Estimating the Capacity of Urban Transportation Networks with an Improved Sensitivity Based Method

The throughput of a given transportation network is always of interest to the traffic administrative department, so as to evaluate the benefit of the transportation construction or expansion project before its implementation. The model of the transportation network capacity formulated as a mathematic programming with equilibrium constraint (MPEC) well defines this problem. For practical applications, a modified sensitivity analysis based (SAB) method is developed to estimate the solution of this bilevel model. The high-efficient origin-based (OB) algorithm is extended for the precise solution of the combined model which is integrated in the network capacity model. The sensitivity analysis approach is also modified to simplify the inversion of the Jacobian matrix in large-scale problems. The solution produced in every iteration of SAB is restrained to be feasible to guarantee the success of the heuristic search. From the numerical experiments, the accuracy of the derivatives for the linear approximation could significantly affect the converging of the SAB method. The results also show that the proposed method could obtain good suboptimal solutions from different starting points in the test examples.

[1]  Hai Yang,et al.  Sensitivity Analysis of Network Traffic Equilibrium Revisited: The Corrected Approach , 2007 .

[2]  Shing Chung Josh Wong,et al.  Reserve capacity of a signal-controlled road network , 1997 .

[3]  Hai Yang.  Heuristic algorithms for the bilevel origin-destination matrix estimation problem , 1995 .

[4]  Hai Yang,et al.  Traffic assignment and signal control in saturated road networks , 1995 .

[5]  Hai Yang,et al.  Modeling the capacity and level of service of urban transportation networks , 2000 .

[6]  Hai Yang,et al.  An algorithm for the inflow control problem on urban freeway networks with user-optimal flows , 1994 .

[7]  M. Bell.  STOCHASTIC USER EQUILIBRIUM ASSIGNMENT IN NETWORKS WITH QUEUES , 1995 .

[8]  Anthony Chen,et al.  Modeling capacity flexibility of transportation networks , 2011 .

[9]  Stephen D. Clark,et al.  Probit-Based Sensitivity Analysis for General Traffic Networks , 2000 .

[10]  Michael G. H. Bell,et al.  Reserve Capacity for a Road Network Under Optimized Fixed Time Traffic Signal Control , 2004, J. Intell. Transp. Syst..

[11]  Song Yifan,et al.  A reserve capacity model of optimal signal control with user-equilibrium route choice , 2002 .

[12]  Anthony Chen,et al.  ANALYSIS OF TRANSPORTATION NETWORK CAPACITY RELATED TO DIFFERENT SYSTEM CAPACITY CONCEPTS , 2005 .

[13]  Hai Yang,et al.  An equivalent continuously differentiable model and a locally convergent algorithm for the continuous network design problem , 2001 .

[14]  Norbert Oppenheim.  Equilibrium trip distribution/assignment with variable destination costs , 1993 .

[15]  Suh-Wen Chiou,et al.  Optimization of Area Traffic Control for Equilibrium Network Flows , 1999, Transp. Sci..

[16]  Suh-Wen Chiou,et al.  Bilevel programming for the continuous transport network design problem , 2005 .

[17]  David E. Boyce,et al.  Origin-based algorithms for combined travel forecasting models , 2003 .

[18]  Hesham Rakha,et al.  Sensitivity Analysis of Combined Distribution–Assignment Model with Applications , 2012 .

[19]  Terry L. Friesz,et al.  Sensitivity Analysis for Equilibrium Network Flow , 1988, Transp. Sci..

[20]  Huijun Sun,et al.  A continuous equilibrium network design model and algorithm for transit systems , 2004 .

[21]  Neil Genzlinger.  A. and Q , 2006 .

[22]  Hillel Bar-Gera,et al.  Origin-Based Algorithm for the Traffic Assignment Problem , 2002, Transp. Sci..

[23]  Jiang Qian Ying,et al.  Sensitivity Analysis for Stochastic User Equilibrium Network Flows - A Dual Approach , 2001, Transp. Sci..

[24]  William H. K. Lam,et al.  Maximum car ownership under constraints of road capacity and parking space , 2000 .

[25]  Hai Yang,et al.  Sensitivity analysis for the elastic-demand network equilibrium problem with applications , 1997 .

[26]  Terry L. Friesz,et al.  Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints , 1990, Math. Program..

[27]  Stephen D. Clark,et al.  Sensitivity analysis of the probit-based stochastic user equilibrium assignment model , 2002 .

[28]  Ziyou Gao,et al.  An improved origin-based algorithm for solving the combined distribution and assignment problem , 2008, Eur. J. Oper. Res..

[29]  Chao Yang,et al.  Sensitivity analysis of the combined travel demand model with applications , 2009, Eur. J. Oper. Res..