approach, automatic map processing | 2268 |

Country | City | No. of Streets | No. of Street Fragments | No. of Segments Cut by Intersection | No. of Segments Cut by Intersection and Crossings | Area [km${}^{2}$] [34] | Population [34] |
---|---|---|---|---|---|---|---|

Switzerland | Zurich | 1888 | 6491 | 8223 | 20,791 | 87.88 | 407,447 |

Italy | Florence | 2317 | 6134 | 8262 | 18,946 | 102 | 382,258 |

Poland | Kraków | 4336 | 10,672 | 12,985 | 23,632 | 327 | 761,900 |

Poland | Warsaw | 8933 | 21,448 | 26,608 | 54,195 | 517.24 | 1,753,977 |

Hungary | Budapest | 9015 | 24,711 | 34,326 | 45,117 | 525.14 | 1,744,665 |

Spain | Madrid | 11,913 | 28,222 | 39,360 | 105,561 | 604.46 | 3,182,981 |

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**MDPI and ACS Style**

Ernst, S.; Łabuz, M.; Środa, K.; Kotulski, L. Graph-Based Spatial Data Processing and Analysis for More Efficient Road Lighting Design. *Sustainability* **2018**, *10*, 3850.
https://doi.org/10.3390/su10113850

**AMA Style**

Ernst S, Łabuz M, Środa K, Kotulski L. Graph-Based Spatial Data Processing and Analysis for More Efficient Road Lighting Design. *Sustainability*. 2018; 10(11):3850.
https://doi.org/10.3390/su10113850

**Chicago/Turabian Style**

Ernst, Sebastian, Marek Łabuz, Kamila Środa, and Leszek Kotulski. 2018. "Graph-Based Spatial Data Processing and Analysis for More Efficient Road Lighting Design" *Sustainability* 10, no. 11: 3850.
https://doi.org/10.3390/su10113850