Total Trip Length on Fuel Consumption
It is strongly required to enhance energy conservation to reduce fossil-fuel consumption to cope with global warming. In Japan, energy consumption in the industrial sector is almost stable after the oil crises. However, the commercial, residential and transportation sectors have a trend of increasing energy consumption. Especially reducing energy consumption in transportation sector is an important issue because it depends mainly on the use of fossil fuel.
There are many measures to reduce fuel for transportation, for example, shifting to public transportation from private cars or increasing the number of passengers per trip of each vehicle. In this study, the authors focus on the land use of urban areas. It is also effective to construct land use to reduce trip length or fuel consumption in urban areas. Some studies are carried out from the viewpoint of decreasing traffic congestion around the center of a city. Suzuki reported the effect of rearranging inhabitants over a residential district around Tokyo with respect to reducing trip time. However, the land use of the business and residential districts is fixed in this study and no optimality of land use is discussed.
The objective of this study is to achieve optimal land use in urban areas to attain minimal trip length or fuel consumption. The authors have developed two models to investigate urban land use. One minimizes the total trip length under a condition of constant congestion rate (called the minimal-trip-length model), the other minimizes the fuel consumption directly where congestion generates endogenously in the model (called the minimal-fuel model). Optimal solutions derived from numerical simulations are compared with the actual land use in the Central Business District (CBD) of Tokyo.
The following are assumed in this study.
1. The city has a shape of circle;
2. The land use is for residential and business activities as well as radial and circular roads;
3. only automobile transportation is considered;
4. commuting and business trips occur;
5. all inhabitants commute to and from business areas;
6. radial and circular roads can exist at any place;
7. trips take the shortest path; and
8. a stable state is considered.
The minimal-trip-length model neglects the time domain while the minimal-fuel model takes commuting and business trip hours into account.
(1) Minimal-trip-length model: Actual cities generally suffer traffic congestion and the construction of more roads is usually advocated to mitigate it. Since no congestion is ideal, this model describes a constant congestion city, which implies stable and smooth transportation ensues. This condition gives a proportional relationship between total fuel consumption and total trip length because the fuel consumption-rate is constant as the traffic condition is always the same at any place in the city. Therefore, the optimum land use of minimal fuel consumption can be achieved by minimization of the total trip length.
(2) Minimal-fuel model: There is trade-off relationship between trip length and fuel consumption. Trip length can decrease when business and residential areas concentrate around the center of a city, while fuel consumption may increase because traffic congestion occurs heavily around the center. This model allows traffic congestion in contrast with the minimal-trip-length model if the total fuel consumption is reduced. In other words, this model takes energy consumption as the priority, not the ideal traffic condition.
(1) Use of circular roads: It is assumed that trips occur between any places. Path connecting two points consist of the combination of radial and circular roads. The condition where circular road is used is represented by Eq. 1 from the viewpoint of the shortest path.
(1)?<2,
where ? denotes the angle between origin and destination. If the angle of two points is within 2 radian, the path does not pass through the center of the city and gets the destination point via circular road. The model assumes to have a rotary area which only road occupies at the center because it is impossible for trips to pass just on the center.
Inward direction:
Case 1 Origin O1 in the area A to the inner area of C.
Case 2 Origin O1 in the area A to the outer area of B.
Outward direction:
Case 2 (the same as above).
Case 3 Origin O2 in the area C to the outer area of A or B.
(3) Trips in circular direction: As far as circular road concerns, trips passing along the circle of radius r occur in the case where origin or destination is/are located on the circle, which Fig. 2 shows.
(4) Principle of trips: It is assumed that inhabitants at the origin (X1) who travel to the business area (X2) are proportional to the working population at the destination with respect to both cases of business trips and commuting trips. Eq. 2 represents this principle.
where X1 and X2 denote origin and destination, respectively. It is also assumed here that each person gets on one vehicle. The number of trips multiplied by generating rate give the load of traffic.
(1) Trips in radial directions: Business trips in radial directions are formulated as Eq. 3 and Eq. 4 below and based on the trip patterns shown in Fig. 1. Inward and outward direction have the same number of trips.
The first term means the trips which occur between the points on the circle of radius r and the points in outer area, and the second between the points both of which are on the circle. Here, trips passing across the angle of ? in an anti-clockwise direction occur under the following condition.
(1) Trips in radial directions: Commuting trips connecting residential and business areas can be formulated in the same way as for business trips, which Eq. 7 and Eq. 8 represent. It should be noted that the amounts of inward and outward trips are different in this case in contrast with the case of the business trips.
The left-hand side means road area supplied at radius r, while the right-hand side represents road area which is needed to deal with the traffic at that point. Eq. 10 shows that the constant-congestion condition implies that at any point in the city the road supply and demand are equal.
(1) Objective function: The main consideration of this model is the total trip length even though not all of the inhabitants commute by automobile. The length of the business trips, L1, is expressed by Eq. 11, and that of commuting trips, L2, can be given by an analogous procedure.
Tags: trip length
