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Dynamic User Equilibrium Model for Combined Activity-Travel Choices Using Activity-Travel Supernetwork Representation

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Abstract

Integrated urban transportation models have several benefits over sequential models including consistent solutions, quicker convergence, and more realistic representation of behavior. Static models have been integrated using the concept of Supernetworks. However integrated dynamic transport models are less common. In this paper, activity location, time of participation, duration, and route choice decisions are jointly modeled in a single unified dynamic framework referred to as Activity-Travel Networks (ATNs). ATNs is a type of Supernetwork where virtual links representing activity choices are added to augment the travel network to represent additional choice dimensions. Each route in the augmented network represents a set of travel and activity arcs. Therefore, choosing a route is analogous to choosing an activity location, duration, time of participation, and travel route. A cell-based transmission model (CTM) is embedded to capture the traffic flow dynamics. The dynamic user equilibrium (DUE) behavior requires that all used routes (activity-travel sequences) provide equal and greater utility compared to unused routes. An equivalent variational inequality problem is obtained. A solution method based on route-swapping algorithm is tested on a hypothetical network under different demand levels and parameter assumptions.

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Notes

  1. Includes departure time options 7:00, 7:05, ... 7:35 and 4 travel routes

  2. Including 4 locations, 2 travel routes, and 6 non-work activity duration options for individuals departing at 7:00 AM and 7:05 AM, 5 for 7:10 AM departures, 4 for 7:15 AM departures and so on - totaling to 27 activity duration combinations.

References

  • Abdelghany AF, Mahmassani HS, Chiu YC (2001) Spatial microassignment of travel demand with activity trip chains. Transp Res Rec 1777:36–46

    Article  Google Scholar 

  • Abdelghany AF, Mahmassani HS, Chiu YC (2003) Spatial microassignment of travel demand with activity trip chains. Transp Res Rec 1831:89–97

    Article  Google Scholar 

  • Ban XJ, Liu HX, Ferris MC, Ran B (2008) A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations. Transp Res Part B Methodol 42(9):823–842

    Article  Google Scholar 

  • Ben-Akiva M, Bierlaire M, Burton D, Koutsopoulos HN, Mishalani R (2001) Network state estimation and prediction for real-time traffic management. Netw Spatial Econ 1(3–4):293–318

    Article  Google Scholar 

  • Boyce D, Lee DH, Ran B (2001) Analytical models of the dynamic traffic assignment problem. Netw Spatial Econ 1(3-4):377–390

    Article  Google Scholar 

  • Carey M (2001) Dynamic traffic assignment with more flexible modelling within links. Netw Spatial Econ 1(3-4):349–375

    Article  Google Scholar 

  • Daganzo CF (1994) The cell transmission model: a simple dynamic representation of highway traffic. Transp Res Part B 28:269–287

    Article  Google Scholar 

  • Daganzo CF (1995) The cell transmission model, part ii: network traffic. Transp Res Part B 29:79–93

    Article  Google Scholar 

  • de Palma A, Marchal F (2002) Network state estimation and prediction for real-time traffic management. Netw Spatial Econ 2(4):347–369

    Article  Google Scholar 

  • Friesz TL, Bernstein D, Smith TE, Tobin RL, Wie BW (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res 41:179–191

    Article  Google Scholar 

  • Friesz TL, Bernstein D, Suo Z, Tobin R (2001) Dynamic network user equilibrium with state-dependent time lags. Netw Spatial Econ 1(3–4):319–347

    Article  Google Scholar 

  • Gartner N, Messer C, Rath A (eds) (2001) Monograph on traffic flow theory. Special Report of Transportation Research Board

  • Huang HJ, Lam WHK (2002) Modeling and solving the dynamic user equilibrium route and departure time choice problem in network with queues. Transp Res Part B 36:253–273

    Article  Google Scholar 

  • Kim H, Oh JS, Jayakrishnan R (2006) Activity chaining model incorporating time use problem and its application to network demand analysis. In: Proceedings of the 85th transportation research board meeting, Washington DC, January 2006

  • Lam WH, Huang HJ (2003) Combined activity/travel choice models: time-dependent and dynamic versions. Netw Spatial Econ 3:323–347

    Article  Google Scholar 

  • Lo HK, Szeto W (2002) A cell-based variational inequality formulation of the dynamic user optimal assignment problem. Transp Res Part B 36:421–443

    Article  Google Scholar 

  • Mahmassani HS (2001) Dynamic network traffic assignment and simulation methodology for advanced system management applications. Netw Spatial Econ 1(3–4):267–292

    Article  Google Scholar 

  • Mounce R, Carey M (2008) Route swap processes and convergence measures in dynamic traffic assignment. In: 2nd international symposium on dynamic traffic assignment, Leuven, 18–20 June 2008

  • Nagurney A, Zhang D (1997) Projected dynamical systems in the formulation, stability analysis, and computation of fixed-demand traffic network equilibria. Transp Sci 31:147–158

    Article  Google Scholar 

  • Nokel K, Schmidt M (2002) Parallel dynemo: meso-scopic traffic flow simulation on large networks. Netw Spatial Econ 2(4):387–403

    Article  Google Scholar 

  • Peeta S, Ziliaskopoulos A (2001) Foundations of dynamic traffic assignment: the past, the present and the future. Netw Spatial Econ 1(3–4):233–265

    Article  Google Scholar 

  • Ran B, Boyce D (1996) Modeling dynamic transportation networks: an intelligent transportation systems oriented approach (second revised ed). Springer, New York

    Google Scholar 

  • Ran B, Hall RW, Boyce D (1996) A link-based variational inequality model for dynamic departure time/route choice. Transp Res Part B 30:31–46

    Article  Google Scholar 

  • Rieser M, Nagel K, Beuck U, Balmer M, Rümenapp J (2007) Agent-oriented coupling of activity-based demand generation with multiagent traffic simulation. Transp Res Rec 2021:10–17

    Article  Google Scholar 

  • Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall Inc, Englewood Cliffs

    Google Scholar 

  • Sheffi Y, Daganzo C (1979) Hypernetworks and supply-demand equilibrium obtained with disaggregate demand models. Transp Res Rec 673:113–121

    Google Scholar 

  • Sheffi Y, Daganzo C (1980) Computation of equilibrium over transportation networks: the case of disaggregate demand models. Transp Sci 14(2):155–173

    Article  Google Scholar 

  • Szeto W, Lo HK (2006) Dynamic traffic assignment: properties and extensions. Transportmetrica 2:31–52

    Article  Google Scholar 

  • Szeto WY, Lo HK (2004) A cell-based simultaneous route and departure time choice model with elastic demand. Transp Res Part B 38:593–612

    Article  Google Scholar 

  • Wardrop J (1952) Some theoretical aspects of road traffic research. In: Proceedings of the Institute of Civil Engineers, Part II, pp 325–378

  • Wie BW, Tobin RL, Carey M (2002) The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation. Transp Res Part B 36:897–918

    Article  Google Scholar 

  • Zhang HM, Nie X (2005) Some consistency conditions for dynamic traffic assignment problems. Netw Spatial Econ 5(1):71–87

    Article  Google Scholar 

  • Zhang X, Zhang HM (2007) Simultaneous departure time/route choices in queuing networks and a novel paradox. Netw Spat Econ. doi:10.1007/s11067-007-9026-7

  • Zhang X, Yang H, Huang HJ, Zhang HM (2005) Integrated scheduling of daily work activities and morning–evening commutes with bottleneck congestion. Transp Res Part A 39:41–60

    Google Scholar 

  • Ziliaskopoulos A (2000) A linear programming model for the single destination system optimum dta problem. Transp Sci 34:37–49

    Article  Google Scholar 

Download references

Acknowledgements

We thank two anonymous referees for their comments on an earlier version of the paper. Parts of this work were supported by September 11th Memorial Program for Regional Transportation Planning administered by the New York Metropolitan Transportation Council (NYMTC) and the Emerging Scholars Grant from the University Transportation Research Center, New York City. Any opinions, findings, and conclusions expressed in this paper are those of the authors.

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Correspondence to Satish Ukkusuri.

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Ramadurai, G., Ukkusuri, S. Dynamic User Equilibrium Model for Combined Activity-Travel Choices Using Activity-Travel Supernetwork Representation. Netw Spat Econ 10, 273–292 (2010). https://doi.org/10.1007/s11067-008-9078-3

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