SOLUTIONS Micro-scale modelling: Method and initial results

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1 SOLUTIONS Micro-scale modelling: Method and initial results Geoffrey Caruso The Martin Centre, University of Cambridge Draft Working Paper November 30, 2005 Sustainability Of Land Use and Transport In Outer NeighbourhoodS 1 Introduction This research aims at developing, calibrating and validating a micro-scale simulation tool for testing the sustainability of different neighbourhood designs for new urban developments in outer suburbs. Outer suburbs are very important both demographically and spatially and, thus, are likely to impact greatly on the overall sustainability of an urban region. Households undertake increased commuting distances to benefit from more spacious housing and lower density environments. This behaviour represents the major trend in residential location choice and leads to further urban dispersion. The environmental and social costs of this dispersion are often emphasised in the urban sprawl literature, while compact city policies are also largely disputed (e.g. Breheny, 1995; Brueckner, 2000; Gordon and Richardson, 1989). The impact of local spatial configurations is much less analysed. The ability of various local designs in balancing the benefits and costs of dispersion might therefore be understated. It is assumed here that it is necessary, for proposing spatial policies that are socially, economically and environmentally desirable, to 1

2 better understand how different local spatial arrangements of networks, houses and facilities in outer suburbs affect global social costs and the welfare of individuals. This work package of the SOLUTIONS project (WP11) is therefore focussed at developing a spatially disaggregated model of land use and travel patterns at the scale of building blocks or parcels, using a detailed representation of the local road and path networks. In this paper we sketch the general methodology (section 2) and then describe the simulation of residential land use, as developed so far (section 3). We mainly emphasize the theoretical construction of the residential choice model and its micro-economic assumptions. We then provide examples of model outputs from preliminary tests to Northstowe, a new development area situated beyond the green belt, NW of Cambridge city (section 4). We present outputs for two simplistic but contrasted neighbourhood design scenarios. 2 General methodology The method consists in disaggregating the output of a MEPLAN-type Land Use and Transport Interaction Model (see Williams, 1994; Echenique et al., 1990; Jin and Williams, 2002, and SOLUTIONS WP2) within a particular zone. Moreover, within the zone, residential and travel choices are adapted so as to account for intra-neighbourhood variations in locational attributes. The level and variation of the neighbourhood attributes themselves depend on local planning scenarios. A set of different local designs will be proposed (and liaised to WP3 and WP4) so that a systematic variation can be undertaken of spatial components that may be key to the sustainability of neighbourhoods. The following four variables will be considered (varied): i. the connectivity of local network for different modes, ii. the time access to public transport, iii. residential density thresholds and local variations in density, iv. the relative position of different land use activities. By assumption, these characteristics can affect the spatial distribution of households across a development site as well as their mobility pattern. These charac- 2

3 teristics thus impact on the level of well-being achieved and on transport mode choices, and therefore, on the general sustainability of the site. Many Land Use and Transportation Interaction models tend to have disaggregated components or embed full microsimulation modules (see e.g; Urban- Sim (Waddell, 2002), MUSSA(Martinez and Donoso, 2004), ILUMASS (Strauch et al., 2004)). There are also dynamic models of land use at the micro-level which also relate to a regional macro-model (see e.g. agent-based/cellular automata models of the type of White and Engelen (1997)). The most sophisticated microsimulation models disaggregate decisions down to individuals and can simulate a large set of complex travel and activity decisions. Some models also incorporate housing submarkets, household life-cycles, etc. These models may be very computer intensive, as well as highly demanding on parameter calibration and on the analysis of complex inter-related results. Our model is aimed at answering the specific question of the impact of neighbourhood planning on the sustainability of new suburban developments and the city as a whole. Therefore, we seek to build a framework that is both well theoretically founded and sufficiently realistic without having to calibrate too many parameters, so that a wide sensitivity analysis can be undertaken for testing different planning scenarios. In addition, the strength of our framework is intended to reside in i. the focus on interconnecting models at two scales, with feedbacks and loops between macro- (or strategic or metropolitan) and micro-levels, ii. the use of a vector-based structure (rather than a raster (pixel)-based) for representing space and the location of residents and activities, iii. the development of a method for simulating a residential market equilibrium (short-run) that is consistent with a long-run equilibrium seeking approach at the strategic scale iv. the use of a detailed local traffic simulation where pedestrian and cycling modes are explicitly considered Our modelling strategy is presented in Figure 1. For a given prospective time (e.g. 2016), different strategic planning scenarios are tested at the macro-level (see WP2, here denoted by OPT-I, OPT-II, 3

4 Figure 1: Micro-scale modelling strategy OPT-III, OPT-IV,... ). For each of these scenarios, aggregate outputs from the strategic Land Use Transport model are acquired for the zone z where the micro-scale model takes place. The main aggregate outputs are (i) the total population in z, N z, and its subdivision in different socio-economic groups s (N z,s ), (ii) the total floorspace of each land use activities (surface of industry, retails and offices), and (iii) travel flow volumes from and to z. Additionally, the average rent level (R) and the time of intra-zonal trips by different modes and purpose are also recorded. These characteristics are hold constant in the micro-scale model whatever the local planning scenario tested. The local planning options (OPT-i, OPT-ii, OPT-iii, OPT-iv,... ) are operationalised within a GIS. In practice this step consists in vectorizing local networks and parcels, and allocating the total floorspace of each land use activities from the macro-model to the different parts of the development site. The process is thus similar, although more theoretical, to designing a local master plan for each of the local options, given the constraints implied by the strategic options. For each parcel, i, that can potentially be occupied by a household, a set of attributes is measured based on the local design GIS. They characterize the neighbourhood environment and the local accessibility of each parcel (or block). 4

5 These characteristics are then used within a residential choice model, together with the budget and preference characteristics of each socio-economic group. The residential model allocates the whole population (N z ) within the available parcels using bid-rent theory. The model therefore outputs a mapping of rents across the site. Once population is allocated, how much each household group benefits for the different local attributes can be computed. This local welfare level (and its distribution across household groups) can then be used in a sustainability assessment, and relationships drawn with the attractiveness factor of the zone at the strategic scale. Moreover, the model uses assumptions on travel preferences that, eventually, can be used to derive the modal split for intra-zonal trips. Again this result can be fed-back into the macro-scale as, for example, it may change the load of cars or public transport on several segments of the strategic network. Indeed, the last stage of the micro-scale simulation will consist in running a more detailed traffic simulation at the scale of the zone and its connections with neighbouring ones. Fewer model developments is needed for this last stage, which will be based on existing tools. Attention will be put on the modelling of cycling and walking. 3 The residential model We first present the micro-economic assumptions made at the strategic level (3.1). Second, we introduce stepwise the changes made at the micro-scale: (3.2.1) showing the implementation of the residential choice from the macroto the micro-level, (3.2.2) defining additional location preferences attached to neighbourhood qualities, and (3.2.3) updating the transport cost to account for intra-neighbourhood variations of accessibility. The third part (3.3) describes the method used to define the equilibrium pattern of households location and residential rent within the development site. 3.1 Macro-model assumptions At the strategic (macro-) level, households from different groups are assumed to minimize the total cost of their consumption and maintain a given utility level, 5

6 U, which is different for each household group. The total cost of consumption for a household corresponds to its budget net of commuting costs, Y, and is defined by: (index of household group is removed for clarity) Y = G + RDwel + Other (1) where G = p F in F in + p Ret Ret + p Edu Edu + p Ser Ser (2) Dwel = H 0 + H (3) Other = Z 0 + Z (4) G represents the total expenditure of households in finance, retail, education and services. The quantities F in, Ret, Edu and Ser represent minimum consumption levels. They have been adjusted so that the global demand for each good is met at the strategic scale (WSP, 2005), and depend on household characteristics (family size in the case of the Cambridge application). The prices of these goods include the transport cost related to their consumption. They can vary from zone to zone at the strategic level but are constant within a given zone. H 0 and Z 0 are minimum consumption levels of housing and composite good. The remaining consumption of housing and composite goods, H and Z, determine the utility level according to a Cobb-Douglas function. The minimisation of the total cost (1) is thus subject to U(Z, H) Z 1 γ H γ = U (5) with 0 < γ < 1. We know from the first order conditions that R = γz ( = U/ H ) βh U/ Z (6) from which we extract H (respectively Z) to input into the utility constraint (5) in order to find the Hicksian (compensated) demand function for Z (respectively 6

7 H): Z = H = ( ) γ 1 γ UR γ (7) γ ( ) 1 γ γ UR γ 1 (8) 1 γ We can combine these demands with the required minimum consumptions (3) and (4), and input them into the budget definition (1) so as to find the expenditure function, i.e. the total cost of achieving the level of utility U given all prices: ( ) 1 γ γ Y = G + Z 0 + RH 0 + R UR γ γ = G + Z 0 + RH 0 + UR γ γ γ (1 γ) ( 1 γ) The level of income is thus endogenous in the macro-model. ( ) γ 1 γ UR γ (9) γ (10) 3.2 Micro model assumptions Macro-Micro consistency In the micro-scale model, income level is exogenous and taken from the macromodel. Group definition and total population per group is also kept the same. Therefore, the level of utility achieved by a given household group may change according to the quality of the local design. We therefore consider the inverse of the expenditure function (10) to define the utility level given income and prices, i.e. the indirect utility function: V = (Y G Z 0 RH 0 ) R γ γ γ (1 γ) 1 γ (11) The difference between the utility level computed at the micro-scale using this equation and U can thus be used as a criteria for evaluating the level, and distribution across household groups, of well-being provided by the various local design scenarios tested. Moreover, the value of the housing rent may change from place to place within the development site so as to capitalize local qualities at the parcel or street-block scale. 7

8 In order to achieve this goal, we build on the macro model and further assume that households trade-off the local characteristics of available parcels with the variable part of the housing and other good consumptions, i.e. H and Z. The part of the housing expenditure related to the required minimum housing consumption, RH 0, is considered as fixed at the micro-level. A part of the final rent thus still captures metropolitan effects as output from the strategic model, such as the relative position of the zone towards employment activities and competition with other zones. (One can also note from (5) that H 0 and Z 0 were not part of the trade-off anyway in the macro-model). This assumption implies no change in writing the price of Z as it is the numeraire good (its price is unity). However additional definition is needed for the rent. We denote by r the rent at the micro-level. Also denote by G 0 the whole set of fixed expenditures that constraint the micro-scale decision making: G 0 = G+RH 0 +Z 0 = p F in F in+p Ret Ret+p Edu Edu+p Ser Ser+RH 0 +Z 0 (12) We can then change the macro budget constraint (1) into : Y G 0 = rh + Z (13) and then update the macro-scale indirect utility function (11) by simply updating notations or solving the primal problem, i.e. maximising (5) (unchanged) subject to the budget constraint (13): The Marshallian demands are Z = (1 γ) (Y G 0 ) (14) H = γ (Y G 0 ) r 1 (15) and the indirect utility is V = (Y G 0 ) r γ γ γ (1 γ) 1 γ (16) Finally we define the bid-rent Ψ, the amount a household is ready to pay for acquiring a unit of housing H (in addition to H 0 ) and obtain a utility level U. Ψ = (Y G 0 ) 1/γ U 1/γ γ(1 γ) (1 γ)/γ (17) 8

9 Full consistency between micro and macro behaviour is ensured as the whole set of parameters in the indirect utility or bid-rent functions is taken from the macro-model calibration (i.e. demands and prices within the budget constraint as well as γ). Note that consistency between micro and macro assumptions will also be sought after by adapting the local transport costs (see 3.2.3) and the equilibrium mean rent (see 3.3.1). In the following section, local preferences are encroached to this model structure. These local attributes could not be modelled at the macro-scale because of the aggregate representation of space Local preferences A set of local characteristics of plots are added to the utility function. They imply no change in the budget as they are considered as externalities. They are available to a household at no price once the choice of a plot has been made. Consider the following utility function U = Z 1 γ H γ A1 α1 A2 α2... Ak αk (18) = Z 1 γ H γ K k=1 A α k k (19) where α k 0 represent the liking for local externalities, A k. These attributes can be measured for each parcel before location choice. They are characteristics of the street-block or computed as radius functions around a parcel to take account of geographical features of the neighbourhood. Many neighbourhood externalities can be considered in the location decision. The importance of low neighbourhood density and open-spaces is emphasized in models that seek to understand the spatial patterns of sprawl (Irwin and Bockstael, 2002; Cavailhès et al., 2004; Caruso, 2005). For example, households may prefer a high percentage of open green space (or non-urban land uses) around their house, parts of the town designated to lower residential density, streets at the bottom of the hierarchy of streets in order to avoid exposure to traffic (end of cul-de-sac), or dislike locations that are too close from non-population serving industries or rail-tracks, etc. Among these factors, we emphasize the role of open-space and parcels density in subsequent simulations. The latter is used because zoning 9

10 by density thresholds is often seen in practice as a key tool to plan sustainable communities. We would like to incorporate this method in our analysis. Open-space is considered because it is increasingly seen in the literature as a quite local public good, that needs to be treated to have a better understanding of the relationship between sprawl and welfare (Nechyba and Walsh, 2004). Although the relationship between proximal green space and land prices is complex, private developers have incentives to provide efficient levels of open-space. NIMBY-type reactions towards new development as well as the fact that Green Belt issues are very sensitive locally point also in this direction. Some local attributes cannot be measured ex-ante, because their value in each residential plot depends on the residential occupation in other plots of the same street or around. A typical example is the housing density, which depends not only on parcel size but also on whether neighbouring parcels will eventually be developed and with what intensity. Density can represent closure of the landscape, reduced privacy,... Other examples are related to the socioeconomic condition of the neighbourhood. These can be represented by the average income in the street or the block, the share of people of the same group or high income group in a given radius,... but are known only after the location of the population. Brock and Durlauf (2000) emphasize the impact of these kind of neighbourhood interactions on the mix or residential socioeconomic groups in a city. Dealing with theses externalities within a discrete settings can be seen as a continuation of Schelling (1978) s work. Reaching an equilibrium allocation of all households with these types of externalities can be difficult and necessitate a dynamic approach. We do not treat these endogenous externalities in the prototype model developed here, but the intention is to include them in further model developments together with assumptions on the phasing of residential development by planners and land developers. Caruso (2005) proposed a dynamic path to achieving an equilibrium when households value endogenous neighbourhood density. This approach emphasizes the spatial impact of a gradual migration of households in a newly developed periurban zone. α k values are supposed to be known and can vary with socio-economic groups. Their value is to be taken from the literature or from hedonic esti- 10

11 mations in existing suburban developments Local transport cost The total transport cost in the macro-model accounts for trips within the zone and trips outside the zone. Both are paid by households when commuting or when travelling to consume the different goods. The local network being designed, the local part of the transport cost can be updated and thus differentiate the available parcels i in terms of accessibility. Note that Mollins and Timmermans (2002) suggest that although accessibility has some influence on the residential choice decision, the importance of this location factor is significantly less than the importance of housing characteristics and characteristics of the environment. We choose to adapt the cost of internal home-based trips only (flows with a destination within the zone). The remaining part (inter-zonal travel costs) is assumed to be the same whatever the location within the site, and is given by the macro-model. This treatment is simplistic because a change in the local transport cost may also impact on the cost of external trips, e.g. by facilitating a transfer from car to public services. To avoid double-counting in the budget equation, we use the difference between the internal transport cost from the macro model, T z,s (comprised within Y s and goods prices), and a new local transport cost, T i,s, specific of each location and obtained from the local network and location of local destinations (employment areas, retail places, schools). Denote by T i,s the difference T i,s = T i,s T z,s (20) We consider T as a trip-weighted logsum cost (Q) of travel time over available modes. The approach consists therefore by simply changing zonal average access times by parcel-specific access times. Three purposes p are considered: work, personal business trips, and educational trips. For each purpose, destinations are given based on local proximity. As we know the total number of intrazonal flows for each purpose from the strategic model, we can distribute the flows amongst the household groups and then to individual households: w p,s is 11

12 the number of trips that accrue to a household of group s for purpose p. The transport cost is thus T i,s = (w p,s Q i,p,s ) (21) p and T z,s is reconstructed similarly. The logsum corresponds to a nested logit formulation of mode choice where car, bus or slow mode is chosen first (level 1), and slow modes then subdivided by cycle or walk (level 2). With m1 = car, bus and m2 = car, bus, we have Q i,p,s = 1 λ1 ln ( m1 (e ( λ1τi,p,s,m1)) + e 1 λ2 ln ( m2 e( λ2τ i,p,s,m2) )) (22) where τ are the respective time-costs, and λ1, λ2 the choice sensitivity parameters. Corresponding mode probabilities are derived to output modal split for intrazonal trips. T can now be used to update the budget constraint (13), which is now Y G 0 T = rh + Z (23) Similarly to (17) and re-integrating indices of locations and socio-economic groups, the bid-rent of a household belonging to group s for a potential parcel i, is derived from the maximisation of (19) subject to (23) Ψ i,s = (Y s G 0,s T i,s ) 1/γs U 1/γs s K k=1 A 1/γs k,i γ s (1 γ s ) (1 γs)/γs (24) where we can see that the bid of a household for a given plot takes into account the local attributes of the plot both in terms of neighbourhood externalities and accessibility. 3.3 Equilibrium If the volume of households that can be allocated to a zone is unconstrained and if migration between all zones is free and instantaneous, all rents within the zone would be adjusted upwards until the utility in the zone is the same 12

13 as elsewhere, i.e. U s. This is the long-run equilibrium stage where, as long as no exogenous event arise, no migration is further needed. At that moment, rents in each residential parcel are given by Ψ(U s ) and occupied by the group, s, with the maximum bid. At long-run equilibrium, certain household groups might disappear partly or totally of the zone. The problem is different in this case as the population to allocate is given by the macro-model while the level of utility, U s is endogenous. All households have to find a location in the zone whatever the utility they can acquire. Therefore, utility surplus or deficit can occur. A disequilibrium situation relative to the external zones is thus modelled. Such a disequilibrium asks for a readjustment of population between zones in subsequent time steps at the macro-level (e.g. via attractiveness factors). The level of utility surplus or deficit, U s = U s U s is used to compare the different local planning options, i.e. the quality of the supply at a given moment in time. As space is discrete and includes externalities, the equilibrium is derived by simulation. Land use and rent patterns are determined separately. In the first stage, the households are allocated within the available plots according to their reservation bid-rent. In the second stage, utility levels and rents are computed for each plot Allocation procedure The first stage consists in the allocation of the different household types into the different available parcels according to their reservation bid-rents, i.e. the amount they are ready to pay for a given parcel in order to obtain the external utility level.reservation bid-rents Ψ i,s (U s ) are calculated for each household group (subgroup) and possible locations. Given the population constraint, a given parcel i in the zone is allocated to the best bidder group at the condition that the households in this group cannot find another location (i) where they are also the best bidder and (ii) where utility is higher. Because of the population constraint, therefore, some locations may be occupied by second (or more)-best bidders as regards to the reservation utility. For a given group, it is equivalent to sort locations by decreasing reservation bid-rents or by decreasing utilities given a fixed rent. The bid-rent approach 13

14 has the advantage to solve the competition between the groups and ensure the maximum rent to the landowner. The double condition (i) and (ii) of the previous paragraph is assessed from the matrix of reservation bid rents Ψ i,s (U s ), although we know that for some groups the utility achieved might be closer to U s than for others. The competition between the groups is thus imperfectly rendered. At least this procedure replicates the right pattern of location when applied to a long-run equilibrium city. For a given group, each location i is attributed a rank qi s = 1,..., I in decreasing order of Ψ i,s (U s ), and for a given location, each group is attributed a rank qs i = 1,..., S in decreasing order of Ψ i,s (U s ). At the first iteration, if qi s N s and qs i = 1, then i is allocated to group s. In all other cases, i is not allocated. n s is the number of group s households that have been allocated after this iteration. All locations i that have been allocated, whatever the group, are removed from the matrix. Moreover, if n s = N s for a given group after this iteration, all the Ψ i,s (U s ) are removed from the matrix for that group, i.e. the whole vector s is removed. A second iteration starts by re-calculating qi s and qs i (thus with some missing i and possibly some missing s). If qi s N s n s and qs i = 1, then i is allocated to group s. n s is increased by the number of newly allocated s households, the newly allocated i are removed from the matrix, and if n s = N s for a given group, all the Ψ i,s (U s ) are set to 0 for that group. New iterations are run similarly until n s = N s s. At that moment, the whole population is allocated within the residential plots Equilibrium utility and rents Whatever its location, every household of a given group is assumed to have the same level of utility at the end the allocation procedure because he is identical in taste and income with the other members of its group. An internal equilibrium situation for each group is assumed within the zone. If two households of the same group were to occupy a locations and get different utility levels, U i > U i, the household who is going to occupy the worst location i is happy to increase its bid and move to i. The rents are therefore adjusted upwards in every place occupied by a given group in order to equilibrate utility levels to the lowest utility level achieved by a member of the group. This utility (i.e. equivalent to 14

15 the utility level at the edge of the city in standard urban economy with single household type or to the utility at the outer boundary of a ring in the case of multiple household types) defines the utility level achieved by a household group at equilibrium, U s, and thus the utility surplus, U s. Let i be the occupied location where Ψ i (U) is the lowest, i.e the edge of the city. The utility level of the household situated in i, while paying r 0, is U i (r 0 ), which is obtained from the indirect utility (where r 0 replaces r). All the members of this group, s, in their respective location, will enjoy the same utility level: U s = U s,i (r 0) i ( = min s,i Ψs,i (U s ) ) (25) with i representing the plots occupied after the allocation process presented before. In each place occupied by s the equilibrium rent is known: r = Ψ s (U s) (26) We then find the group s with the next lowest reservation bid rent. We assume that this group shares a boundary with s, i.e. there is a crossing point between the bid rents of s and s. This point, i is approximated by the parcel where the utility U s is the lowest given that the rent to be paid is the rent that would be paid by a member of s in i. U s is thus function of U s. Therefore, we can see that the level of utility of one group depends on the level of utility of the groups that have lower minimum bids, and consequently on the initial rent R 0 at the edge of the city. The value of the rent in the places occupied by s are then calculated as previously in order to equilibrate utility within the group. Then this rent, at the next group boundary, is used to define the utility of the groups with the next lowest bid. The whole procedure is somewhat similar to the backward procedure described in Fujita (1989, p ). The method is however simpler because space is discrete and not distance-based. Therefore lot size and land availability do not influence the position of the boundary between two groups. At the end of the process, the average rent of all occupied parcels in the zone, r, is calculated and compared to the rent, R, provided by the macro-scale 15

16 model (which also applies to H 0. If r R > 0, the local rents are overestimated on average and thus the utility levels obtained are lower. In this case, the whole rents need to be translated downwards. r 0 is thus gradually adapted downwards up until the moment where r = R. If r R < 0, r 0 is adjusted upwards. This convergence process is used to ensure consistency of rent levels between the micro and macro scales. A simple bi-section iterative algorithm is used to reach convergence. After convergence, the resulting utilities can be used to explain parts of the attractiveness factor exogenously set to the zone at the macro-level (if the micro-simulation is run for a sample of zones so that a reasonable relationship can be drawn before updating macro-model assumptions). There is however a theoretical difficulty with the convergence process because it implies a change in utility at the edge of the site. If inferior to U, households would then avoid migrating in the zone and prefer to locate elsewhere! Therefore, we also record rents and utilities prior to convergence for further analyses. Under this condition, the group that occupies the worst parcel, would pay the macro rent (R) when occupying a parcel with macro characteristics (A k = 1 k and T = 0). In other words, whatever the local design scenario, there is always a group for which the utility surplus, U s, is null. One can also interpret the difference between the converged and non-converged rents as a taxation of each household for the provision of externalities through local design Final rent and housing consumption r i is the equilibrium rent that capitalizes the neighbourhood qualities perceived in i and the accessibility of i to intra-zonal destinations. Using (15), H i is then the housing consumption in i given r i. The total dwelling consumption is obtained by adding H i to the minimum consumption define at the macro-scale. Using (3), we have Dwel i = H 0 + H i (27) and the rent per unit of dwelling for a given parcel i is thus finally obtained as 16

17 a weighted sum: Rent i = (R i H 0 + r i H i )/Dwel i (28) 4 First application In this section, we give an example of model outputs for the Northstowe development site, 11km NW of Cambridge. 4.1 Cambridge strategic model outputs We use strategic outputs from the Structure plan scenario of the MEPLAN- MENTOR model of the Cambridge sub-region developed under the Cambridge Futures 2 project and calibrated under the 1991 census (Echenique and Hargreaves, 2003). According to this model and scenario, 5756 households are to be allocated at Northstowe by They can be grouped within 30 household classes depending on car availability, family size and socio-economic status as shown on Table 1. Within a given group, households have same preference, income and intra-zonal travel pattern. All groups differ in terms of income (Y s ) and reservation utility level (U s ). The share of housing in the net budget (γ s ) depends on the socio-economic status. The total of fixed consumptions (F in s, Ret s, Edu s, Ser s ) vary with family size. The disutility of a unit of travel time (τ i,s ) vary with car ownership. All households, whatever the group, consume a minimum of H 0 = 0.8 unit of dwelling, the remainder, H i, will be determined from the micro-simulation and depends on location. The average rent for the zone, R, is per unit of dwellings per month. Again, the micro-simulation will determine the local part of the rent, r i, specific to each location within Northstowe. Total floorspace of industry, retail and offices is also shown on Table 1. They constraint the design of the local plans. 4.2 Local design and neighbourhood attributes Two simple and highly theoretical local scenarios have been built for Northstowe for the purpose of developing the model. They are shown on Figure 2. 17

18 ID Group description Nb households 1 SEG1,1adult,0car 6 2 SEG1,1adult,1car SEG1,2adults,0car 11 4 SEG1,2adults,1car SEG1,2adults,2cars SEG2,1adult,0car 18 7 SEG2,1adult,1car SEG2,2adults,0car 25 9 SEG2,2adults,1car SEG2,2adults,2cars SEG3,1adult,0car 7 12 SEG3,1adult,1car SEG3,2adults,0car SEG3,2adults,1car SEG3,2adults,2cars SEG4,1adult,0car SEG4,1adult,1car SEG4,2adults,0car SEG4,2adults,1car SEG4,2adults,2cars Unemployed,1adult,0car Unemployed,1adult,1car Unemployed,2adults,0car Unemployed,2adults,1car Unemployed,2adults,2cars 2 26 Inactive,1adult,0car Inactive,1adult,1car Inactive,2adults,0car Inactive,2adults,1car Inactive,2adults,2cars 11 Total 5756 Floorspace m 2 Industrial Office Retail Table 1: Household groups 18

19 Common to the two options, is the central location of a town centre where the total surface of retails and offices is assigned. The town centre is chosen as the destination of all personal business trips. It is also a part of the intra-zonal working destination. The remaining part is an industrial area, situated in both cases at the north of the development. Three local schools have been located evenly across the site and are the destinations of intra-zonal education trips. The key difference between the two options is the local network. For the sake of the example, a single multi-modal network has been designed in the two case. The Grid pattern is characterized by very high connectivity and no dangling segment. The Tree pattern is characteristic of an extreme cul-desac development, with a topology such that there is no circuit. The design is adapted from a fractal tree made of four independent branches. No transit is possible from one branch to the other, even for cycling or walking. Residential street blocks are constructed from a buffer every 100m along the network. Parcel depth is given (25m) so that in the grid pattern, no gaps exist between gardens. Parcel width is not spatially represented but calculated so that, using the total length of the network, and given an average density of 20 dwellings/ha 1, the total number of dwellings correspond to the total number to be made available as from the macro-model (here 1household=1dwelling). One can readily see that the Grid pattern is more compact than the Tree, i.e. occupies less of the available space. Following the assumption of a valuation by residents of low density and green-space externalities, we compute a greenness index for each residential block. 2 The share of non-built up surface within a 100m radius is used and plotted on the maps (Figure 2). Higher levels and a more even distribution of greenness is obtained with the Tree design. Greenness is used as a first local attribute (A 1 ) in the next simulations. The second attribute (A 2 ) that is considered in these examples is the size of 1 This value is below target density for new developments (40dwellings/ha), but is a gross measure because several surface consuming features are not represented, but should be taken out of the residential surface, e.g. roads, schools, entertainment centre,... The total surface of the residential parcel is 299ha in the Tree case, and 255 in the Grid case, while according to the current Master Plan of Northstowe for 8,000 dwellings, residential space over the same development site should only occupy 187ha. Proportions are thus broadly respected if 20ha density is used (i.e. 1/2 of 40), as the residential surface would be 1.8 (grid) or 2.1 (tree) greater if the two designs were extended to 8,000 dwellings 2 Inhabitants in the neighbourhood of the new development have declared their attachment to a green separation between the existing settlements and the new development. This support our assumption. 19

20 Figure 2: Grid- and Tree designs applied to Northstowe: location of activities and greenness index 20

21 the parcels, i.e. gardens. Instead of a homogeneous dwellings density, we choose to double the density in a radius of 500m around the town centre. Within this radius, households will therefore face a disamenity, and will seek to compensate with higher consumption of composite goods or housing. For the sake of the example, and in absence of further calibration, the preference for greenness,α 1, and parcel size, α 2, are given an identical value whatever the household group, although one might hypothesize that they vary with family size and/or socio-economic status. 4.3 Output example The left-hand map on Figure 3 shows the allocation of households within residential blocks of the Grid design. Each block is coloured according to the group that is the majority in the block. Some parcels may however be occupied by other groups. The spatial distribution is quite segregated and driven by the accessibility except at the borders where households can benefit for greenness. Some blocks are left unoccupied (the supply is slightly superior to the demand). They correspond to less accessible parcels within the 500m radius of the town, where density is increased and represent a loss in parcel size for the households. In absence of a proper calibration of the local preferences, their importance with respect to accessibility can be under- or over-estimated. The relative location of the different household groups should therefore not be described further. In this example, one can see however that SEG1 and 2 tends to occupy the southern part of the site and SEG4 and inactive households the northern part (better accessibility or more greenness). We can also note that, with current parameters, most of the best parcels in terms of greenness are occupied by the better-off households of SEG3 or SEG4 both in the north and south part of the development. The equilibrium rent pattern is shown on the right side of Figure 3. Rents are lower in the denser part of the settlement and higher where greenness is available. The pattern is not smooth as it depends on the household groups located. The allocation and rent pattern for the tree case is presented on Figure 4. A similar description can be made although the distribution of green and thus of 21

22 the better sites is more complex. Because of this distribution, some groups (e.g. of SEG 1 and 2) who could not benefit for better local attributes in the Grid can have these benefits in the Tree. This can also be shown when equilibrium utility levels are examined. The Grid 2 and Tree 2 columns in Table 2 are the utility levels corresponding to the previous maps. One can see that for groups 6, 10-13, 15 or 19, their utility is largely increased (by more than 5 percent) in the Tree case when compared to the Grid case. The Grid 1 and Tree 1 columns in Table 2 refers to another simulation where it is assumed that local qualities have no importance. In that case, only local accessibility is taken into account in the residential choice. We can observe that the Grid design then tend to perform better for most of the groups. More than the spatial distributions themselves, it is important to note from these examples that the level of well-being depends on the local design options because these provide different levels and distribution of local externalities and transport costs. Moreover, the benefits may not be shared equally across household groups. Another aspect of the sustainability of a local design resides in its ability to induce changes in the use of polluting transport modes, at least for local trips. The local accessibility measure being based on a logit formulation, we can use the same logit structure to derive the probability of using a particular mode for a particular home-based trip. Once the allocation of households is made (see maps above), and given the number of trips by each individual, the probability can be used to derive number of flows by mode in each location. We can then aggregate all flows per mode and purpose at the scale of the development site and use mode split table to evaluate the quality of a local design. Percentage use of the different modes for intra-zonal trips are reported on Table 3. The upper part of the table refers to the simulation presented before (see maps) where both green space and parcel size are valued. The second set (middle) corresponds to the simulation where only local accessibility differentiate parcels. The third set (bottom) consists in a benchmark case where population is allocated at random (no preference and no differentiating transport costs across the site). The difference between this case and the first two shows the importance of simulating households location based on local attributes. As 22

23 Figure 3: Grid: Household group allocation and rents 23

24 Figure 4: Tree: Household group allocation and rents 24

25 Grid 1 Tree 1 Grid 2 Tree 2 Group U U( U%) U( U%) U( U%) U( U%) ( 0.98) 45.80( 1.77) 45.80( 1.77) 44.99( -0.02) ( 0.54) 55.69( 1.26) 55.70( 1.28) 54.92( -0.14) ( 0.85) 61.01( 1.68) 61.02( 1.71) 59.71( -0.48) ( 0.74) 80.93( 1.17) 80.96( 1.20) 79.51( -0.61) ( 0.58) ( 1.32) ( 1.33) ( -0.03) ( 2.70) 30.59( 1.96) 30.64( 2.14) 32.07( 6.89) ( -0.01) 40.19( 0.47) 39.62( -0.94) 39.98( -0.05) ( 2.31) 40.69( 1.72) 40.73( 1.82) 40.13( 0.34) ( 1.21) 55.07( 0.13) 54.90( -0.19) 54.21( -1.43) ( 0.07) 70.38( 0.55) 70.42( 0.60) 74.38( 6.26) ( 3.08) 30.40( 1.33) 30.80( 2.66) 34.89( 16.29) ( 0.87) 34.66( -0.96) 33.56( -4.10) 37.77( 7.92) ( 2.98) 40.44( 1.11) 40.97( 2.42) 43.31( 8.29) ( 1.37) 49.23( -1.53) 48.28( -3.44) 49.11( -1.77) ( 0.46) 64.55( -0.69) 62.12( -4.43) 70.98( 9.21) ( 33.28) 24.31( 21.56) 26.85( 34.25) 27.34( 36.68) ( 8.14) 25.33( 1.33) 26.97( 7.86) 27.28( 9.13) ( 23.48) 33.82( 12.73) 37.31( 24.38) 38.03( 26.78) ( 9.42) 40.69( 1.73) 43.80( 9.49) 45.63( 14.09) ( 4.76) 47.46( -5.07) 52.17( 4.35) 51.82( 3.64) ( 4.23) 14.09( -6.08) 15.59( 3.95) 16.60( 10.68) ( -4.13) 19.13( -4.34) 18.43( -7.86) 19.29( -3.54) ( 5.55) 18.40( -8.02) 21.02( 5.12) 20.05( 0.27) ( 1.73) 23.44( -6.26) 23.17( -7.30) 23.59( -5.65) ( -3.90) 33.57( -4.08) 32.25( -7.86) 33.86( -3.25) ( 2.23) 14.63( -2.48) 14.57( -2.86) 14.48( -3.46) ( -2.19) 19.56( -2.21) 19.00( -5.02) 19.53( -2.33) ( 3.49) 19.09( -4.56) 20.47( 2.36) 19.15( -4.26) ( -2.49) 29.23( -2.58) 28.66( -4.47) 28.92( -3.60) ( -0.69) 39.39( -0.61) 38.02( -4.95) 39.32( -1.71) 1 no preference for local attributes 2 preference for green and parcel size Table 2: Equilibrium utility and surplus per household group 25

26 shown on the table, a random allocation may, in this case, underestimate the importance of walking by 6 % for local commuting trips while overestimating the use of car by 4%. Comparing the resulting table for the Grid and the Tree structures, we observe important mode shifts for the different purpose. Modal shares are also reported on graphs on Figure 5. The more connective network, i.e. the Grid, decreases the total share of cars by 6% on average. Also noticeable is the shift from walking to cycling for education and personal trips when a Tree structure is used instead of a Grid. About a third of the walking flows in the Grid design are transferred to another mode on the Tree design, half part to car and the other half to cycling. On Figure 5, the comparison is also drawn with the modal split output of the macro-model. Its structure is close to the Tree assumption, although walking trips are underestimated on average despite that they are overestimated for education trips. Grid Tree Car Cycle Walk Bus Car Cycle Walk Bus Local preference for green and parcel size Work Person Educ All No local preference Work Person Educ All Random allocation Work Person Educ All Table 3: Mode split (%) for intra-zonal flows (Total flow volume per day is 1181 for work, 256 for personal business, 925 for education) 26

27 Figure 5: Mode split for intra-zonal flows: Grid (up), Tree (middle), Macro model (bottom) 27

28 5 Conclusion In this paper, we proposed a micro-scale model that can be used to evaluate the sustainability of various local plan scenarios at the scale of parcels. The microeconomic assumptions in the model are made consistent with the underlying assumptions of a MEPLAN-type Land Use and Transport Interaction model. Average zonal attributes of the macro-scale model are updated according to the local design of streets and parcels, and additional locational attributes are added so as to complement the standard residential trade-off between accessibility and housing space. The general framework has been described as well as the detailed method for obtaining a discrete spatial equilibrium. Preliminary results of an application to the Northstowe area shows the impact of varying network connectivity and the provision of local externalities in the form of green space and larger parcels on the spatial distribution of households, residential rent pattern, and households well-being. It also shows how useful it is to model the location choice of various household groups in order to estimate the potential travel mode shift that a local design can generate for local home-based trips. Both the level of well-being and the reduction in car use must be taken into account when evaluating local planning policies. The advantages/disadvantages of more compact or more connective local neighbourhood are to be balanced with the loss/gain in the locational characteristics that are highly valued by residents. Also the distribution of advantages and disadvantages amongst socio-economic categories must be analysed. This work is in progress. Further work for the residential part of the model will include (i) a proper calibration of the local parameters, (ii) the design of a larger experiment where small variations of key features of the local planning scenarios are systematically tested, (iii) the integration of feedbacks to the macro-model, (iv) the addition to the framework of endogenous externalities together with a dynamic assignment of the population (v) applications to suburban sites of different size, of other socio-economic profile, and within different metropolitan areas. 28

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