Behavioral dynamics of pedestrian’s movements: Theoretical aspects of commercial arterial road frontage activities

The common scientific approaches to the reasoning of problems are mathematical reasoning or statistical reasoning. Mathematical or formal reasoning is usually deductive, therein one reason from general assumptions to specifics using symbolic logic and axioms for multi criteria decision-making. Mathematical probability, which is the basis of all statistical theories, had its beginning in the past. The aim of this paper is to explore a number of the mathematical and statistical aspects of the disposition and behavior of road frontage activities, which are of importance in pedestrian behavior as considered. It's shown that number of crossings from right to left is proportional to the pedestrian on the right (PXRL ∝ NR) and therefore, the number of crossings left to right is proportional to the pedestrians on the left (PXLR ∝ NL). Frequency distributions of the pedestrians generated for a given shopping string arterial were of 4 kinds, one related to pedestrians passing through not crossing the road, not going into and out of outlets. The second kind related to pedestrians crossing the road for the aim of going into and out of outlets, etc. the third kind related to pedestrian going into shops and eventually, the fourth kind related to others, e.g. Pedestrians generated from parking vehicles, buses, etc. A formula is given for the frequency with crossing from left to right and right to leave based on the land-use activities on the left and right. In considering the capacity of road systems it should be remembered that increases in traffic flow generally produce corresponding decreases in speed. However, it's an assumption that a rise in population generated along the footpath can cause the crossing the road, and usually produce corresponding decreases in vehicle speed. The paper concludes with a constatation of the pedestrian movements at a continuing rate that expressed in mathematical form.