Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities

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Abstract

An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first-in-first-out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems.To remove problems (a) and (b) we extend the link travel-time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel-time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.
LanguageEnglish
Pages90-104
JournalTransportation Research Part B
Volume65
DOIs
Publication statusPublished - Jul 2014

Fingerprint

Travel time
travel
time
traffic
traffic behavior
realism

Keywords

  • Travel-time functions
  • First-in-first-out
  • Link flow capacity
  • Spillback
  • Dynamic network loading
  • Dynamic traffic assignment

Cite this

@article{793956da5c04433fa3fb7d41f7c9852c,
title = "Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities",
abstract = "An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first-in-first-out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems.To remove problems (a) and (b) we extend the link travel-time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel-time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.",
keywords = "Travel-time functions, First-in-first-out, Link flow capacity, Spillback, Dynamic network loading, Dynamic traffic assignment",
author = "Malachy Carey and Paul Humphreys and Marie McHugh and Ronan McIvor",
note = "Reference text: Adamo, V., Astarita, V., Florian, M., Mahut, M. and Wu, J.H., 1999a. Modelling the spillback of congestion in link based dynamic network loading models: A simulation models with application. Pages 555-573, in Transportation and Traffic Theory: Proceedings of the 14th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. A. Ceder). Pergamon/ Elsevier, New York. Adamo, V., Astarita, V., Florian, M., Mahut, M. and Wu, J.H., 1999b. Analytical modelling of intersections in traffic flow models with queue spill-back. IFORS' 99 15th Triennial Conference, hosted by the Operations Research Society of China (ORSC) Beijing, P.R. China, August 16–20, 1999. Astarita, V. (1995). Flow Propagation Description in Dynamic Network Loading Models, Pages 599–603 in Proceedings of IV International Conference on Application of Advanced Technologies in Transportation Engineering (AATT), Y. J. Stephanedes and F. Filippi (eds), American Society of Civil Engineers (ASCE). Astarita, V., 1996. A continuous time link model for dynamic network loading based on travel time function. Pages 79-103 in Transportation and Traffic Theory: Proceedings of the 13th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. J.-B. Lesort). Pergamon/ Elsevier. Astarita, V., Er-Rafia, K., Florian, M., Mahut, M., Velan, S. 2001. Comparison of three methods for dynamic network loading. Transportation Research Record, 1771:179-190. Bliemer, B.C.J., 2006. Dynamic queuing and spillback in an analytical multiclass dynamic traffic assignment model. In: Proceedings of the 1st International Symposium on Dynamic Traffic Assignment, held 21-23 June 2006, The University of Leeds, UK. Boyce, D., Lee, D.-H., Ran, B., 2001. Analytical models of the dynamic traffic assignment problem. Networks and Spatial Economics 1(3-4), 377–390. Carey, M., 2004. Link travel times I: desirable properties. Networks and Spatial Economics 4(3), 257-268. Carey, M. and Ge, Y.E., 2003a. Comparing whole-link travel time models. Transportation Research Part B 37(10), 905–926. Carey, M. and Ge, Y.E., 2003b. Dynamic Traffic Assignment (DTA) Models for Road Traffic Networks, A bibliography for dynamic traffic assignment (1970 to August 2003). http://www.qub.ac.uk/research-centres/TransportResearch/NetworkAssignmentandSimulation/ (accessed 19 Oct. 2013). Carey, M. and Ge, Y.E., 2004. Efficient discretisation of link travel time models. Networks and Spatial Economics 4(3), 269-290. Carey, M. and Ge, Y.E., 2005a. Convergence of whole-link travel time models used in DTA. Transportation Science 39(1), 25-38. Carey, M. and Ge, Y.E. 2005b. Alternative conditions for a well-behaved travel-time model. Transportation Science 39(3), 417–428. Carey, M., McCartney, M., 2002. Behavior of a whole-link travel time model used in dynamic traffic assignment. Transportation Research Part B 36(1), 83–95. Carey, M., Subrahmanian, E., 2000. An approach to modelling time-varying flows on congested networks. Transportation Research Part B 34(3), 157–183. Cayford, R., Lin, W.-H. and Daganzo, C.F., 1997. The NETCELL simulation package: technical description. PATH Research Report UCB-ITS-PRR-97-23. Department of Civil Engineering and Institute of Transportation Studies, University of California, Berkeley, CA. Celikoglu, H.B., 2007. A dynamic network loading model for traffic dynamics modeling, IEEE Transactions on Intelligent Transportation Systems 8(4), 575-583. Chen, H.-K., (1999). Dynamic travel choice models: a variational inequality approach. Springer, Heidelberg. Chen, H.-K., and Hsueh, C.F., (1998). A model and an algorithm for the dynamic user-optimal route choice problem. Transportation Research Part B 32(3), 219-234. Chiu, Y.-C., Bottom, J., Mahut, M., Paz, A., Balakrishna, R., Waller,T. and Hicks, J., 2011. Dynamic Traffic Assignment A Primer. Transportation Research Circular E-C153. For the Transportation Network Modeling Committee of the Transportation Research Board, Washington, DC. Chow, A.H.F., 2009) Properties of dynamic system optimal assignment and its solution method. Transportation Research Part B 43(3), 325-344. Daganzo, C.F., 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 28(4), 269–287. Daganzo, C.F., 1995a. The cell transmission model part II: network traffic. Transportation Research Part B 29(2), 79–93. Daganzo, C.F., 1995b. Properties of link travel time functions under dynamic loads. Transportation Research Part B 29(2), 95-98. Daganzo, C.F., 1995c. A finite difference approximation of the kinematic wave model of traffic flow. Transportation Research Part B 29(4), 261–276. Fernandez, J.E. and De Cea, J. 1994. Flow Propagation Description in Dynamic Network Assignment Models. TRISTAN II Triennial International Symposium on Transportation Analysis, Capri, June 1994. Friesz, T.L., Bernstein, D., Smith, T.E., Tobin, R.L. and Wei, B.W., 1993. A variational inequality formulation of the dynamic network equilibrium problem. Operation Research 41(1), 179–191. Friesz, T.L. and Bernstein, D., 2007. Analytical dynamic traffic assignment models. Pages 221-237 in D.A. Hensher and K.J. Button, eds. Handbook of transport modelling. Second Edition. Elsevier Science. Friesz, T.L., Bernstein, D., Suo, Z., Tobin, R.L., 2001. Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1(3-4), 319–347. Friesz, T.L., Luque, F., Smith, R., Wie, B.W., 1989. Dynamic network traffic assignment considered as a continuous time optimal control problem. Operations Research 37(6), 893–901. Friesz, T.L. and Mookherjee, R., 2006. Solving the dynamic network user equilibrium problem with state-dependent time shifts. Transportation Research Part B 40(3), 207–229. Garc{\'i}a-R{\'o}denas, R., L{\'o}pez-Garc{\'i}a, M.L., Ni{\~n}o-Arbelaez, A. and Verastegui-Rayo, D., 2006. A continuous whole-link travel time model with occupancy constraint. European Journal of Operational Research 175(3), 1455-1471. Ge, Y.E. and Carey, M. 2004. Travel time computation of link and path flows and first-in-first-out. Pages 326-335 in Proceedings of the 4th International Conference on Traffic and Transportation Studies,(ICTTS), B. Mao, Z. Tian and Q. Sun (eds). Held August 2-4, 2004, Dalian, China. Beijing: Science Press. Gentile G., Meschini L., Papola N., 2007. Spillback congestion in dynamic traffic assignment: a macroscopic flow model with time-varying bottlenecks, Transportation Research Part B 41(10), 1114-1138. Heydecker, B.G., Addison, J.D., 1966. An exact expression of dynamic equilibrium, Pages 359-384 in Transportation and Traffic Theory: Proceedings of the 13th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. J.-B. Lesort). Pergamon/ Elsevier. Heydecker, B.G., Addison, J.D., 1998. Analysis of traffic models for dynamic equilibrium traffic assignment. In: Bell, M.G.H. (Ed.), Transportation Networks: Recent Methodological Advances. Pergamon, Oxford, pp. 35–49. Huang, H.J. and Lam, W.H.K., 2002. Modeling and solving dynamic user equilibrium route and departure time choice problem in network with queues. Transportation Research Part B 36(3), 253-273. Jayakrishnan, R., Tsai, W.K. and Chen, A., 1995. A dynamic traffic assignment model with traffic-flow relationships. Transportation Research Part C 3(1), 51–72. Jin, W.L. and Li, L., 2007. First-in-first-out is violated in real traffic. Proceedings of Transportation Research Board Annual Meeting, 2007, Washington DC, USA. Jin, W.L., Zhang, Y. and Chu, L., 2006. Measuring first-in-first-out violation among vehicles. Proceedings of Transportation Research Board Annual Meeting, 2006, Washington DC, USA. Kachani, S. and Perakas, G., 2009. A dynamic travel time model for spillback. Networks and Spatial Economics 9(4), 595-618. Lin, W.-H. and Liu, H., 2010. Enhancing realism in modeling merge junctions in analytical models for system-optimal dynamic traffic assignment. IEEE Transactions on Intelligent Transportation Systems 11(4), 838-845. Long, J., Gao, Z. and Szeto, W.Y., 2001. Discretised link travel time models based on cumulative flows: Formulations and properties. Transportation Research Part B 45(1), 232-254. Magumba, B., 2007. Dynamic modelling of queue spillbacks. Thesis for MSc (Eng) Transport Planning and Engineering, Institute for Transport Studies, University of Leeds, UK. Mun, J.-S., 2007. Traffic Performance Models for Dynamic Traffic Assignment: An Assessment of Existing Models. Transport Reviews 27(2), 231-249. Mun, J.-S., 2009. Some features of non-linear travel time models for dynamic traffic assignment. Transportation Planning and Technology 32(3), 261-288. Nie, X. and Zhang, H.M., 2005a. Delay-function-based link models: their properties and computational issues. Transportation Research Part B 39(8), 729–751. Nie, X. and Zhang, H.M., 2005b. A comparative study of some macroscopic link models used in dynamic traffic assignment. Networks and Spatial Economics 5(1), 89-115. Peeta, S. and Ziliaskopoulos, A., 2001. Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics 1(3-4), 233–265. Ran, B., Boyce, D.E., LeBlanc, L.J., 1993. A new class of instantaneous dynamic user-optimal traffic assignment models. Operations Research 41(1), 192–202. Ran, B., Boyce, D.E., 1996. A link-based variational inequality formulation of ideal dynamic optimal route choice problem. Transportation Research Part C 4(1), 1–12. Ran, B., Lo, H. and Boyce, D.E., 1996. A formulation and solution algorithm for a multi-class dynamic traffic assignment problem. In Lesort (ed.), Transportation and Traffic Theory, Pergamon-Elservier, New York, 195-216. Rubio-Ardanaz, J.M., Wu, J.H. and Florian, M., 2001. A numerical analytical model for the continuous dynamic network equilibrium problem with limited capacity and spillback. In: The IEEE Intelligent Transportation Systems Conference Proceedings, 25-29 August 2001, Oakland, CA, USA. pp. 263-267. Rubio-Ardanaz, J.M., Wu, J.H. and Florian, M. 2003. Two improved numerical algorithms for the continuous dynamic network loading problem. Transportation Research Part B 37(2), 171–190. Szeto, W.Y. and Lo, H.K., 2005. Dynamic Traffic assignment: review and future research directions. Journal of Transportation Systems Engineering and Information Technology 5(5), 85-100. Szeto, W.Y. and Lo, H.K., 2006. Dynamic traffic assignment: properties and extensions. Transportmetrica 2(1), 31-52. Wie, B., Tobin, R. and Carey, M., 2002. The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation. Transportation Research Part B 36(10), 897–918. Wu, J.H., Chen, Y. and Florian, M., 1995. The continuous dynamic network loading problem: a mathematical formulation and solution method. Presented at the 3rd Euro Working Group Meeting on Urban traffic and transportation, Barcelona, 27–29 September. Wu, J.H., Chen, Y. and Florian, M., 1998. The continuous dynamic network loading problem: a mathematical formulation and solution method. Transportation Research Part B 32(3), 173–187. Xu, Y. W., Wu, J. H., Florian M. (1998) An efficient algorithm for the continuous network loading problem: a DYNALOAD implementation. Transportation Networks: Recent Methodological Advances, M.G.H. Bell (ed), 51-66, Pergamon. Xu, Y.W., J.H. Wu, J.H, Florian, M., Marcotte, P. and Zhu, D.L., 1999. Advances in the continuous dynamic network loading problem. Transportation Science 33(4), 341–353. Yang, H. and Meng, Q., 1998. Departure time, route choice and congestion toll in a queuing network with elastic demand. Transportation Research Part B 32(4), 247-260. Yperman, I., 2007. The link transmission model for dynamic network loading. PhD Thesis, Katholieke Universiteit Leuven, Belgium. Zhang, H.M. and Nie, X., 2005. Some consistency conditions for dynamic traffic assignment problems. Networks and Spatial Economics 5(1), 71-87. Zhu, D. and Marcotte, P., 2000. On the existence of solutions to the dynamic user equilibrium problem. Transportation Science 34(4), 402-414.",
year = "2014",
month = "7",
doi = "10.1016/j.trb.2014.04.002",
language = "English",
volume = "65",
pages = "90--104",
journal = "Transportation Research Part B: Methodological",
issn = "0191-2615",
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TY - JOUR

T1 - Extending travel-time based models for dynamic network loading and assignment, to achieve adherence to first-in-first-out and link capacities

AU - Carey, Malachy

AU - Humphreys, Paul

AU - McHugh, Marie

AU - McIvor, Ronan

N1 - Reference text: Adamo, V., Astarita, V., Florian, M., Mahut, M. and Wu, J.H., 1999a. Modelling the spillback of congestion in link based dynamic network loading models: A simulation models with application. Pages 555-573, in Transportation and Traffic Theory: Proceedings of the 14th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. A. Ceder). Pergamon/ Elsevier, New York. Adamo, V., Astarita, V., Florian, M., Mahut, M. and Wu, J.H., 1999b. Analytical modelling of intersections in traffic flow models with queue spill-back. IFORS' 99 15th Triennial Conference, hosted by the Operations Research Society of China (ORSC) Beijing, P.R. China, August 16–20, 1999. Astarita, V. (1995). Flow Propagation Description in Dynamic Network Loading Models, Pages 599–603 in Proceedings of IV International Conference on Application of Advanced Technologies in Transportation Engineering (AATT), Y. J. Stephanedes and F. Filippi (eds), American Society of Civil Engineers (ASCE). Astarita, V., 1996. A continuous time link model for dynamic network loading based on travel time function. Pages 79-103 in Transportation and Traffic Theory: Proceedings of the 13th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. J.-B. Lesort). Pergamon/ Elsevier. Astarita, V., Er-Rafia, K., Florian, M., Mahut, M., Velan, S. 2001. Comparison of three methods for dynamic network loading. Transportation Research Record, 1771:179-190. Bliemer, B.C.J., 2006. Dynamic queuing and spillback in an analytical multiclass dynamic traffic assignment model. In: Proceedings of the 1st International Symposium on Dynamic Traffic Assignment, held 21-23 June 2006, The University of Leeds, UK. Boyce, D., Lee, D.-H., Ran, B., 2001. Analytical models of the dynamic traffic assignment problem. Networks and Spatial Economics 1(3-4), 377–390. Carey, M., 2004. Link travel times I: desirable properties. Networks and Spatial Economics 4(3), 257-268. Carey, M. and Ge, Y.E., 2003a. Comparing whole-link travel time models. Transportation Research Part B 37(10), 905–926. Carey, M. and Ge, Y.E., 2003b. Dynamic Traffic Assignment (DTA) Models for Road Traffic Networks, A bibliography for dynamic traffic assignment (1970 to August 2003). http://www.qub.ac.uk/research-centres/TransportResearch/NetworkAssignmentandSimulation/ (accessed 19 Oct. 2013). Carey, M. and Ge, Y.E., 2004. Efficient discretisation of link travel time models. Networks and Spatial Economics 4(3), 269-290. Carey, M. and Ge, Y.E., 2005a. Convergence of whole-link travel time models used in DTA. Transportation Science 39(1), 25-38. Carey, M. and Ge, Y.E. 2005b. Alternative conditions for a well-behaved travel-time model. Transportation Science 39(3), 417–428. Carey, M., McCartney, M., 2002. Behavior of a whole-link travel time model used in dynamic traffic assignment. Transportation Research Part B 36(1), 83–95. Carey, M., Subrahmanian, E., 2000. An approach to modelling time-varying flows on congested networks. Transportation Research Part B 34(3), 157–183. Cayford, R., Lin, W.-H. and Daganzo, C.F., 1997. The NETCELL simulation package: technical description. PATH Research Report UCB-ITS-PRR-97-23. Department of Civil Engineering and Institute of Transportation Studies, University of California, Berkeley, CA. Celikoglu, H.B., 2007. A dynamic network loading model for traffic dynamics modeling, IEEE Transactions on Intelligent Transportation Systems 8(4), 575-583. Chen, H.-K., (1999). Dynamic travel choice models: a variational inequality approach. Springer, Heidelberg. Chen, H.-K., and Hsueh, C.F., (1998). A model and an algorithm for the dynamic user-optimal route choice problem. Transportation Research Part B 32(3), 219-234. Chiu, Y.-C., Bottom, J., Mahut, M., Paz, A., Balakrishna, R., Waller,T. and Hicks, J., 2011. Dynamic Traffic Assignment A Primer. Transportation Research Circular E-C153. For the Transportation Network Modeling Committee of the Transportation Research Board, Washington, DC. Chow, A.H.F., 2009) Properties of dynamic system optimal assignment and its solution method. Transportation Research Part B 43(3), 325-344. Daganzo, C.F., 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B 28(4), 269–287. Daganzo, C.F., 1995a. The cell transmission model part II: network traffic. Transportation Research Part B 29(2), 79–93. Daganzo, C.F., 1995b. Properties of link travel time functions under dynamic loads. Transportation Research Part B 29(2), 95-98. Daganzo, C.F., 1995c. A finite difference approximation of the kinematic wave model of traffic flow. Transportation Research Part B 29(4), 261–276. Fernandez, J.E. and De Cea, J. 1994. Flow Propagation Description in Dynamic Network Assignment Models. TRISTAN II Triennial International Symposium on Transportation Analysis, Capri, June 1994. Friesz, T.L., Bernstein, D., Smith, T.E., Tobin, R.L. and Wei, B.W., 1993. A variational inequality formulation of the dynamic network equilibrium problem. Operation Research 41(1), 179–191. Friesz, T.L. and Bernstein, D., 2007. Analytical dynamic traffic assignment models. Pages 221-237 in D.A. Hensher and K.J. Button, eds. Handbook of transport modelling. Second Edition. Elsevier Science. Friesz, T.L., Bernstein, D., Suo, Z., Tobin, R.L., 2001. Dynamic network user equilibrium with state-dependent time lags. Networks and Spatial Economics 1(3-4), 319–347. Friesz, T.L., Luque, F., Smith, R., Wie, B.W., 1989. Dynamic network traffic assignment considered as a continuous time optimal control problem. Operations Research 37(6), 893–901. Friesz, T.L. and Mookherjee, R., 2006. Solving the dynamic network user equilibrium problem with state-dependent time shifts. Transportation Research Part B 40(3), 207–229. García-Ródenas, R., López-García, M.L., Niño-Arbelaez, A. and Verastegui-Rayo, D., 2006. A continuous whole-link travel time model with occupancy constraint. European Journal of Operational Research 175(3), 1455-1471. Ge, Y.E. and Carey, M. 2004. Travel time computation of link and path flows and first-in-first-out. Pages 326-335 in Proceedings of the 4th International Conference on Traffic and Transportation Studies,(ICTTS), B. Mao, Z. Tian and Q. Sun (eds). Held August 2-4, 2004, Dalian, China. Beijing: Science Press. Gentile G., Meschini L., Papola N., 2007. Spillback congestion in dynamic traffic assignment: a macroscopic flow model with time-varying bottlenecks, Transportation Research Part B 41(10), 1114-1138. Heydecker, B.G., Addison, J.D., 1966. An exact expression of dynamic equilibrium, Pages 359-384 in Transportation and Traffic Theory: Proceedings of the 13th International Symposium on Transportation and Traffic Theory (ISTTT), (ed. J.-B. Lesort). Pergamon/ Elsevier. Heydecker, B.G., Addison, J.D., 1998. Analysis of traffic models for dynamic equilibrium traffic assignment. In: Bell, M.G.H. (Ed.), Transportation Networks: Recent Methodological Advances. Pergamon, Oxford, pp. 35–49. Huang, H.J. and Lam, W.H.K., 2002. Modeling and solving dynamic user equilibrium route and departure time choice problem in network with queues. Transportation Research Part B 36(3), 253-273. Jayakrishnan, R., Tsai, W.K. and Chen, A., 1995. A dynamic traffic assignment model with traffic-flow relationships. Transportation Research Part C 3(1), 51–72. Jin, W.L. and Li, L., 2007. First-in-first-out is violated in real traffic. Proceedings of Transportation Research Board Annual Meeting, 2007, Washington DC, USA. Jin, W.L., Zhang, Y. and Chu, L., 2006. Measuring first-in-first-out violation among vehicles. Proceedings of Transportation Research Board Annual Meeting, 2006, Washington DC, USA. Kachani, S. and Perakas, G., 2009. A dynamic travel time model for spillback. Networks and Spatial Economics 9(4), 595-618. Lin, W.-H. and Liu, H., 2010. Enhancing realism in modeling merge junctions in analytical models for system-optimal dynamic traffic assignment. IEEE Transactions on Intelligent Transportation Systems 11(4), 838-845. Long, J., Gao, Z. and Szeto, W.Y., 2001. Discretised link travel time models based on cumulative flows: Formulations and properties. Transportation Research Part B 45(1), 232-254. Magumba, B., 2007. Dynamic modelling of queue spillbacks. Thesis for MSc (Eng) Transport Planning and Engineering, Institute for Transport Studies, University of Leeds, UK. Mun, J.-S., 2007. Traffic Performance Models for Dynamic Traffic Assignment: An Assessment of Existing Models. Transport Reviews 27(2), 231-249. Mun, J.-S., 2009. Some features of non-linear travel time models for dynamic traffic assignment. Transportation Planning and Technology 32(3), 261-288. Nie, X. and Zhang, H.M., 2005a. Delay-function-based link models: their properties and computational issues. Transportation Research Part B 39(8), 729–751. Nie, X. and Zhang, H.M., 2005b. A comparative study of some macroscopic link models used in dynamic traffic assignment. Networks and Spatial Economics 5(1), 89-115. Peeta, S. and Ziliaskopoulos, A., 2001. Foundations of dynamic traffic assignment: the past, the present and the future. Networks and Spatial Economics 1(3-4), 233–265. Ran, B., Boyce, D.E., LeBlanc, L.J., 1993. A new class of instantaneous dynamic user-optimal traffic assignment models. Operations Research 41(1), 192–202. Ran, B., Boyce, D.E., 1996. A link-based variational inequality formulation of ideal dynamic optimal route choice problem. Transportation Research Part C 4(1), 1–12. Ran, B., Lo, H. and Boyce, D.E., 1996. A formulation and solution algorithm for a multi-class dynamic traffic assignment problem. In Lesort (ed.), Transportation and Traffic Theory, Pergamon-Elservier, New York, 195-216. Rubio-Ardanaz, J.M., Wu, J.H. and Florian, M., 2001. A numerical analytical model for the continuous dynamic network equilibrium problem with limited capacity and spillback. In: The IEEE Intelligent Transportation Systems Conference Proceedings, 25-29 August 2001, Oakland, CA, USA. pp. 263-267. Rubio-Ardanaz, J.M., Wu, J.H. and Florian, M. 2003. Two improved numerical algorithms for the continuous dynamic network loading problem. Transportation Research Part B 37(2), 171–190. Szeto, W.Y. and Lo, H.K., 2005. Dynamic Traffic assignment: review and future research directions. Journal of Transportation Systems Engineering and Information Technology 5(5), 85-100. Szeto, W.Y. and Lo, H.K., 2006. Dynamic traffic assignment: properties and extensions. Transportmetrica 2(1), 31-52. Wie, B., Tobin, R. and Carey, M., 2002. The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation. Transportation Research Part B 36(10), 897–918. Wu, J.H., Chen, Y. and Florian, M., 1995. The continuous dynamic network loading problem: a mathematical formulation and solution method. Presented at the 3rd Euro Working Group Meeting on Urban traffic and transportation, Barcelona, 27–29 September. Wu, J.H., Chen, Y. and Florian, M., 1998. The continuous dynamic network loading problem: a mathematical formulation and solution method. Transportation Research Part B 32(3), 173–187. Xu, Y. W., Wu, J. H., Florian M. (1998) An efficient algorithm for the continuous network loading problem: a DYNALOAD implementation. Transportation Networks: Recent Methodological Advances, M.G.H. Bell (ed), 51-66, Pergamon. Xu, Y.W., J.H. Wu, J.H, Florian, M., Marcotte, P. and Zhu, D.L., 1999. Advances in the continuous dynamic network loading problem. Transportation Science 33(4), 341–353. Yang, H. and Meng, Q., 1998. Departure time, route choice and congestion toll in a queuing network with elastic demand. Transportation Research Part B 32(4), 247-260. Yperman, I., 2007. The link transmission model for dynamic network loading. PhD Thesis, Katholieke Universiteit Leuven, Belgium. Zhang, H.M. and Nie, X., 2005. Some consistency conditions for dynamic traffic assignment problems. Networks and Spatial Economics 5(1), 71-87. Zhu, D. and Marcotte, P., 2000. On the existence of solutions to the dynamic user equilibrium problem. Transportation Science 34(4), 402-414.

PY - 2014/7

Y1 - 2014/7

N2 - An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first-in-first-out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems.To remove problems (a) and (b) we extend the link travel-time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel-time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.

AB - An important class of models for macroscopic dynamic network loading (DNL) and dynamic traffic assignment (DTA) is based on treating link travel times as a function of link occupancy. However, these models suffer from some problems or deficiencies namely (a) the link outflows can violate first-in-first-out (FIFO), (b) the link outflows can exceed the link outflow capacities, (c) the link inflows can exceed the link inflow capacities, and (d) the link occupancies can exceed the link occupancy capacities. In this paper we introduce methods to overcome each of these problems.To remove problems (a) and (b) we extend the link travel-time model to better reflect behaviour when traffic flow is varying over time. To remove problems (c) and (d) we introduce more substantial changes in the model, to introduce capacities, spillback and queues compatible with the model. These extensions strengthen the realism, behavioural basis and usability of the link travel-time model and the DNL and DTA models that are based on it. They have no obvious adverse implications or side effects and require little additional computational effort. The original model is a special case of the new/extended model: the above extensions are activated if and only if any of the problems (a)–(d) arise, otherwise the new model reduces to the original model.

KW - Travel-time functions

KW - First-in-first-out

KW - Link flow capacity

KW - Spillback

KW - Dynamic network loading

KW - Dynamic traffic assignment

U2 - 10.1016/j.trb.2014.04.002

DO - 10.1016/j.trb.2014.04.002

M3 - Article

VL - 65

SP - 90

EP - 104

JO - Transportation Research Part B: Methodological

T2 - Transportation Research Part B: Methodological

JF - Transportation Research Part B: Methodological

SN - 0191-2615

ER -