Optimal Regional Allocation of Future Population and Employment under Urban Boundary and Density Constraints: A Spatial Interaction Modeling Approach
Abstract
:1. Introduction
1.1. Historical Overview of Urban Modeling
1.2. Spatial Interaction Modeling: Structure and Variables
1.3. Planning Optimization Models and Spatial Interaction Modeling
1.4. Sprawl versus Compact City: Cost Assessment
1.5. Summary and Research Goals
- Develop a new SIM for commuting trip distribution, based on Tobit regression estimation [49] and including spatial structure variables measured by competing destinations (CD) [5] and intervening opportunity (IO) [6] factors. It is expected that incorporating these factors will better represent commuting behavior and commuting costs.
- Using the Tobit commuting SIM, develop a new commuting cost minimization model that simultaneously allocates target increments in the population and employment to geographical units across a city or metropolitan area under various scenarios of (a) population and employment densities (land consumption per resident and per employee) and (b) land availability in each geographical unit, as determined by the growth boundaries and environmental constraints. The results of this optimization include a minimum commuting cost surface, which is then to be estimated by polynomial regression, with the densities as independent variables.
- Combining the polynomial commuting cost model with estimated land development cost models and synthetic congestion cost models, develop a total cost minimization model to determine the optimal densities under various growth boundary scenarios and various parametric assumptions for the congestion cost functions.
- Use data on a specific U.S. metropolitan area to test the feasibility of the above-methodological goals. This would be a proof-of-concept goal, but is not intended to provide an actual plan for the local authorities of this metropolitan area.
2. Data and Methods
2.1. Overview of the Study Area
2.2. Data Sources
2.2.1. CTPP 2000
2.2.2. Property Data
- Real Estate Taxes|Fredericksburg, VA—Official Website (fredericksburgva.gov);
- Stafford County, VA (staffordcountyva.gov);
- Assessment Office, Spotsylvania County, VA; Real Estate, Caroline County, VA;
- Real Estate, King George County, VA (kinggeorgecountyva.gov).
Residential Property | Workplace Property | |||||||
---|---|---|---|---|---|---|---|---|
Jurisdiction | Average Size (Acre) | Average Property Value (USD) | Average Land Value (USD) | Average Building Value (USD) | Average Size (Acre) | Average Property Value (USD) | Average Land Value (USD) | Average Building Value (USD) |
Caroline | 2.3658 | 220,462 | 47,598 | 162,618 | 5.3395 | 576,642 | 144,972 | 304,321 |
Fredericksburg | 0.3525 | 260,831 | 53,914 | 178,740 | 1.2749 | 945,372 | 388,820 | 506,586 |
King George | 3.2624 | 245,225 | 72,054 | 167,082 | 4.5400 | 517,810 | 196,227 | 271,619 |
Spotsylvania | 1.3127 | 147,640 | 65,580 | 82,059 | 14.0769 | 3,717,248 | 3,330,981 | 386,267 |
Stafford | 1.1375 | 372,153 | 102,621 | 269,531 | 3.3182 | 1,241,485 | 479,788 | 761,687 |
FAMPO | 1.4254 | 247,782 | 77,390 | 167,696 | 8.3923 | 2,309,510 | 1,809,006 | 481,376 |
2.3. Variables
2.3.1. Dependent Variable
2.3.2. Independent Variables
Group A
- -
- Percentage of workers driving alone from their residence (P_DA_RES);
- -
- Percentage of workers carpooling from their residence (P_CP_RES);
- -
- Percentage of male workers driving alone from their residence (P_MDA_RES);
- -
- Percentage of male workers carpooling from their residence (P_MCP_RES).
- -
- Percentage of residents in sales or service occupations (P_OCC1_RES);
- -
- Percentage of residents in clerical or administrative support occupations (P_OCC2_RES);
- -
- Percentage of residents in manufacturing, construction, or maintenance occupations (P_OCC3_RES);
- -
- Percentage of residents in professional, managerial, or technical occupations (P_OCC4_RES);
- -
- Percentage of male residents in sales or service occupations (P_MOCC1_RES);
- -
- Percentage of male residents in clerical or administrative support occupations (P_MOCC2_RES);
- -
- Percentage of male residents in manufacturing, construction, or maintenance occupations (P_MOCC3_RES);
- -
- Percentage of male residents in professional, managerial, or technical occupations (P_MOCC4_RES).
- -
- Percentage of Hispanic or Latino residents (P_HIS_RES);
- -
- Percentage of White residents (P_WHT_RES);
- -
- Percentage of Black or African American residents (P_BLK_RES).
- -
- Percentage of resident households with an income of USD 75,000 or more in 1999 (P_HINC_RES);
- -
- Median resident household income (MHI_RES);
- -
- Percentage of resident workers with high earnings (USD 50,000+) in 1999 (P_HERN_RES);
- -
- Percentage of resident workers below the poverty level in 1999 (P_POV_RES);
- -
- Percentage of households with self-owned housing (P_OWNSELF_RES);
- -
- Percentage of households with owned housing with and without a mortgage (P_OWN_RES).
Group B
- -
- Percentage of employees below the poverty level (P_BlwPov_EMP);
- -
- Mean travel time (MTT_EMP);
- -
- Percentage of workers with low earnings (P_LERN_EMP);
- -
- Percentage of workers that carpool (P_CarPool_EMP).
- -
- Percentage of workers in manufacturing (P_Mfg_EMP);
- -
- Percentage of workers in wholesale trade (P_WhlTrd_EMP);
- -
- Percentage of workers in retail trade (P_RetTrd_EMP);
- -
- Percentage of workers in service industries (P_serv_EMP);
- -
- Percentage of workers in public administration (P_Pub_EMP).
Group C
Group D
2.4. Statistical and Optimization Methodology
TOTAL COST = commuting cost (TCOM) |
+ land development cost (LDC) |
+ congestion cost (TCON) |
3. Results
3.1. Tobit Regression
3.2. Minimizing Commuting Costs in the Allocation of Population and Employment
3.2.1. Scenarios
- ULP: (0.10–0.50) by 0.05 increments
- ULE: (0.05–0.25) by 0.025 increments
3.2.2. Model Formulation
3.2.3. Optimization Results
3.3. Minimizing All Costs in the Allocation of Population and Employment
3.3.1. Overview of Costs
3.3.2. Estimation of the Commuting Cost Surface
3.3.3. Estimation of Land Development Costs
acreage; employees)
- IR = average mortgage interest rate over 1997~2006 = 6.71% = 0.0671
- N = number of periods = 30 years (normal mortgage payment period)
3.3.4. Congestion Cost Synthetic Functions
3.3.5. Total Development Cost Minimization
- K1 = 0.1, 0.3, 0.5;
- K2 = 0.1, 0.3, 0.5;
- b = 1.0, 3.0, 5.0;
- d = 1.0, 3.0, 5.0.
4. Conclusions and Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Jurisdiction | Population | % | Employment | % |
---|---|---|---|---|
Caroline | 22,120 | 9.2% | 1945 | 2.3% |
Fredericksburg | 19,275 | 8.0% | 19,760 | 23.2% |
King George | 16,805 | 7.0% | 9912 | 11.6% |
Spotsylvania | 90,405 | 37.5% | 26,521 | 31.1% |
Stafford | 92,460 | 38.4% | 27,059 | 31.8% |
Total | 241,065 | 100.0% | 85,197 | 100.0% |
Flow | % | |||
---|---|---|---|---|
FAMPO | Internal | 7125 | 10.61 | |
TAZ-to-TAZ | 60,023 | 89.39 | ||
Jurisdiction | Caroline | Internal | 1261 | 1.88 |
Jurisdiction-to-Jurisdiction | 203 | 0.30 | ||
Fredericksburg | Internal | 4056 | 6.04 | |
Jurisdiction-to-Jurisdiction | 12,699 | 18.91 | ||
King George | Internal | 4314 | 6.42 | |
Jurisdiction-to-Jurisdiction | 3173 | 4.73 | ||
Spotsylvania | Internal | 15,863 | 23.62 | |
Jurisdiction-to-Jurisdiction | 6377 | 9.50 | ||
Stafford | Internal | 11,469 | 17.08 | |
Jurisdiction-to-Jurisdiction | 7733 | 11.52 | ||
Total Flow | 67,148 | 100% |
Variable | N | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|
F: flow | 3469 | 19.35 | 34.17 | 4.00 | 990.00 |
P: population | 3469 | 2332.27 | 2659.69 | 15.00 | 15,730.00 |
E: employees | 3469 | 1683.79 | 1687.31 | 4.00 | 6415.00 |
D: distance | 3469 | 10.51 | 6.97 | 0.42 | 41.07 |
Variable | N | Mean | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|
F: flow | 31875 | 0 | 0 | 0 | 0 |
P: population | 31875 | 1167.99 | 1765.41 | 0 | 15,730.00 |
E: employees | 31875 | 319.25 | 734.31 | 0 | 6415.00 |
D: distance | 31875 | 18.76 | 9.25 | 0.70 | 50.53 |
Variable | N | Mean | Median | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|---|
P | 188 | 1282.26 | 625.00 | 1903.91 | 0.0 | 15,730.0 |
P_DA_RES | 188 | 0.7601 | 0.7782 | 0.1498 | 0.0 | 1.000 |
P_BLK_RES | 188 | 0.1525 | 0.1165 | 0.1421 | 0.0 | 0.674 |
P_OCC1_RES | 188 | 0.1618 | 0.1627 | 0.0844 | 0.0 | 0.600 |
P_OCC2_RES | 188 | 0.1858 | 0.1920 | 0.0914 | 0.0 | 0.455 |
P_OCC3_RES | 188 | 0.2150 | 0.2000 | 0.1140 | 0.0 | 0.580 |
P_OCC4_RES | 188 | 0.1769 | 0.1700 | 0.1002 | 0.0 | 0.495 |
P_M_RES | 188 | 0.4981 | 0.4912 | 0.0918 | 0.0 | 0.984 |
P_UNEMP_RES | 188 | 0.0214 | 0.0165 | 0.0256 | 0.0 | 0.150 |
P_MUNEMP_RES | 188 | 0.0189 | 0.0000 | 0.0305 | 0.0 | 0.200 |
P_CP_RES | 188 | 0.1480 | 0.1334 | 0.1031 | 0.0 | 0.700 |
P_MDA_RES | 188 | 0.7538 | 0.7802 | 0.1866 | 0.0 | 1.000 |
P_MCP_RES | 188 | 0.1517 | 0.1303 | 0.1305 | 0.0 | 1.000 |
P_MOCC1_RES | 188 | 0.1232 | 0.1172 | 0.1031 | 0.0 | 0.667 |
P_MOCC2_RES | 188 | 0.0837 | 0.0817 | 0.0696 | 0.0 | 0.400 |
P_MOCC3_RES | 188 | 0.3279 | 0.3094 | 0.1731 | 0.0 | 1.000 |
P_MOCC4_RES | 188 | 0.2047 | 0.2000 | 0.1375 | 0.0 | 0.695 |
P_HIS_RES | 188 | 0.0185 | 0.0000 | 0.0309 | 0.0 | 0.192 |
P_WHT_RES | 188 | 0.7876 | 0.8220 | 0.1699 | 0.0 | 1.000 |
P_DIS_RES | 188 | 0.1429 | 0.1250 | 0.1028 | 0.0 | 0.600 |
P_HINC_RES | 188 | 0.4013 | 0.4006 | 0.2163 | 0.0 | 1.000 |
MHI_RES | 188 | 54,720.88 | 52,675.00 | 18,921 | 0 | 109,770 |
P_HERN_RES | 188 | 0.2071 | 0.2032 | 0.1140 | 0.0 | 0.5052 |
P_POV_RES | 188 | 0.0218 | 0.0112 | 0.0331 | 0.0 | 0.250 |
P_OWNSELF_RES | 188 | 0.1881 | 0.1667 | 0.1385 | 0.0 | 1.000 |
P_OWN_RES | 188 | 0.7895 | 0.8546 | 0.2137 | 0.0 | 1.125 |
P_3VEH_RES | 188 | 0.3406 | 0.3354 | 0.1614 | 0.0 | 0.769 |
P_OCCU_RES | 188 | 0.9131 | 0.9486 | 0.1428 | 0.0 | 1.000 |
HEDU_RES | 188 | 0.0384 | 0.0341 | 0.0381 | 0.0 | 0.388 |
Variable | N | Mean | Median | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|---|
EMP | 188 | 453.1755 | 75.0000 | 964.605 | 0.0000 | 6415.0 |
P_Full_EMP | 188 | 0.3321 | 0.3099 | 0.2435 | 0.0000 | 1.0000 |
P_Veh2Plus_EMP | 188 | 0.7334 | 0.8265 | 0.2895 | 0.0000 | 1.0000 |
P_BlwPov_EMP | 188 | 0.0364 | 0.0108 | 0.0698 | 0.0000 | 0.6667 |
MTT_EMP | 188 | 24.712 | 25.000 | 15.369 | 0.0000 | 102.3 |
P_LERN_EMP | 188 | 0.3681 | 0.3631 | 0.2498 | 0.0000 | 1.0000 |
P_CarPool_EMP | 188 | 0.0883 | 0.0809 | 0.0923 | 0.0000 | 0.4000 |
P_Mfg_EMP | 188 | 0.0379 | 0.0000 | 0.0948 | 0.0000 | 0.7500 |
P_WhlTrd_EMP | 188 | 0.0192 | 0.0000 | 0.0480 | 0.0000 | 0.4000 |
P_RetTrd_EMP | 188 | 0.0864 | 0.0106 | 0.1413 | 0.0000 | 1.0000 |
P_serv_EMP | 188 | 0.3687 | 0.3637 | 0.3014 | 0.0000 | 1.0000 |
P_Pub_EMP | 188 | 0.0327 | 0.0000 | 0.0777 | 0.0000 | 0.4427 |
P_Finan_EMP | 188 | 0.0561 | 0.0000 | 0.1341 | 0.0000 | 1.0000 |
Variable | N | Mean | Median | Standard Deviation | Minimum | Maximum |
---|---|---|---|---|---|---|
D | 35,344 | 17.947 | 17.380 | 9.379 | 0.420 | 50.530 |
Parameter | Estimate | Standard Error | t-Value | Approx Pr > |t| |
---|---|---|---|---|
Intercept | −80.267754 | 4.532873 | −17.71 | <0.0001 |
P | 0.011133 | 0.000426 | 26.13 | <0.0001 |
EMP | 0.027680 | 0.001218 | 22.73 | <0.0001 |
D | −3.966485 | 0.158067 | −25.09 | <0.0001 |
IO_E | −0.000324 | 0.000024329 | −13.33 | <0.0001 |
CD_E | 0.000160 | 0.000035343 | 4.53 | <0.0001 |
P_DA_RES | 28.859800 | 3.679491 | 7.84 | <0.0001 |
P_BLK_RES | 9.602796 | 3.023634 | 3.18 | 0.0015 |
P_OCC1_RES | 23.840650 | 6.515631 | 3.66 | 0.0003 |
P_OCC2_RES | 12.881209 | 5.595655 | 2.30 | 0.0213 |
P_OCC3_RES | 16.725051 | 4.991596 | 3.35 | 0.0008 |
P_OCC4_RES | 17.346662 | 5.671378 | 3.06 | 0.0022 |
P_Mfg_EMP | 36.628397 | 4.083194 | 8.97 | <0.0001 |
P_WhlTrd_EMP | 53.338335 | 7.888539 | 6.76 | <0.0001 |
P_RetTrd_EMP | 22.840645 | 3.075172 | 7.43 | <0.0001 |
P_Pub_EMP | 43.681025 | 5.569463 | 7.84 | <0.0001 |
P_Serv_EMP | 19.602157 | 1.794940 | 10.92 | <0.0001 |
P_Finan_EMP | 21.147896 | 2.754040 | 7.68 | <0.0001 |
P2 | −0.000000662 | 3.1856992 × 10−8 | −20.78 | <0.0001 |
E2 | −0.000002661 | 0.000000158 | −16.87 | <0.0001 |
D2 | 0.048005 | 0.004843 | 9.91 | <0.0001 |
POPEMP | 0.000002331 | 0.000000113 | 20.68 | <0.0001 |
EMPCD | −0.000000109 | 1.807805 × 10−8 | −6.03 | <0.0001 |
R-square | 0.4657 | |||
Pseudo-R2 | 0.2394 | |||
Log-likelihood | −20,466 |
Jurisdiction | 2035 | ||
---|---|---|---|
Employment | Population | ||
Caroline County | 14,216 | 47,007 | |
Fredericksburg | 43,679 | 29,852 | |
King George County | 17,821 | 40,744 | |
Spotsylvania County | 62,551 | 236,885 | |
Stafford County | 69,574 | 238,208 | |
Total GWRC (PD 16) | 207,841 | 592,696 | |
2000 (Existing) | Increments | ||
Employment | Population | ΔE | ΔP |
85,197 | 241,065 | 122,644 | 351,631 |
Scenario L2 | To | |||||
---|---|---|---|---|---|---|
ULP = 0.400 | ULE = 0.200 | CR | FR | KG | SF | SP |
From | CR | 1000 | 3830 | 4849 | 7395 | 4223 |
FR | 0 | 961 | 33 | 528 | 802 | |
KG | 9 | 2205 | 5531 | 2891 | 2369 | |
SF | 0 | 4481 | 1575 | 10,991 | 3796 | |
SP | 40 | 5855 | 1545 | 6215 | 10,695 | |
Scenario L2 | To | |||||
ULP = 0.100 | ULE = 0.050 | CR | FR | KG | SF | SP |
From | CR | 29 | 1582 | 382 | 967 | 1463 |
FR | 0 | 812 | 0 | 341 | 562 | |
KG | 0 | 350 | 92 | 20 | 282 | |
SF | 0 | 2016 | 0 | 3251 | 1322 | |
SP | 0 | 2848 | 0 | 1417 | 3936 | |
Scenario L4 | To | |||||
ULP = 0.400 | ULE = 0.200 | CR | FR | KG | SF | SP |
From | CR | 136 | 288 | 1349 | 2304 | 1415 |
FR | 0 | 780 | 48 | 472 | 592 | |
KG | 0 | 813 | 1057 | 1405 | 919 | |
SF | 0 | 3836 | 1146 | 9045 | 2751 | |
SP | 0 | 4886 | 1544 | 5245 | 8266 | |
Scenario L4 | To | |||||
ULP = 0.100 | ULE = 0.050 | CR | FR | KG | SF | SP |
From | CR | 2 | 7 | 0 | 0 | 23 |
FR | 0 | 763 | 0 | 357 | 549 | |
KG | 0 | 0 | 17 | 0 | 0 | |
SF | 0 | 1787 | 0 | 4030 | 1170 | |
SP | 16 | 4038 | 0 | 2075 | 3837 |
Land Scenario | Density Scenario | ||
---|---|---|---|
ULP = 0.400 | ULP = 0.100 | ||
ULE = 0.200 | ULE = 0.050 | ||
L2 | Objective function | 838,777 | 113,647 |
Total flows | 81,819 | 21,671 | |
Average commuting distance | 10.25 | 5.24 | |
L4 | Objective function | 473,283 | 106,347 |
Total flows | 48,294 | 18,671 | |
Average commuting distance | 9.80 | 5.70 |
Normalized | ||||||||||
Land Scenario L2 | ULE | |||||||||
0.050 | 0.075 | 0.100 | 0.125 | 0.150 | 0.175 | 0.200 | 0.225 | 0.250 | ||
ULP | 0.10 | 12.21 | 15.05 | 17.09 | 17.17 | 17.23 | 19.56 | 20.26 | 21.67 | 22.12 |
0.15 | 15.06 | 16.24 | 17.56 | 18.32 | 20.61 | 22.26 | 22.99 | 23.18 | 23.44 | |
0.20 | 26.31 | 27.15 | 28.03 | 28.16 | 28.42 | 28.92 | 29.06 | 29.15 | 29.55 | |
0.25 | 33.14 | 39.99 | 40.34 | 41.25 | 41.32 | 42.06 | 44.21 | 45.06 | 45.30 | |
0.30 | 40.62 | 46.95 | 53.61 | 57.55 | 59.47 | 61.18 | 62.55 | 64.59 | 66.17 | |
0.35 | 48.17 | 60.51 | 66.65 | 71.39 | 79.09 | 81.80 | 85.00 | 87.99 | 91.40 | |
0.40 | 53.13 | 64.22 | 70.87 | 78.52 | 80.79 | 85.27 | 90.12 | 100.00 | ||
0.45 | 63.43 | 76.50 | 80.40 | |||||||
0.50 | ||||||||||
Normalized | ||||||||||
Land Scenario L4 | ULE | |||||||||
0.050 | 0.075 | 0.100 | 0.125 | 0.150 | 0.175 | 0.200 | 0.225 | 0.250 | ||
ULP | 0.10 | 18.96 | 20.82 | 21.69 | 25.55 | 26.88 | 27.71 | 28.01 | 28.72 | 29.08 |
0.15 | 23.10 | 23.41 | 26.63 | 29.99 | 32.82 | 36.03 | 36.15 | 36.26 | 36.39 | |
0.20 | 31.63 | 35.46 | 38.57 | 39.61 | 39.90 | 40.13 | 40.33 | 40.50 | 40.73 | |
0.25 | 39.40 | 40.17 | 41.09 | 41.72 | 42.26 | 42.71 | 43.14 | 43.56 | 43.97 | |
0.30 | 44.12 | 46.64 | 51.31 | 53.13 | 53.93 | 54.71 | 55.55 | 56.36 | 57.20 | |
0.35 | 48.18 | 51.69 | 56.12 | 65.54 | 69.32 | 71.19 | 71.22 | 72.31 | 73.40 | |
0.40 | 49.13 | 56.64 | 64.89 | 71.43 | 80.24 | 83.10 | 84.40 | 85.64 | 87.05 | |
0.45 | 51.15 | 59.24 | 65.18 | 74.43 | 81.43 | 83.41 | 85.23 | 86.67 | 88.28 | |
0.50 | 55.52 | 63.55 | 72.26 | 80.09 | 88.76 | 92.80 | 95.45 | 97.63 | 100.00 |
Variables | Land Development Strategy | |
---|---|---|
L2 | L4 | |
Intercept | 188,109 (1.71) * | 100,497 (2.16) * |
ULP | −3,410,307 (−3.34) ** | −377,350 (−1.07) |
ULE | 2,816,147 (1.89) * | 117,457 (0.17) |
ULP × ULP | 19,994,468 (5.65) ** | 3,921,962 (3.54) ** |
ULE × ULE | −14,772,237 (−1.68) * | 2,136,213 (0.48) |
ULP × ULE | −4,477,808 (−0.93) | 878,521 (0.52) |
ULP × ULP × ULP | −26,345,984 (−6.61) ** | −5,919,163 (−5.02) ** |
ULE × ULE × ULE | 31,053,141 (1.72) * | −3,265,161 (−0.35) |
ULP × ULP × ULE | 24,799,246 (3.94) ** | 9,630,043 (4.90) ** |
ULP × ULE × ULE | −6,222,188 (−0.62) | −13,204,059 (−3.36) * |
R2 | 0.987 | 0.983 |
Land Development Cost (Residential) | Land Development Cost (Employment) | ||||||
---|---|---|---|---|---|---|---|
Intercept | 11.218 | 262.90 (<0.0001) | R2 0.85 | Intercept | 10.810 | 93.39 (<0.0001) | R2 0.78 |
LN(P_2006) | 1.000 | Infty (<0.0001) | LN(E_2006) | 1.000 | Infty (<0.0001) | ||
LN(ULP) | 0.014 | 0.34 (0.7311) | LN(ULE) | 0.502 | 10.40 (<0.0001) | ||
RESTRICT | 16.899 | 2.37 (0.0173) | RESTRICT | 98.442 | 5.01 (<0.0001) |
K1 | ||||||||
---|---|---|---|---|---|---|---|---|
0.1 | 0.3 | 0.5 | ||||||
K2 | b | d | ULP | ULE | ULP | ULE | ULP | ULE |
0.1 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.0805 | 0.1000 L | 0.0805 | 0.1000 L | 0.0805 | ||
5.0 | 0.1000 L | 0.2211 | 0.1000 L | 0.2211 | 0.1000 L | 0.2211 | ||
3.0 | 1.0 | 0.1447 | 0.0500 L | 0.1930 | 0.0500 L | 0.2206 | 0.0500 L | |
3.0 | 0.1443 | 0.0805 | 0.1917 | 0.0803 | 0.2186 | 0.0801 | ||
5.0 | 0.1435 | 0.2213 | 0.1876 | 0.2212 | 0.2121 | 0.2209 | ||
5.0 | 1.0 | 0.3135 | 0.0500 L | 0.5000 U | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3089 | 0.0793 | 0.5000 U | 0.0763 | 0.5000 U | 0.0763 | ||
5.0 | 0.2952 | 0.2194 | 0.3594 | 0.2174 | 0.3989 | 0.2160 | ||
0.3 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.1108 | 0.1000 L | 0.1108 | 0.1000 L | 0.1108 | ||
5.0 | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | ||
3.0 | 1.0 | 0.1447 | 0.0500 L | 0.1930 | 0.0500 L | 0.2206 | 0.0500 L | |
3.0 | 0.1439 | 0.1108 | 0.1905 | 0.1105 | 0.2168 | 0.1103 | ||
5.0 | 0.1435 | 0.2500 U | 0.1872 | 0.2500 U | 0.2113 | 0.2500 U | ||
5.0 | 1.0 | 0.3135 | 0.0500 L | 0.5000 U | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3051 | 0.1090 | 0.5000 U | 0.1042 | 0.5000 U | 0.1042 | ||
5.0 | 0.2932 | 0.2500 U | 0.3551 | 0.2500 U | 0.3917 | 0.2500 U | ||
0.5 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.1285 | 0.1000 L | 0.1285 | 0.1000 L | 0.1285 | ||
5.0 | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | ||
3.0 | 1.0 | 0.1447 | 0.0500 L | 0.1930 | 0.0500 L | 0.2206 | 0.0500 L | |
3.0 | 0.1438 | 0.1285 | 0.1899 | 0.1283 | 0.2158 | 0.1280 | ||
5.0 | 0.1435 | 0.2500 U | 0.1872 | 0.2500 U | 0.2113 | 0.2500 U | ||
5.0 | 1.0 | 0.3135 | 0.0500 L | 0.5000 U | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3031 | 0.1265 | 0.5000 U | 0.1205 | 0.5000 U | 0.1205 | ||
5.0 | 0.2932 | 0.2500 U | 0.3551 | 0.2500 U | 0.3917 | 0.2500 U |
K1 | ||||||||
---|---|---|---|---|---|---|---|---|
0.1 | 0.3 | 0.5 | ||||||
K2 | b | d | ULP | ULE | ULP | ULE | ULP | ULE |
0.1 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.0810 | 0.1000 L | 0.0810 | 0.1000 L | 0.0810 | ||
5.0 | 0.1000 L | 0.2218 | 0.1000 L | 0.2218 | 0.1000 L | 0.2218 | ||
3.0 | 1.0 | 0.1476 | 0.0500 L | 0.2064 | 0.0500 L | 0.2412 | 0.0500 L | |
3.0 | 0.1470 | 0.0809 | 0.2048 | 0.0807 | 0.2387 | 0.0806 | ||
5.0 | 0.1474 | 0.2223 | 0.2030 | 0.2227 | 0.2346 | 0.2228 | ||
5.0 | 1.0 | 0.3399 | 0.0500 L | 0.4456 | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3351 | 0.0801 | 0.4273 | 0.0794 | 0.5000 U | 0.0787 | ||
5.0 | 0.3248 | 0.2226 | 0.3991 | 0.2220 | 0.4423 | 0.2215 | ||
0.3 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.1108 | 0.1000 L | 0.1108 | 0.1000 L | 0.1108 | ||
5.0 | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | ||
3.0 | 1.0 | 0.1476 | 0.0500 L | 0.2064 | 0.0500 L | 0.2412 | 0.0500 L | |
3.0 | 0.1466 | 0.1107 | 0.2037 | 0.1106 | 0.2368 | 0.1104 | ||
5.0 | 0.1480 | 0.2500 U | 0.2036 | 0.2500 U | 0.2351 | 0.2500 U | ||
5.0 | 1.0 | 0.3399 | 0.0500 L | 0.4456 | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3316 | 0.1097 | 0.4170 | 0.1089 | 0.4783 | 0.1081 | ||
5.0 | 0.3243 | 0.2500 U | 0.3973 | 0.2500 U | 0.4391 | 0.2500 U | ||
0.5 | 1.0 | 1.0 | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L | 0.1000 L | 0.0500 L |
3.0 | 0.1000 L | 0.1281 | 0.1000 L | 0.1281 | 0.1000 L | 0.1281 | ||
5.0 | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | 0.1000 L | 0.2500 U | ||
3.0 | 1.0 | 0.1476 | 0.0500 L | 0.2064 | 0.0500 L | 0.2412 | 0.0500 L | |
3.0 | 0.1465 | 0.1281 | 0.2032 | 0.1280 | 0.2360 | 0.1279 | ||
5.0 | 0.1480 | 0.2500 U | 0.2036 | 0.2500 U | 0.2351 | 0.2500 U | ||
5.0 | 1.0 | 0.3399 | 0.0500 L | 0.4456 | 0.0500 L | 0.5000 U | 0.0500 L | |
3.0 | 0.3299 | 0.1272 | 0.4126 | 0.1262 | 0.4676 | 0.1254 | ||
5.0 | 0.3243 | 0.2500 U | 0.3973 | 0.2500 U | 0.4391 | 0.2500 U |
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Lee, D.J.-H.; Guldmann, J.-M. Optimal Regional Allocation of Future Population and Employment under Urban Boundary and Density Constraints: A Spatial Interaction Modeling Approach. Land 2023, 12, 433. https://doi.org/10.3390/land12020433
Lee DJ-H, Guldmann J-M. Optimal Regional Allocation of Future Population and Employment under Urban Boundary and Density Constraints: A Spatial Interaction Modeling Approach. Land. 2023; 12(2):433. https://doi.org/10.3390/land12020433
Chicago/Turabian StyleLee, David Jung-Hwi, and Jean-Michel Guldmann. 2023. "Optimal Regional Allocation of Future Population and Employment under Urban Boundary and Density Constraints: A Spatial Interaction Modeling Approach" Land 12, no. 2: 433. https://doi.org/10.3390/land12020433