Method of Parameter Calibration for Error Term in Stochastic User Equilibrium Traffic Assignment Model

Stochastic User Equilibrium (SUE) model is a widely
used traffic assignment model in transportation planning, which is
regarded more advanced than Deterministic User Equilibrium (DUE)
model. However, a problem exists that the performance of the SUE
model depends on its error term parameter. The objective of this
paper is to propose a systematic method of determining the
appropriate error term parameter value for the SUE model. First, the
significance of the parameter is explored through a numerical
example. Second, the parameter calibration method is developed
based on the Logit-based route choice model. The calibration process
is realized through multiple nonlinear regression, using sequential
quadratic programming combined with least square method. Finally,
case analysis is conducted to demonstrate the application of the
calibration process and validate the better performance of the SUE
model calibrated by the proposed method compared to the SUE
models under other parameter values and the DUE model.

• Xiang Zhang
• David Rey
• S. Travis Waller

• Parameter calibration
• sequential quadratic programming
• Stochastic User Equilibrium
• traffic assignment
• transportation planning.

[1] Ralf Sprenger, Lars Mönch, “A methodology to solve large-scale
cooperative transportation planning problems,” European Journal of
Operational Research, vol. 223, 2012, pp. 626–636.
[2] Reza Zanjirani Farahani, Elnaz Miandoabchi, W.Y.Szeto, Hannaneh
Rashidi, “A review of urban transportation network design problems,”
European Journal of Operational Research, Vol.229, 2013, pp. 281–
302.
[3] Si, B., Ming, Z., “An improved dial’s algorithm for logit-based traffic
assignment within directed acyclic network,” Transportation Planning
and Technology, vol. 33, no. 2, 2010, pp. 123–137.
[4] Wardrop, J. G. “Some theoretical aspects of road traffic research,”
Proceedings of the Institution of Civil Engineers, vol. 1, no. 2, 1952, pp.
325–378.
[5] Patriksson M, The Traffic Assignment Problems: Models and Methods.
VSP: Utrecht, the Netherlands, 1994, pp.25–71.
[6] Sheffi Y, Urban Transportation Networks: Equilibrium Analysis with
Mathematical Programming Models. Prentice Hall, INC: Englewood
Cliffs, New Jersey, 1985, pp. 2-46.
[7] Zhou, J, “Stochastic user equilibrium assignment model with its
equivalent variational inequality problem,” Journal of Systems Science
and Mathematical Science, vol. 1, 2003, pp. 120–127.
[8] Bekhor, S., Toledo, T., “Investigating path-based solution algorithms to
the stochastic user equilibrium problem,” Transportation Research Part
B, vol. 39, no. 3, 2005, pp. 279–295.
[9] Bekhor, S., Toledo, T., Reznikova, L., “A path-based algorithm for the
cross-nested logit stochastic user equilibrium,” Computer-Aided Civil
and Infrastructure Engineering, vol. 24, no. 1, 2008, pp. 15–25.
[10] Sheffi, Y., Powell, W., “A comparison of stochastic and deterministic
traffic assignment over congested networks,” Transportation Research
Part B, vol. 15, no. 1, 1981, pp. 53–64.
[11] Zhou, Z., Chen, A., Bekhor, S, “C-logit stochastic user equilibrium
model: formulations and solution algorithm,” Transportmetrica, vol. 8,
no. 1, 2012, pp. 17–41.
[12] Prashker, J.N., Bekhor, S., “Route choice models used in the stochastic
user equilibrium problem: a review,” Transport Reviews, vol. 24, 2004,
pp. 437–463.
[13] Liu, Z., & Meng, Q, “Distributed computing approaches for large-scale
probit-based stochastic user equilibrium problems,” Journal of
Advanced Transportation, vol. 47, no. 6, 2013, pp. 553–571.
[14] Joseph N. Prashker, Shlomo Bekhor, “Route Choice Models Used in the
Stochastic User Equilibrium Problem: A Review,” Transport Reviews,
vol. 24, no. 4, July 2004, pp. 437–463.
[15] Chen, A., Pravinvongvuth, S., et al. “Examining the scaling effect and
overlapping problem in logit-based stochastic user equilibrium models.”
Transportation Research Part A, vol. 46, no. 8, 2012, pp. 1343–1358.
[16] Anthony Chen, Surachet Pravinvongvuth, Xiangdong Xu, Seungkyu
Ryu, Piya Chootinan, “Examining the scaling effect and overlapping
problem in logit-based stochastic user equilibrium models,”
Transportation Research Part A, vol. 46, 2012, pp. 1343 – 1358.
[17] Fisk, C. “Some developments in equilibrium traffic assignment”,
Transportation Research Part B, vol. 14, no. 3, 1980, pp. 243–255.
[18] Roger P. Roess, Elena S. Prassas, and William R. McShane, Traffic
Engineering (4th Edition). Pearson Higher Education Inc., Upper Saddle
River, New Jersey, United States of America, 2010, pp. 274-315.
[19] Thomas R. Currin, Introduction to Traffic Engineering: A Manual for
Data Collection and Analysis. Australia: Pacific Grove, Calif.:
Brooks/Cole. 2001, pp. 45-128.
[20] G.A.F. Seber, and C.J. Wild, Nonlinear Regression, John Wiley & Sons
Inc., Hoboken, New Jersey, United States of America, 1989, pp. 21 –
190.
[21] Frank E. Curtis, and Michael L. Overton, “A Sequential Quadratic
Programming Algorithm for Nonconvex, Nonsmooth Constrained
Optimization,” Siam Journal On Optimization, vol.22, no.2, 2012,
pp.474-500.
[22] Marija J. Norusis, IBM SPSS Statistics 19 Advanced Statistical
Procedures Companion, Prentice Hall Inc., Upper Saddle River, New
Jersey, United States of America, 2012, pp. 195-340.