The inner traffic analysis of urban skyscrapers

There are many skyscrapers in large cities such as Tokyo, Beijing, Shanghai etc., mainly with rectangular parallelepiped shapes and some with frustum shapes, which is caused by the soaring of the land price. In a very big building with many people, it is well known that the inner traffic can not be ignored and it is important to forecast the inner traffic so that a sufficiently large inner traffic space is designed to guarantee the people to move in the building smoothly. Here, the inner traffic generally means the vertical inner traffic. Basically, there are two kinds of the inner traffic inside a skyscraper. One is the so-called Outside–Inside inner traffic, which is the traffic by the people coming from outside to inside or by the people going from inside to outside. Another one is the so-called Inside–Inside inner traffic, which is the traffic by the people acting within a skyscraper. As an example of Outside–Inside inner traffic, Okudaira gave a formulation in 1976. By considering the rush hours when the elevators are mostly occupied by the working people, he derived the theoretical distribution of the inner traffic area and the dwelling area in a rectangular skyscraper. Also as an example of Inside–Inside inner traffic, Taguchi gave another formulation in 1994. By considering the communication among the people inside a skyscraper, he calculated the distribution of the inner traffic area and the dwelling area in a rectangular skyscraper by combining a theoretical method and Newton numerical method. The above two models are formulated based on one kind of the inner traffic and they are reasonable for some special cases. For instance, Okudaira model may be valid for an office building during the rush hours, and Taguchi model may be valid for a residential building in the holidays. However, we daily experience that several kinds of the inner traffic generally exist in a skyscraper, for example, with respect to Inside–Inside inner traffic, there exist not only the traffic due to the communication among the people inside a skyscraper, but also the traffic caused by the allocation of a public facility etc., showing the incorporation of these traffics is meaningful. On the other hand, the above two models are limited to a rectangular skyscraper. However, there appear and more frustum skyscrapers recently, meaning the generalization of the shape of a skyscraper is also important. Here in this paper, we give the formulation combining one Outside–Inside inner traffic and one Inside–Inside inner traffic in a frustum skyscraper. Concretely, we consider Okudaira model for Outside–Inside inner traffic, and we consider Taguchi model, the allocation problem proposed in this paper for Inside–Inside inner traffic respectively. Moreover, since most skyscrapers have the shape of rectangular type, not frustum one, also in this paper, we theoretically analyze the distribution of the inner traffic area and the dwelling area with respect to rectangular case. Finally, we apply all of them to some examples for various parameter values. The numerical analysis shows that the result obtained by Okudaira and Taguchi, which says that the remainder of building volume after taking the elevator passage is scarcely dependent on the height of the building and thus most of the investment on a high skyscraper may be wasted, is also meaningful in such an extension. Further, it shows that the dwelling area is much more affected by the bottom area and the location of a public facility as the occurring rate of Outside–Inside inner traffic decreases in a skyscraper.