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Modeling Residential and Workplace Location Assessment on Car Commuting Energy

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Modeling Residential and Workplace Location Assessment on Car Commuting Energy Transactions on the Built Environment vol 41, © 1999 WIT Press, www.witpress.com, ISSN 1743-3509 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. Transactions on the Built Environment vol 41, © 1999 WIT Press, www.witpress.com, ISSN 1743-3509 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 by residential 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 Transactions on the Built Environment vol 41, © 1999 WIT Press, www.witpress.com, ISSN 1743-3509 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, by p = p(r) = a+br, q = q(r) = c + dr (1) where /?, q = resident, workplace 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. So 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 \ ) , from 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 Transactions on the Built Environment vol 41, © 1999 WIT Press, www.witpress.com, ISSN 1743-3509 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 Transactions on the Built Environment vol 41, © 1999 WIT Press, www.witpress.com, ISSN 1743-3509 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.
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