Forecasting travel on congested urban transportation networks: Review and prospects for network equilibrium models

Networks and Spatial Economics

Volumn 7, Issue 2, 2007, Pages 99-128

  Boyce, David ^a,b  

^a Northwestern University   (United States)

^b NONE   (United States)

Author keywords

Sequential procedure; Traffic assignment; Traffic network equilibrium; Urban travel forecasting; User equilibrium route choice

Indexed keywords

FORECASTING; SOFTWARE DESIGN; TRAFFIC CONTROL;

ROUTE CHOICE; SEQUENTIAL PROCEDURES; TRAFFIC ASSIGNMENT; TRAFFIC NETWORKS; URBAN TRAVELS;

URBAN TRANSPORTATION;

EID: 34147177708     PISSN: 1566113X     EISSN: 15729427     Source Type: Journal    
DOI: 10.1007/s11067-006-9009-0     Document Type: Article

References (167)

1. Aashtiani HZ, Magnanti TL (1981) Equilibria on a congested transportation network. SIAM J Algebr Discrete Methods 2:213-226
2. Abdulaal M, LeBlanc LJ (1979) Methods for combining modal split and equilibrium assignment models. Transp Sci 13:292-314
3. Abrahamsson T (1996) Network equilibrium approaches to urban transportation markets. Ph.D. thesis, Regional Planning, Royal Institute of Technology, Stockholm, Sweden
4. Abrahamsson T, Lundqvist L (1999) Formulation and estimation of combined network equilibrium models with applications to Stockholm. Transp Sci 33:80-100
5. AJH Associates (2005) Quick Response System II, http:/my.execpc.com/&ajh/
6. Allsop RE (1968) Fourth international symposium of theory of traffic flow. Traffic Eng Control 10:263-264
7. Almond J (1967) Traffic assignment with flow-dependent journey times. In: Edie LC, Herman R, Rothery R (eds) Vehicular traffic science, proceedings of the third international symposium on the theory of traffic flow. American Elsevier, New York, pp 222-234
8. Atkins (2005) SATURN, http://www.its.leeds.ac.uk/software/saturn/
9. Bar-Gera H (2002) Origin-based algorithms for the traffic assignment problem. Transp Sci 36:398-417
10. Bar-Gera H, Boyce D (2003) Origin-based algorithms for combined travel forecasting models. Transp Res 37B:405-422
11. Bates JJ, Ashley DJ, Hyman G (1987) The nested incremental logit model: theory and application to modal choice. Proceedings, 15th PTRC Summer Annual Meeting, Seminar C, Bath, UK
12. Beckmann M (1951) Optimum transportation on networks. Cowles Commission Discussion Paper: Economics No. 2023, August 29
13. Beckmann M (1952a) Efficient transportation in networks. Cowles Commission Discussion Paper: Economics No. 2049, with the assistance of C. B. McGuire, Chicago, August 5
14. Beckmann M (1952b) Efficient transportation in networks. Cowles Commission Discussion Paper: Economics No. 2049A, November 7
15. Beckmann M (1953) Efficient transportation in networks continued. Cowles Commission Discussion Paper: Economics No. 2049B, April 27
16. Beckmann M (2004) Comments on 'forecasting travel on congested urban transportation networks: Review and prospects for network equilibrium models' presented at Tristan V by D. Boyce, 2004
17. Beckmann M, McGuire CB (1953) The determination of traffic in a road network - an economic approach. P-437. Rand Corporation, Santa Monica, CA, October 6
18. Beckmann M, McGuire CB, Winsten CB (1956) Studies in the economics of transportation, with an Introduction by T. C. Koopmans, Yale University Press, New Haven; published as RM-1488, Rand Corporation, Santa Monica, CA, 1955.
19. Beckmann MJ (1967a) On optimal tolls for highways, tunnels and bridges. In: Edie LC, Herman R, Rothery R (eds) Vehicular traffic science, proceedings of the third international symposium on the theory of traffic flow. American Elsevier, New York, pp 331-341
20. Beckmann MJ (1967b) On the theory of traffic flow in networks. Traffic Q 21:109-116
21. Bell MGH, Iida Y (1997) Transportation network analysis. Wiley, Chichester
22. Ben-Akiva ME (1974) Structure of passenger travel demand models. Transp Res Rec 526:26-42
23. Bly P, Emmerson P, Van Vuren T, Ash A Paulley N (2001) User-friendly multistage modelling advice, phase 2: Modelling parameters, calibration and validation. Project report for the integrated transport economic appraisal division, UK Department for Transport, Local Government and the Regions, London
24. Boyce D, Bar-Gera H (2003) Validation of urban travel forecasting models combining origin-destination, mode and route choices. J Reg Sci 43:517-540
25. Boyce D, Bar-Gera H (2004) Multiclass combined models for urban travel forecasting. Network Spatial Econ 4:115-124
26. Boyce DE (1984) Network models in transportation/land use planning. In: Florian M (ed) Transportation planning models. North-Holland, Amsterdam, pp 475-498
27. Boyce DE (1990) Network equilibrium models of urban location and travel choices: A new research agenda. In: Chatterji M, Kuenne RE (eds) New frontiers in regional science. New York University Press, New York, pp 238-256
28. Boyce DE, Chon, KS, Lee, YJ, Lin KT, LeBlanc LJ (1983) Implementation and computational issues for combined models of location, destination, mode and route choice. Environ Plann A 15:1219-1230
29. Boyce DE, Daskin MS (1997) Urban transportation. In: ReVelle C, McGarity A (eds) Chapter 7, Design and operation of civil and environmental engineering systems. Wiley, New York, pp 277-341
30. Boyce DE, Day ND, McDonald C (1970) Metropolitan plan making. Regional Science Research Institute, Philadelphia
31. Boyce DE, LeBlanc LJ, Chon KS (1988) Network equilibrium models of urban location and travel choices: A retrospective survey. J Reg Sci 28:159-183
32. Boyce DE, Lundqvist L (1987) Network equilibrium models of urban location and travel choices: Alternative formulations for the Stockholm region. Pap Reg Sci Assoc 61:91-104
33. Boyce DE, Mahmassani HS, Nagurney A (2005) A retrospective on Beckmann, McGuire and Winsten's Studies in the economics of transportation. Pap Reg Sci 84:85-103
34. Boyce DE, Williams HCWL (2005) Urban travel forecasting in the USA and UK. In: Reggiani A, Schintler L (eds) Methods and models in transport and telecommunications: Cross-atlantic perspectives. Springer, Berlin Heidelberg New York, pp 25-44
35. Braess D (1968) Uber ein Paradoxon aus der Verkerhsplanung. Unternehmensforschung 12:258-268
36. Braess D, Nagurney A, Wakolbinger T (2006) On a paradox of traffic planning. (translation from the original German) Transp Sci 39:446-450
37. Bruynooghe M, Gibert A, Sakarovitch M (1969) Une methode d'Affectation du trafic. In: Leutzbach W, Baron P (eds) Proceedings of the 4th international symposium on the theory of road traffic. Bundesminister für Verkehr, Abt. Strassenbau, Bonn, Germany, pp 198-204
38. Caliper Corporation (2005) TransCAD, http://www.caliper.com/
39. Campbell EW (1956) A mechanical method for assigning traffic to expressways. Highw Res Bull 130:27-46
40. Campbell ME (1952) Foreword to Traffic Assignment. Highw Res Bull 61:iIi-iv
41. Carey M (1985) The dual of the traffic assignment problem with elastic demands. Transp Res 19B:227-237
42. Carroll JD Jr (1959) A method of traffic assignment to an urban network. Highw Res Bull 224:64-71
43. Carroll JD Jr, Creighton RL (1957) Planning and urban area transportation studies. Proceedings of the thirty-sixth annual meeting, Highway Research Board, pp 1-7
44. Charnes A, Cooper WW (1958) Extremal principles for simulating traffic flow in a network. Proc Natl Acad Sci U. S. A. 44:201-204
45. Charnes A, Cooper WW (1961) Multicopy traffic networks. In: Herman R (ed) Theory of traffic flow. Elsevier, Amsterdam, pp 85-96
46. Christ CF (1952) History of the Cowles Commission, 1932-1952. In economic theory and measurement, Cowles Commission for research in economics, Chicago; complete text available at, http://cowles.econ.yale.edu/reports/20yr/his_index.htm
47. Citilabs (2005). CUBE, http://www.citilabs.com/
48. Cooper WW (2002) Abraham Charnes and W. W. Cooper (et al.): A brief history of a long collaboration in developing industrial uses of linear programming. Oper Res 50:35-41
49. Dafermos S (1980) Traffic equilibrium and variational inequalities. Transp Sci 14:42-54
50. Dafermos S (1982) The general multimodal network equilibrium problem with elastic demand. Networks 12:57-72
51. Dafermos S (1983) An iterative scheme for variational inequalities. Math Program 26:40-47
52. Dafermos SC (1968) Traffic assignment and resource allocation in transportation networks, Ph.D. thesis, Operations Research, Johns Hopkins University, Baltimore
53. Dafermos SC (1971) An extended traffic assignment model with applications to two-way traffic. Transp Sci 5:366-389
54. Dafermos SC (1972) The traffic assignment problem for multiclass-user transportation networks. Transp Sci 6:73-87
55. Dafermos SC (1973) Toll patterns for multi-class user transportation networks. Transp Sci 7:211-223
56. Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J Res Natl Bur Stand 73B:91-118
57. Dafermos SC, Sparrow FT (1971) Optimal resource allocation and toll patterns in user-optimized transportation networks. J Transp Econ Policy 5:184-200
58. Daly AJ, Zachary S (1978) Improved multiple choice models. In: Hensher DA, Dalvi MQ (eds) Determinants of travel choice, Saxon House, Westmead, UK
59. Dantzig GB (2002) Linear programming. Oper Res 50:42-47
60. de Cea J, Fernández JE (2001) ESTRAUS: A simultaneous equilibrium model to analyze and evaluate multimodal urban transportation systems with multiple user classes. Proceedings of the ninth world conference on transport research, Seoul, Korea
61. de Cea J, Fernández JE, DeKock V, Soto A, Friesz. TL (2003). "ESTRAUS: A computer package for solving supply-demand equilibrium problems on multimodal urban transportation networks with multiple user classes," presented at the annual meeting of the Transportation Research Board, Washington, DC
62. Deakin, Harvey, Skabardonis, Inc. (1993) Manual of regional transportation modeling practice for air quality, National Association of Regional Councils, Washington, DC
63. Dickson TJ (1977) Traffic assignment. Traffic Studies Group, University College London, London
64. Duffin RJ (1947) Nonlinear networks. IIa. Bull, New Ser, Am Math Soc 53:963-971
65. Enke S (1951) Equilibrium among spatially separated markets: Solution by electric analogue. Econometrica 19:40-47
66. Erlander S, Stewart NF (1990) The gravity model in transportation analysis. VSP, Utrecht
67. Evans SP (1973) Some applications of optimisation theory in transport planning, Ph.D. thesis, Civil Engineering, University College London, London
68. Evans SP (1976) Derivation and analysis of some models for combining trip distribution and assignment. Transp Res 10:37-57
69. Florian M (1977) A traffic equilibrium model of travel by car and public transit modes. Transp Sci 11:169-179
70. Florian M, Chapleau R, Nguyen S, Achim C, James-Lefebvre L, Galarneau S, Lefebvre J, Fisk C (1979) Validation and application of an equilibrium based two-mode urban transportation planning method (EMME). Transp Res Rec 728:14-23
71. Florian M, Hearn D (1995) Network equilibrium models and algorithms. In: Ball MO, Magnanti TL, Monma CL, Nemhauser GL (eds) Network routing, Handbooks in operations research and management science 8, Elsevier Science, Amsterdam, pp 485-550
72. Florian M, Nguyen S (1976) An application and validation of equilibrium trip assignment methods. Transp Sci 10:374-389
73. Florian M, Nguyen S (1978) A combined trip distribution modal split and assignment model. Transp Res 12:241-246
74. Florian M, Nguyen S, Ferland J (1975) On the combined distribution-assignment of traffic. Transp Sci 9:43-53
75. Florian M, Spiess H (1983) On binary mode choice/assignment models. Transp Sci 17:32-47
76. Frank C (1978) A study of alternative approaches to combined trip distribution-assignment modeling, Ph.D. thesis, Regional Science, University of Pennsylvania, Philadelphia
77. Frank M, Wolfe P (1956) An algorithm for quadratic programming. Nav Res Logist Q 3:95-110
78. Friesz TL (1985) Transportation network equilibrium, design and aggregation: Key developments and research opportunities. Transp Res 19A:413-427
79. Gale D, Kuhn HW, Tucker AW (1951) Linear programming and the theory of games. In: TC Koopmans (ed) Activity analysis of production and allocation, Wiley, New York, pp 317-329
80. Garrett M, Wachs M (1996) Transportation planning on trial. Sage, Thousand Oaks, CA
81. Gass SI (2002) The first linear-programming shoppe. Oper Res 50:61-68
82. Gibert A (1968) A method for the traffic assignment problem when demand is elastic. LBS-TNT-85, Transport Network Theory Unit, London Business School, London.
83. Haikalis G, Joseph H (1961) Economic evaluation of traffic networks. Highw Res Bull 306:39-63
84. Hasan MK, AlGadhi SA (1998) Application of simultaneous and sequential transportation network equilibrium models to Riyadh, Saudi Arabia. Transp Res Rec 1645:127-132
85. Hasan MK, Safwat, KN (2000) Comparison of two transportation network equilibrium modeling approaches. J Transp Eng 126:35-40
86. Highways Agency (1997) Design manual for roads and bridges, vol 12. Traffic appraisal of road schemes. Section 2, Part 2: Induced traffic appraisal. The Stationery Office, London
87. Hildreth C (1986) The Cowles Commission in Chicago, 1939-1955. Lecture notes in economics and mathematical systems 271. Springer, Berlin Heidelberg New York
88. Hutchinson BG (1974) Principles of urban transport systems planning. McGraw-Hill, New York
89. INRO Consultants, Inc. (2005) EMME/2. http://www.inro.ca/
90. Irwin NA, Von Cube, HG (1962) Capacity restraint in multi-travel mode assignment programs. Highw Res Bull 347:258-287
91. Jewell WS (1967) Models for traffic assignment Transp Res 1:31-46
92. Johnson MB (1964) On the economics of road congestion. Econometrica 32:137-150
93. Jorgensen NO (1963) Some aspects of the urban traffic assignment problem. ITTE Graduate Report #1963:9, M.S. thesis, Civil Engineering, University of California, Berkeley; available from the Institute of Transportation Studies Library
94. Knight FH (1924) Some fallacies in the interpretation of social cost. Q J Econ 38:582-606
95. Kohl JE (1841) Der verkehr und die ansiedelungen der menschen in ihrer abhangigkeit von der gestaltung der erdorberflache. Dresden, Leipzig, Germany
96. Koopmans TC (1949) Optimum utilization of the transportation system. Econometrica 17(supplement):136-146
97. Koopmans TC (ed) (1951) Activity analysis of production and allocation. Wiley, New York
98. Kuhn HW (1976) Nonlinear programming: A historical view. In: Cottle R, Lemke CE (eds) Nonlinear Programming, SIAM-AMS Proceedings 9:1-26
99. Kuhn HW (2002) Being in the right place at the right time. Oper Res 50:132-134
100. Kuhn HW, Tucker AW (1951) Nonlinear programming. In: Neyman J (ed) Proceedings of the second Berkeley symposium on mathematical statistics and probability, University of California Press, Berkeley, pp 481-492 (presented summer of 1950)
101. Lam WHK, Huang H-J (1992a) A combined trip distribution and assignment model for multiple user classes. Transp Res 26B:275-287
102. Lam WHK, Huang H-J (1992b) Calibration of the combined trip distribution and assignment model for multiple user classes. Transp Res 26B:289-305
103. Lam WHK, Huang H-J (1994) Comparison of results of two models of transportation demand in Hong Kong: CDAM and a version of MicroTRIPS. J Adv Transp 28:107-126
104. LeBlanc LJ (1973) Mathematical programming algorithms for large scale network equilibrium and network design problems, Ph.D. thesis, Industrial Engineering and Management Sciences, Northwestern University, Evanston, IL
105. LeBlanc LJ, Farhangian K (1981) Efficient algorithms for solving elastic demand traffic assignment problems and mode-split assignment problems. Transp Sci 15:306-317
106. LeBlanc LJ, Morlok EK, Pierskalla WP (1975) An efficient approach to solving the road network equilibrium traffic assignment problem. Transp Res 9:309-318
107. Leventhal T, Nemhauser, GL, Trotter L Jr (1973) A column generation algorithm for optimal traffic assignment. Transp Sci 7:168-176
108. Los Alamos National Laboratory (2005) TRANSIMS, http://www-transims.tsasa.lanl.gov/
109. Manheim ML (1979) Fundamentals of transportation systems analysis. The MIT Press, Cambridge, MA
110. Martin BV, Memmott FW 3rd, Bone AJ (1961) Principles and techniques of predicting future demand for urban area transportation, research report No. 38, MIT, Cambridge, MA.
111. McFadden D (1978) Modeling the choice of residential location. In: Karlqvist A, Lundqvist L, Snickars F, Weibull F (eds) Spatial interaction theory and planning models. North-Holland, Amsterdam, pp 75-96
112. McGuire CB (1952) Highway Capacity and Traffic Congestion: A Preliminary Study. Cowles Commission Discussion Paper: Economics No. 2048, July 23.
113. MCT, Ltda (2005) ESTRAUS, http://www.MCTsoft.com/
114. Moore EF (1957) The shortest path through a maze. Proceedings, international symposium on the theory of switching, part II, Harvard University, Cambridge, MA
115. Mott MacDonald (2003) DIADEM Overview of the algorithms, software and convergence requirements. Presented at the SATURN User Group Meeting, Epsom, UK
116. Murchland JD (1966) Some remarks on the gravity model of traffic distribution, and an equivalent maximization formulation. Report LSE-TNT-38, Transport Network Theory Unit, London Business School, London
117. Murchland JD (1967) Two remarks on congested assignment. Report LBS-TNT-53, Transport Network Theory Unit, London Business School, London
118. Murchland JD (1970) Road network traffic distribution in equilibrium. In: Henn R, Kunzi HP, Schubert H (eds) Mathematical models in the social sciences 8, Anton Hain Verlag, Meisenheim am Glan, pp. 145-183. In German, translation by HA Paul.
119. Nagurney A (1993) Network economics (2nd edition in 1999). Kluwer, Boston
120. Nagurney A (2004) Network economics course and sustainable transportation course. http://supernet.som.umass.edu/ austria_lectures/fulmain.html
121. Nagurney A, Boyce D (2006) Preface to 'on a paradox of traffic planning.' Transp Sci 39:443-445
122. Nash JF (1951) Noncooperative games. Ann Math 54:286-298
123. Newell GF (2002) Memoirs on highway traffic flow theory in the 1950s. Oper Res 50:173-178 (published posthumously)
124. Nguyen S (1973) Une approche unifiée des méthodes d'équilibre pour l'affectation du traffic. Ph.D. thesis, Informatique, Université de Montréal, Montréal
125. Nguyen S (1974) An algorithm for the traffic assignment problem. Transp Sci 8:203-216
126. Nguyen S (1976) A unified approach to equilibrium methods for traffic assignment. In: Florian M (ed) Traffic equilibrium methods, Lecture notes in economics and mathematical systems 18, Springer, Berlin, pp 148-182
127. Oppenheim N (1995) Urban travel demand modeling. Wiley, New York
128. Ortúzar J de D, Willumsen LG (2001) Modelling transport, 3rd Ed., Wiley, New York
129. Overgaard KR (1967) Testing a traffic assignment algorithm. In: Edie LC, Herman R, Rothery R (eds) Vehicular traffic science, proceedings of the third international symposium on the theory of traffic flow. American Elsevier, New York, pp 215-221
130. Patriksson M (1994) The traffic assignment problem - Models and methods. VSP, Utrecht
131. Pigou AC (1918) The economics of welfare. Macmillan, New York
132. Potts RB, Oliver RM (1972) Flows in transportation networks. Academic, New York
133. Prager W (1954) Problems of traffic and transportation. Proceedings of the symposium on operations research in business and industry. Midwest Research Institute, Kansas City, MO, pp 105-113
134. Prager W (1955) On the role of congestion in transportation problems. Zeitschrift für Angewandte Mathematik und Mechanik 35:264-268
135. Prais SJ, Winsten CB (1954) Trend estimators and serial correlation. Cowles Commission Discussion Paper #383, Chicago
136. PTV AG (2005) PTV Vision http://www.ptv.de/
137. Rockafellar RT (1967) Convex programming and systems of elementary monotonic relations. J Math Anal Appl 19:543-564
138. Safwat KNA, Hasan MK (1989) Computational experience with a simultaneous transportation equilibrium model under varying parameters. Trans Res Rec 1251:17-23
139. Safwat KNA, Magnanti TL (1988) A combined trip generation, trip distribution, modal split, and trip assignment model. Trans Sci 22:14-30
140. Schneider M (1959) Gravity models and trip distribution theory. Pap Reg Sci Assoc 5:51-56
141. Senior ML, Williams HCWL (1977) Model-based transport policy assessment; part I: The use of alternative forecasting models. Traffic Eng Control 18:402-406
142. Sheffi Y (1985) Urban transportation networks. Prentice-Hall, Englewood Cliffs, NJ
143. Smith MJ (1979) Existence, uniqueness and stability of traffic equilibria. Transp Res 13B:295-304
144. Standing Advisory Committee for Trunk Road Assessment (1994) Trunk roads and the generation of traffic. The Stationery Office, London
145. Tomazinis AR, Wickstrom GV (1962) Forming a comprehensive transportation flows model. Highw Res Bull 347:254-257
146. Tomlin JA (1967) Mathematical programming models for traffic network problems. Doctoral dissertation, Mathematics, University of Adelaide, Adelaide, Australia
147. Tomlin JA (1971) A mathematical programming model for the combined distribution-assignment of traffic. Transp Sci 5:122-140
148. Train KE (2003) Discrete choice methods with simulation. Cambridge University Press, Cambridge; also available at http://emlab.berkeley.edu/ users/train/
149. Transportation Research Board (1995) Expanding metropolitan highways: implications for air quality and energy use. Special Report 245, National Research Council, Washington, DC
150. Tucker AW (1957) Linear and nonlinear programming. Oper Res 5:244-257
151. US Department of Transportation (1977) An introduction to travel demand forecasting: A self-instructional text. Federal Highway Administration and Urban Mass Transportation Administration, Washington, DC
152. Van Vliet D (1982) SATURN: A modern assignment model. Traffic Eng Control 23:575-581
153. Vivona NG (1957a) Predicting urban trip patterns: Growth factor models, C.A.T.S. Res News, vol. 1, no. 11, pp 16-20, June 21, 1957. Chicago Area Transportation Study, Chicago
154. Vivona NG (1957b) Traffic assignment: Toronto approach. C.A.T.S. Res News, vol. 1, no. 19, pp 12-16, October 11, 1957. Chicago Area Transportation Study, Chicago
155. Voorhees AM (1955) A general theory of traffic movement. Proceedings, Institute of Traffic Engineers, New Haven, CT, pp 46-56
156. Walters AA (1961) The theory and measurement of private and social cost of highway congestion. Econometrica 29:676-699
157. Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc - Inst Civ Eng, Part II 1:325-378
158. Wardrop JG (1961) The distribution of traffic on a road system. In: R. Herman (ed) Theory of traffic flow, Elsevier, Amsterdam, pp. 57-78
159. Williams HCWL (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environ Plann A 9:285-344
160. Williams HCWL (2004) Themes in the development and application of transport planning models. In: Lee D-H (ed) Urban and regional transportation modeling, Edward Elgar, Northhampton, pp. 1-24
161. Williams HCWL, Senior ML (1977) Model-based transport policy assessment; part II: Removing fundamental inconsistencies from the models. Traffic Eng Control 18:464-469
162. Williams HCWL, van Vliet D, Kim KS (2001) The contribution of suppressed and induced traffic in highway appraisal, part 1: Reference states, and part 2: Policy tests. Environ Plan A 33:1057-1082 and 1243-1264
163. Wilson AG (1967) A statistical theory of spatial distribution models. Transp Res 1:253-269
164. Wilson AG (1969) The use of entropy maximising models in the theory of trip distribution, mode split and route split. J Transp Econ Policy 3:108-126
165. Wilson AG (1970) Entropy in urban and regional modelling. Pion, London
166. Wilson AG, Hawkins AF, Hill GJ, Wagon DJ (1969) Calibrating and testing the SELNEC transport model. Reg Stud 3:337-350
167. Wooton HJ, Pick GW (1967) A model for trips generated by households. J Transp Econ Policy 1:137-153