Method of successive weighted averages (MSWA) and self-regulated averaging schemes for solving stochastic user equilibrium problem

Networks and Spatial Economics

Volumn 9, Issue 4, 2009, Pages 485-503

  Liu, Henry X ^a   He, Xiaozheng ^a   He, Bingsheng ^b  

^a University of Minnesota   (United States)

^b NANJING UNIVERSITY   (China)

Author keywords

Method of successive averages (MSA); Method of successive weighted averages (MSWA); Self regulated averages; Stochastic user equilibrium

Indexed keywords

FLOW PATTERNS; STATISTICAL METHODS;

COMPUTATIONAL RESULTS; FIXED-POINT PROBLEM; ITERATION NUMBERS; METHOD OF SUCCESSIVE AVERAGES; SELF-REGULATED AVERAGES; STOCHASTIC USER EQUILIBRIUM; TRANSPORTATION NETWORK; WEIGHTED AVERAGES;

ITERATIVE METHODS;

EID: 84892922160     PISSN: 1566113X     EISSN: 15729427     Source Type: Journal    
DOI: 10.1007/s11067-007-9023-x     Document Type: Article

References (21)

1. Akamatsu T (1996) Cyclic flows, Markov process and stochastic traffic assignment. Transp Res Part B 30 (5):369-386
2. Bar-Gera H, Boyce D (2006) Solving a non-convex combined travel forecasting model by the method of successive averages with constant step sizes. Transp Res Part B 40(5):351-367
3. Bell MGH (1995) Alternative to Dial's logit assignment algorithm. Transp Res Part B 29(4):287-295
4. Blum JR (1954) Multidimensional stochastic approximation methods. Ann Math Stat 25(4):737-744
5. Bottom J, Ben-Akiva M, Bierlaire M, Chabini I, Koutsopoulos H, Yang Q (1999) Investigation of route guidance generation issues by simulation with DynaMIT. In: Ceder A (ed) Transportation and traffic theory. Proceedings of the 14th International Symposium on Transportation and Traffic Theory, Pergamon, Amsterdam, pp 577-600
6. Bottom J, Chabini I (2001) Accelerated averaging methods for fixed point problems in transportation analysis and planning. Triennial Symposium on Transportation Analysis (TRISTAN IV). São, Miguel, Azores, Preprints 1, 69-74
7. Cascetta E, Postorino MN (2001) Fixed point approaches to the estimation of O/D matrices using traffic counts on congested networks. Transp Sci 35(2):134-147
8. Chen M, Alfa AS (1991) Algorithms for solving Fisk's stochastic traffic assignment model. Transp Res Part B 25(6):405-412
9. Daganzo CF, Sheffi Y (1977) On stochastic models of traffic assignment. Transp Sci 11(3):253-274
10. Fisk C (1980) Some developments in equilibrium traffic assignment. Transp Res Part B 14(3):243-255
11. Frees E, Ruppert D (1990) Estimation following a sequentially designed experiment. J Am Stat Assoc 85:1123-1129
12. Magnanti TL, Perakis G (1997) Averaging schemes for variational inequalities and system of equations. Math Oper Res 22(3):568-587
13. Maher MJ (1998) Algorithms for logit-based stochastic user equilibrium assignment. Transp Res Part B 32 (8):539-549
14. Maher MJ, Hughes PC (1998) Recent developments in stochastic assignment modeling. Traffic Eng Control 39(3):174-179
15. Nagurney A, Zhang D (1996) Projected dynamical systems and variational inequalities with applications. Kluwer, Boston, Massachusetts
16. Nocedal J, Wright SJ (1999) Numerical optimization. Springer, New York
17. Polyak BT (1990) New method of stochastic approximation type. Autom Remote Control 51(7):937-946
18. Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22(3):400-407
19. Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall, New York
20. Sheffi Y, Powell WB (1982) An algorithm for the equilibrium assignment problem with random link times. Networks 12(2):191-207
21. Wong SC (1999) On the convergence of Bell's logit assignment formulation. Transp Res Part B 33 (8):609-616