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A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time

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Abstract

This paper presents a cumulative perceived value-based dynamic user equilibrium model by applying the prospect theory to formulate the travelers’ risk evaluation on arrival time. The network uncertainty caused by link exit capacity degradation is incorporated into the analysis. The model which considers departure time and route choices simultaneously is expressed by a variational inequality in a discrete time space. Numerical results show that the travelers’ risk preference indeed has big influence on flow distribution. Our study constitutes a deepening of cognition in develo** more realistic dynamic traffic assignment technologies.

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References

  • Avineri E (2004) A cumulative prospect theory approach to passengers behavior modeling: waiting time paradox revisited. J Intell Transp Syst 8:195–204

    Article  Google Scholar 

  • Avineri E (2006) The effect of reference point on stochastic network equilibrium. Transp Sci 40:409–420

    Article  Google Scholar 

  • Avineri E, Prashker JN (2003) Sensitivity to uncertainty-need for a paradigm shift. Transp Res Record 1854:90–98

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Bates J, Polak JW, Jones P, Cook A (2001) The valuation of reliability for personal travel. Transp Res 37E:191–229

    Google Scholar 

  • Bell MGH, Cassir C (2002) Risk-averse user equilibrium traffic assignment: an application of game theory. Transp Res 36B:671–681

    Article  Google Scholar 

  • Carey M (1987) Optimal time-varying flows on congested networks. Oper Res 35:58–69

    Article  Google Scholar 

  • Carey M, Ge YE (2011) Comparison of methods for path flow reassignment for dynamic user equilibrium. Netw Spat Econ, online available

  • Chen HK, Hsueh CF (1998) A model and an algorithm for the dynamic user-optimal route choice problem. Transp Res 32B:219–234

    Article  Google Scholar 

  • Chen HK, Chang MS, Wang CY (2001) Dynamic capacitated user-optimal departure time/path choice problem with time-window. Eur J Oper Res 132:603–618

    Article  Google Scholar 

  • Chow AHF (2009) Properties of system optimal traffic assignment with departure time choice and its solution method. Transp Res 43B:325–344

    Article  Google Scholar 

  • Chung BD, Yao T, **e C, Thorsen A (2011) Robust optimization model for a dynamic network design problem under demand uncertainty. Netw Spat Econ 11:371–389

    Article  Google Scholar 

  • Connors RD, Sumalee A (2009) A network equilibrium model with travelers’ perception of stochastic travel times. Transp Res 43B:614–624

    Article  Google Scholar 

  • Friesz TL, Luque J, Tobin RL, Wie BW (1989) Dynamic network traffic assignment considered as a continuous time optimal control problem. Oper Res 37:893–901

    Article  Google Scholar 

  • Friesz TL, Bernstein DH, 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 

  • Henn V, Ottomanelli M (2006) Handling uncertainty in path choice models: from probabilistic to possibilistic approaches. Eur J Oper Res 175:1526–1538

    Article  Google Scholar 

  • Heydecker BG, Addison JD (1998) Analysis of traffic models for dynamic equilibrium traffic assignment. In: Bell MGH (ed) Transportation Networks: Recent Methodological Advance. Pergamon, Oxford, pp 35–49

    Google Scholar 

  • Heydecker BG, Addison JD (2005) Analysis of dynamic traffic equilibrium with departure time choice. Transp Sci 39:39–57

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Jauffred FJ, Bernstein D (1996) An alternative formulation of the simultaneous path and departure-time choice equilibrium problem. Transp Res 4C:337–357

    Google Scholar 

  • Jou RC, Kitamura R, Weng MC, Chen CC (2008) Dynamic commuter departure time choice under uncertainty. Transp Res 42A:774–783

    Google Scholar 

  • Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Econometrica 47:263–291

    Article  Google Scholar 

  • Kuwahara M, Akamatsu T (1993) Dynamic equilibrium assignment with queues for a one-to-many OD pattern. In: Proc 12th Int Symp Transp Traffic Theory. Berkeley, Elsevier, pp 185–204

  • Kuwahara M, Akamatsu T (1997) Decomposition of the reactive dynamic assignment with queues for a many-to-many origin-destination pattern. Transp Res 31B:1–10

    Article  Google Scholar 

  • Lam WHK, Shao H, Sumalee A (2008) Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply. Transp Res 42B:890–910

    Article  Google Scholar 

  • Lim Y, Heydecker B (2005) Dynamic departure time and stochastic user equilibrium assignment. Transp Res 39B:97–118

    Article  Google Scholar 

  • Lo HK, Tung YK (2003) Network with degradable links: capacity analysis and design. Transp Res 37B:345–363

    Article  Google Scholar 

  • Lo HK, Luo XW, Siu BWY (2006) Degradable transport network: travel time budget of travellers with heterogeneous risk aversion. Transp Res 40B:792–806

    Article  Google Scholar 

  • Lu SF, Liu XM, Dai SQ (2008) A prospect theory and discrete choice integration approach to simultaneous path choice modeling. XV Pan-American Conf Traffic Transp Eng, Cartagena de Indias, Colombia

  • Luque FJ, Friesz TL (1980) Dynamic traffic assignment considered as a continuous time optimal control problem. TIMS/ORSA Joint Natl Meeting, Washington, DC

    Google Scholar 

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

    Article  Google Scholar 

  • Merchant DK, Nemhauser GL (1978a) A model and an algorithm for the dynamic traffic assignment problem. Transp Sci 12:183–199

    Article  Google Scholar 

  • Merchant DK, Nemhauser GL (1978b) Optimality conditions for a dynamic traffic assignment model. Transp Sci 12:200–207

    Article  Google Scholar 

  • Nie Y, Zhang HM (2010) Solving the dynamic user optimal assignment problem considering queue spillback. Netw Spat Econ 10:49–71

    Article  Google Scholar 

  • Noland RB, Polak JW (2002) Travel time variability: a review of theoretical and empirical issues. Transp Rev 22:39–54

    Article  Google Scholar 

  • Noland RB, Small KA (1995) Travel time uncertainty, departure time choice and the cost of the morning commute. Transp Res Record 1493:150–158

    Google Scholar 

  • Noland RB, Small KA, Koskenpja PM, Chu X (1998) Simulating travel reliability. Reg Sci Urban Econ 28:535–564

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Prelec D (1998) The probability weighting function. Econometrica 66:497–527

    Article  Google Scholar 

  • Ramadurai G, Ukkusuri S (2010) Dynamic user equilibrium model for combined activity-travel choices using activity-travel supernetwork representation. Netw Spat Econ 10:273–292

    Article  Google Scholar 

  • Ran B, Boyce DE, LeBlanc LJ (1992) Dynamic user-optimal path choice models based on stochastic path travel times. Sec Int Capri Sem Urban Traffic Netw

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

    Article  Google Scholar 

  • Senbil M, Kitamura R (2004) Reference points in commuter departure time choice: a prospect theoretic test of alternative decision frames. J Intell Transp Sys 8:19–31

    Article  Google Scholar 

  • Shao H, Lam WHK, Tam ML (2006) A Reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand. Netw Spat Econ 6:173–204

    Article  Google Scholar 

  • Siu BWY, Lo HK (2008) Doubly uncertain transport network: degradable capacity and stochastic demand. Eur J Oper Res 191:166–181

    Article  Google Scholar 

  • Siu BWY, Lo HK (2009) Equilibrium trip scheduling in congested traffic under uncertainty. In: Pro of the 18th Int Symp Transp Traffic Theory. Springer, pp 147–168

  • Sumalee A, Connors RD, Luathep P (2009) Network equilibrium under cumulative prospect theory and endogenous stochastic demand and supply. In: Pro of the 18th Int Symp Transp Traffic Theory. Springer, pp 19–38

  • Szeto W, O’Brien L, O’Mahony M (2006) Risk-averse traffic assignment with elastic demands: Ncp formulation and solution method for assessing performance reliability. Netw Spat Econ 6:313–332

    Article  Google Scholar 

  • Tversky A, Kahneman D (1992) Advances in prospect-theory-cumulative representation of uncertainty. J Risk Uncert 5:297–323

    Article  Google Scholar 

  • Vickrey WS (1969) Congestion theory and transport investment. Am Econ Rev 59:251–260

    Google Scholar 

  • Watling D (2002) A second order stochastic network equilibrium model, I: theoretical foundation. Transp Sci 36:149–166

    Article  Google Scholar 

  • Watling D (2006) User equilibrium traffic network assignment with stochastic travel times and late arrival penalty. Eur J Oper Res 175:1539–1556

    Article  Google Scholar 

  • Wie BW, Tobin RL (1998) Dynamic congestion pricing models for general traffic networks. Transp Res 32B:313–327

    Article  Google Scholar 

  • Wie BW, Friesz TL, Tobin RL (1990) Dynamic user optimal traffic assignment on congested multidestination networks. Transp Res 24B:431–442

    Article  Google Scholar 

  • Wie BW, Tobin RL, Friesz TL, Bernstein DH (1995) A discrete time, nested cost operator approach to the dynamic network user equilibrium. Transp Sci 29:79–92

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Yang H, Huang HJ (1997) Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory. Transp Res 31B:425–440

    Article  Google Scholar 

  • Zhang X, Zhang HM (2010) Simultaneous departure time/route choices in queuing networks and a novel paradox. Netw Spat Econ 10:93–112

    Article  Google Scholar 

Download references

Acknowledgements

The research described in this paper was substantially supported by grants from the National Natural Science Foundation of China (70821061, 70931160447), the National Basic Research Program of China (2006CB705503) and the BUAA Innovative Research Foundation for PhD students.

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Correspondence to Hai-Jun Huang.

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Tian, LJ., Huang, HJ. & Gao, ZY. A Cumulative Perceived Value-Based Dynamic User Equilibrium Model Considering the Travelers’ Risk Evaluation on Arrival Time. Netw Spat Econ 12, 589–608 (2012). https://doi.org/10.1007/s11067-011-9168-5

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