Modeling Residential and Workplace Location Assessment on Car Commuting Energy

Modeling residential and workplace location assessment on car commuting energy

S.MyojinO),H.AbeO) ^Faculty of Environmental Science and Technology, Okayama

University, 700-8530, Okayama, Japan Email: [email protected]

Abstract

A model for assessing resident and workplace location on energy for car commute to work is dealt with in the paper. The paper consists of two parts : model building and assessing simplified location patterns. The model is composed of five submodels : location patterns, commute trip distribution, spatial distribution of commute trip density, road traffic speed and energy calculation. Three simplified location patterns are set to resident and workplace respectively, so nine sets of locations are put under assessment The study area is assumed to be circular. The location sets together with commute length distribution form respective spatial distribution of car commute trip density in the area The density is converted to traffic speed Car commuting energy is calculated by applying traffic speed-energy function to the speed distribution. Population is included in some of the submodels so that the model may be applicable over the wide range of population size. The model proved effective for the assessment on the whole on examination of the calculated average traffic speed against the observed in several Japanese cities of different population. The spatial distributions of car commute trip density are grouped into any one of bell, plate and plateau types. Plate typs is dented at and near the center and the plateau is intermediate between bell and plate. Those are, by converting to the density on traffic lane, lumped into those which are more or less depressed at and near the center. This means some increase in traffic speed there. Per capita energy use for car commuting is minimized by such a set of locations in which both resident and workplace densities are lowered toward the margin. The second minimum is achieved by two sets adjoining to the above. Relatively to the results comment is given on residential decentralization in progress in most Japanese cities.

438 Urban Transport and the Environment for the 21st Century

I Introduction

Per capita energy use is still increasing in Japan It showed a 12% increase between 1989 and 1994. Per capita transportation energy use showed the largest increasing rate of 19% over the rates 6% and 18% in industry and people's livelihood, respectively. Public transport service is poorer in smaller cities in Japan This is the cause and effect of intensive motorization in these forty years. Anyway, car is the most inefficient in energy use for passenger transportation

The authors [1] reported recently the possibility of reduction in transportation energy use for commuting by a simple model. It simulated modal shift of commuters from car to railway byresidentia l decentralization along railway though it is opposite to the way shown by, for example, Markovits [2] or Morimoto et al [3].

The present paper is an attempt to generalize the above simulation Instead of residential decentralization, nine sets of typically simplified locations of resident and workplace density are supposed in a circular city having arbitrary population and diameter.

Just car commute trip from home to work is put under assessment The following section outlines the model composed of five submodels. The third section provides several illustrations of the results obtained by calculation of a sample city and subsequently examination with some discussion

2 Model

2.1 Definition

An outline of the model is given in Figure 1. The present study focuses on resident- workplace location assessment on energy for car commuting. Assessment is made in terms of per capita energy use for car commuting. Some details are described following after the flow diagram shown in Figure 1.

Resident-workplace location Commute trip distribution

Spatial distribution of commute trip density

Transport network density ( road, railway) Trafic speed-flow function

Road traffic speed

Speed-fuel function

Energy

Figure 1. Flow diagram for model description

Urban Transport and the Environment for the 21st Century 439

2.2 Resident-Workplace Location

Following functions are assumed for locations of resident and workplace density : (D a linear function decreasing with the distance from the city center and vanishing at the marginal end,

® a linear function starting from zero at the city center and coming to the maximum at the marginal end and (3) flat density, in which the city under study is supposed to be circular and the density to be homogeneous on concentric circle. Resident and workplace locations are given,respectively ,b y p = p(r) = a+br, q = q(r) = c + dr (1) where /?, q = resident,workplac e density, r -the distance from city center and a,b,c and d = constants. By assumption of homogeneity in density on concentric circle, a and b must keep P = ^ 2nrp(r)dr where P and R are population and radius of the study city,respectively .S o we have

• «*'«

where dp is average population density given by PJTiR* and those on the right hand side come from (D,(2) and (3) above, respectively. Similarly,

(3)

where d^ is average workplace density given by IV/nR^ in which W is the whole number of workplaces. Eqns (2) and (3) are used later for illustration of resident and workplace location

2.3 Commute Trip Distribution

The probability p(P\P^} of a commute trip going from origin P\ to destination P^ is assumed as X^^) = ^M(fi)v(f2)/(/) (4) where «(f}) = normalized potential function for commute trip generating that is described by some parameters at P\ , v(/^) = normalized potential function for commute trip attracting that is described by some parameters at /^ , /(/) = commute trip length distribution in which / = trip length defined by /} and P^ and K - constant Integration of the probability p(P^P^ by P^ over the study city must be equal to

\ ) ,fro m which K = l/A(P^ ) . So we have (5) where A(P^) = ^ v(P^} f (l^dP^ (integration of v(P^ )/(/) over the whole possible

440 Urban Transport and the Environment for the 21st Century

points P^ keeping P] fixed, where P^P-i and / are illustrated in Figure 2 with other notations to appear).

2.4 Spatial Distribution of Commute Trip Distribution

The probability (density) of a commute trip passing a point in the study city, multiplied by the whole commute tips to be generated there, gives commute trip density at the point

Though background trip density composed of those with the other purposes must coexist at the point in the real circumstances, commute trip density alone is focused on here in the section.

Assuming that the normalized potential functions u(P\) and v(f^) are proportional to the resident and workplace densities at Pj and P^ , respectively, eqn (5) is changed for

(6) where p(P^) = resident density at Pj , g(f^) = workplace density at P, ,

p 22 arid # = proportional constant introduced on the assumption

. From the definitions of % and /?, it is easy to show a = l/P where P is defined previonsly It is evident that, from the assumption of density homogeniety on concentric circle, we have following expressions : Xfi) = Xn), 0^0,^2*, 9(P2) = 9(,2), 0^0^2^ (7) where (% , ^- ) = polar coordinates of P^ i = 1,2 (Figure 2). The objective probability at PO , for example, standing on the straight line from P, to P^ is expressed by illustrative descriptions ® and ® as follows :

Figure 2. Commute trip from P\ to A through an intermediate point PQ

Urban Transport and the Environment for the 21st Century 441

CD Integrate ^(Pj/^) given by eqn (6) by Pj along the line from PQ to g, after integrating p by P^ along the line from PQ to g% , where Q\ and g% are

intersections of the extended straight line P^ and the marginal end of the study tity, respectively, and

(2) I)o the <%nnj3fdk3SKnHaridk^Fabonl^b%Twigthe line P^ in 360-degrees round

It is also evident that the objective probability obtained is homogeneous on concentric circle, that is, the probability is expressed as p(r) where r is the radial coordinates of an arbitrary point Corresponding commute trip density is given by

d^Xr) (8) where T<. = the whole commute trips to work under consideration.

2.5 Road Traffic Speed

This means traffic speed distribution along lane through the hours under study (rush hours in the morning, because just commute to work is regarded). This needs two matters to get (Figure 1) : transport network and traffic speed-flow function The transport network conditions act on mode choice in commuting and spatial distribution of traffic lane density, which are used for transforming spatial distribution of commute trip density eqn (8), multiplied by the choice ratio of car, to car trip density on traffic lane. Traffic speed-flow function is essential to estimate the traffic speed on lane, supplemented with the background car trip density. The background density is estimated by multiplying car commute density by a factor that is mentioned later. The procedure for road traffic speed is as follows : Assuming linear function of trip density on lane, the speed is expressed by

v=g+/z(^i+^) (9) where d\ - the density of car commute trip, d^ - the density of background car trip and g and /?= constants. Using eqn (8)

^1=^X4^ )/",(/" :f) (10) where ^(f)= choice ratio of car; /?,(/- ;?)= spatial distribution of traffic lane density defined by the total lane length in an infinitely small area and P = population Both r^ and rii include population as parameter This means an implicit introduction of the acts of transport network conditions on commuters' behaviors and road conditions on supposing the general correspondence of population with the conditions. Indeed, those proved to be expressed each by a simple function of population And the background car trip density is dz=fd, (11) where K = the ratio of the backgrounds car trips to the commute car trips and is found on the data

2.6 Energy

442 Urban Transport and the Environment for the 21st Century

Energy use for car commute to work is expressed by

E = J JQ * c/i (r)e(r)rd0dr - J 2;z7Y/} (r)e(r)dr (12) where e(r) = energy rate (kcal / car trip-km) converted from fuel-speed function = e{v(r P)} whoie v(r ; P) is expressed by eqn (9). The fuel-speed function is given by a function identified for Japanese cars.

3 Calculation

3.1 Preparation

3.1.1 Commute IHp Length Distribution: /(/) The following function is introduced ~ -o i /(/) = / /=f (13) where a,fi and 7 are constants. The distribution function, having its peak at

/ = lp = a/ fi, was adopted once for commute length by the authors [1]. In the present paper; no statistically significant difference of the peak position was found between Japanese cities of different populations : 300, 600 and 1,200 X 10*. The estimated parameters are a =0.805, /?= 0.420 and y = 0.238. Figure 3 illustrates the estimated distribution of lp = 1.92 kilometers with three others of lp = 1.0, 2.0 and 4.0 kilometers.

3.1.2 Whole commute trips: T<. This is defined by the average number of daily commutes to work Its percentage to city population proved to be nearly constant ranging from 35.8 to 38.1 % despite of population

So this is assumed as TC = 0.37P. (14)

3.1 J Choice ratio of car: r^(P) In stead of the direct expression of the act of transport network conditions on commuters'

5 10 15 /(km) 20 Figure 3. Commute length distribution

443 Urban Transport and the Environment for the 21st Century behaviors, population is introduced into the choice ratio function. On the data from person

trip survey, the ratio is found as follows : =59.5-9.87x10--3 xf (%),(? : (15)

3.1.4 Spatial distribution of traffic lane density: n^(r \P) This proved to be expressed by a negative exponential function of the type

w, =772"^ (16) where 77 and £ are constants that may depend on population. Through testing, 77

proved to be dependent on population but C, independent of population Then those are identified to 77 = 0.176P and ^=0.355 (Figure 4)

3.1.5 Other factors for road traffic speed: g,h and K These are estimated on the data from traffic census and person trip survey in Japanese

cities : g = 28.5, h = -1.20 and K = 1.37. No statistical significance was found of correlation of K with population. In the following, a sample city is furnished for calculation. The city population is

supposed to be 600,00 that is similar to that of Okayama city where the authors live and work.

3.2 Results

3.2.1 Several aspects of the effects of resident-workplace location

3.2.1.1 Spatial distribution of car commute trip density Figure 5 illustrates car

commute trip density distribution on relativediamete r of the sample city that is supposed to have the area of 300 square kilometers. The peak position /^ is assumed to be 2.0

kilometers, that are near that of Okayama city, and the corresponding traffic lane density function is applied together with the other factors. Refer the numbers attached to distribution curves to the number matrix given by Table 1, where all the possible sets of

(lane-km/knf) 10

population=600,000

4 6 8 10 /"(km) 12

Figure 4. Traffic lane distribution

444 Urban Transport and the Environment for the 21st Century

resident and workplace locations are indicated by number. Figure 5 is separated into two, (1) and (2), only for avoiding complicated illustration Three types of car commute trip density distributions appear: bell, plate (depressed at and near the center) and plateau.

3.2.1.2 Car commute trip density on lane The density on lane is obtained by dividing the car commute trip density above by corresponding traffic lane density given by eqn(16). The density obtained is illustrated in Figure 6 corresponding to Figure 5, respectively. Due to the characteristic of the traffic lane density lowering exponentially, the spatial distribution of the density is lowered near the center but higer near the margin.

3.2.1.3 Traffic speed Figure 7 shows the average traffic speed calculated and observed in the sanple city and the equivalent city of Okayama, respectively, together with those in three other cities having different population for ascertainment The following factors are applied for calculation : the location 1 (Table 1), the choice ratio of car and trafficlane density distribution each corresponding to the city population and the peak position/^ = 2.0 kilometers. Spatial distribution of calculated traffic speed is mentioned later.

3.2.2 Energy use

In Figure 8, per capita energy use for the sample city is shown against every resident- workplace location together with the case of lp =4.0 kilometers for comparison, keeping the other factors each at the same as used so tar.

3.3 Examination and discussion

Three types of spatial distributions of car commute trip density are found for nine sets of typically simplified locations of resident and workplace densities : bell, plate that is depressed at and near the center and plateau that is, so called, intermediate between bell and plate. In the present paper, these are illustrated alone for the sample city having 600,000 population, but these are true to appear as well for the cities of different population despite of the peak position of commute trip length distribution, provided the choice ratio of car is a simple decreasing function of population as it was in the present paper.

Car commute trip density on lane is depressed near the center and raised near the marginal end This is attributed to the characteristics of traffic lane density distribution as well as to the distribution of car commute trip density depending on resident-workplace location A question is raised against the traffic lane density distribution. The traffic lane density distribution applied here is sure to have, more or less, effect to the resident- workplace locations like 1, 2, 4 or 5 because these are, to a certain extent, like existing conditions of the location in Japanese cities, but may not be relevant to, so to say, the imaginary conditions like 3 or 9. Similar question comes to the commute trip length distribution applied here, which is found to stand in existing conditions of the location but may not in the imaginary ones. Different distribution might be appropriate for the location Iike3or9. Per capita energy use is minimized by the resident-workplace location 1 and secondly

Urban Transport and the Environment for the 21st Century 445

tnp density (tnps/km")

6000

0.5 0 0.5 rlR (2) Figure 5. Distribution of car commute tnp to work vs. resident-workplace

locations (refer the number to Table 1)

Table 1. Number matrix for resident-workplace locations

minimized by locations 2 and 4. Note that the locations 2 and 4 are adjacent to location 1.

On the whole, the larger peak position l^ brings the greater per capita energy use. The location 1 is one of the most practical locations in Japanese cities. Residential decentralization, however, has been in progress in most Japanese cities. The residential location in Japanese cities seems to go near such that as shown by 4. Little difference in average traffic speed between the calculated and the observed is one of the convincing

446 Urban Transport and the Environment for the 21st Century

density (trips/km/lane) 7000-

Figure 6. Car commute trip density on lane vs. resident-workplace locations (refer the number to Table 1)

speed(km/h) 30

H observed D model (population)

Tokushima Maebashi Okayama Fukuoka city (263) (286) (594) Figure 7. Average traffic speed

Urban Transport and the Environment for the 21st Century 447

index for (kcal/marrhour) comparison 3.5 2500 3 2000 = 2 km = 4 km 2.5

1500

1000

500 0.5

0 142573869

location number Figure 8. Per capita energy use for car commute

measures for the availability of the model on the whole. Some disparity, however, is found between the calculated and the observed spatial distributions of traffic speed But the model is satisfactorily effective for the authors' objective at present despite of those detailed matters to improve for higher realization.

4. Concluding remarks

On the whole, the course for minimizing per capita energy use for car commuting to work starts out of the north west comer for the south east on Table 1. Though the conclusions reached through model calculation are rather well knowfects ,th e present paper has a merit to give an energy-for-car-commuting assessment to simplified patterns of resident- workplace locations. For example, the locations 2 and 4 increase per capita energy for car commuting by about 10% or little more as compared with the location 1. The fact, however; is that the model keeps holding detailed matters to improve as mentioned above. Some of them are choice ratio of car and traffic speed-flow function. The former should be given an explicit description of railway network and the latter would be improved by introducing the effect of traffic signals.

References

1. Myojin, S., Hirofunri, A Urban transportation energy in Japan and residential location assessment on work trip energy, Selected Proceedings of the 8th World Conference on Transport Research fin printing). 2. Maikovits, J., Transportation implications of economic cluster development, Interim Technical Report, In- state Regional Transportation Commission, Newyork, 4245^4924,1971. 3. Morimoto, A, Omino, T, Sinagawa, J. & Morita, T, A comparison of urban structure and transportation energy in Tokyo metropolitan area, Proceeding of Inflastructure Planning 18(2), Japan Society of Civil Engineers, 131-134,1985.