# Statistical Analysis of the Crosswalk Lighting Design Correctness
## 1 Introduction  
Roadway lighting standards (CEN 13201:2015 in Europe [1; 2; 3], CJJ 45-2015 in China [4], AS/NZS 1158.1.1:2005 in Australia and New Zealand [5], ANSI/IES RP-8-18 in United States [6], ABNT NBR 5101 in Brazil [7], etc.) allow establishing a trade-off between road users comfort and safety, and outdoor lighting system maintenance costs. The latter is determined mainly by an installation's power. Except financial costs, light pollution (caused by over-lighting) has a negative impact on both the environment in terms of greenhouse gas emissions and on human health; thus, a sustainable lighting design is a necessity. Unfortunately, preparation of an optimized lighting project, even for a simple lighting situation, requires considering numerous combinations of input parameters, such as pole height, fixture model/inclination and so on in what leads to complex and multistage calculations. For that reason it is impossible to analyze them all.  
Human designers using their intuition and expertise can reduce this huge search space to a reasonably sized set of variants, which are then verified by some industry standard lighting design software such as DIALux or AGi32 [8; 9]. It is obvious that such a \"guessed\" design is not optimal, but the conservative assumptions regarding area size for instance (i.e., intentional oversize a lighting situation area), guarantee that the final lighting performance meets standard requirements. There are also some promising approaches relying on AI methods [10; 11; 12], but they are academic concepts rather than commercially deployed solutions.  
The increasing number of accidents occurring at pedestrian crossings resulted in regulations and rules regarding those critical zones. For example see [13] (in Poland) or [14; 15] (in Germany). Basically, a typical crosswalk lighting installation consists of two dedicated lamps with asymmetric optics (see Figure 1) and, additionally, the existing or planned road illumination alongside a street.  
Although the aforementioned standards are localized (Poland, Germany), their application reveals the critical problem of applying lighting design methodology used for regular roadways to specific lighting situations, in particular the crosswalks, which are not \"compatible\" with roads in terms of layout, calculation grids and so forth.  
Preliminary analysis of the problem shows that using human intuition and/or expertise may fail; even minor changes of lighting situation properties can cause a standard requirements violation. The example of such a situation is presented in Section 3.  
The key considerations are: (i) whether it is an accidental phenomenon or a common issue; (ii) if the latter, how common is it. To answer the above we proceed in three steps:  
* Generating a set of test layouts (see Section 4) being modifications of a reference lighting situation. In short, it is achieved by modifying reference parameter values by some percentage.
* Preparing the software checking conformity of particular layouts with the relevant lighting standard.
* Performing a final analysis of the generated data.