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Gizem Temelcan, Hale Gonce Kocken, Inci Albayrak
Keywords:fuzzy traffic assignment problem, average speed, vehicle length, link capacity, travel time


This paper focuses on converting the system optimum traffic assignment problem (SO-TAP) to system optimum fuzzy traffic assignment problem (SO-FTAP). The SO-TAP aims to minimize the total system travel time on road network between the specified origin and destination points. Link travel time is taken as a linear function of fuzzy link flow; thus each link travel time is constructed as a triangular fuzzy number. The objective function is expressed in terms of link flows and link travel times in a non-linear form while satisfying the flow conservation constraints. The parameters of the problem are path lengths, number of lanes, average speed of a vehicle, vehicle length, clearance, spacing, link capacity and free flow travel time. Considering a road network, the path lengths and number of lanes are taken as crisp numbers. The average speed of a vehicle and vehicle length are imprecise in nature, so these are taken as triangular fuzzy numbers. Since the remaining parameters, that are clearance, spacing, link capacity and free flow travel time are determined by the average speed of a vehicle and vehicle length, they will be triangular fuzzy numbers. Finally, the original SO-TAP is converted to a fuzzy quadratic programming (FQP) problem, and it is solved using an existing approach from literature. A numerical experiment is illustrated.


Sheffi Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. New Jersey: Prentice Hall; 1985.

LeBlanc LJ, Morlok EK, Pierskalla WP. An Efficient Approach to Solving the Road Network Equilibrium Traffic Assignment Problem. Transportation Research. 1975;9(5): 309-318.

Branston D. Link Capacity Functions: A Review. Transportation Research. 1976;10(4): 223-236.

Carey M, Ge YE. Comparing Whole-Link Travel Time Models. Transportation Research Part B: Methodological. 2003;37(10): 905-926.

Kachroo P, Sastry S. Traffic Assignment Using a Density-Based Travel-Time Function for Intelligent Transportation Systems. IEEE Transactions on Intelligent Transportation Systems. 2016;17(5): 1438-1447.

Beckmann M, McGuire CB, Winsten CB. Studies in the Economics of Transportation. London: Oxford University Press; 1956.

LeBlanc LJ. The Use of Large Scale Mathematical Programming Models in Transportation Systems. Transportation Research. 1976;10(6): 419-421.

Daganzo CF. On the Traffic Assignment Problem with Flow Dependent Costs-I. Transportation Research. 1977;11(6): 433-437.

Daganzo CF. On the Traffic Assignment Problem with Flow Dependent Costs-II. Transportation Research. 1977;11(6): 439-441.

Daganzo CF. Properties of Link Travel Time Functions Under Dynamic Loads. Transportation Research Part B: Methodological. 1995;29(2): 95-98.

Peeta S, Mahmassani HS. System Optimal and User Equilibrium Time-Dependent Traffic Assignment in Congested Networks. Annals of Operations Research. 1995;60(1): 81-113.

Vandaele N, Van Woensel T, Verbruggen A. A Queueing Based Traffic Flow Model. Transportation Research Part D: Transport and Environment. 2000;5(2): 121-135.

Binetti M, De Mitri M. Traffic Assignment Model with Fuzzy Travel Cost. In: Proceedings of the 13th Mini-EURO Conference on Uncertainty in Transportation, Bari, Italy; 2002. p. 805-812.

Ridwan M. Fuzzy Preference Based Traffic Assignment Problem. Transportation Research Part C: Emerging Technologies. 2004;12(3): 209-233.

Liu ST, Kao C. Network Flow Problems with Fuzzy Arc Lengths. IEEE Transactions on Systems, Man, and ybernetics, Part B (Cybernetics). 2004;34(1): 765-769.

Murat YS, Uludag N. Route Choice Modelling in Urban Transportation Networks Using Fuzzy Logic and Logistic Regression Methods. Journal of Scientific and Industrial Research. 2008;67: 19-27.

Ramazani H, Shafahi Y, Seyedabrishami SE. A Fuzzy Traffic Assignment Algorithm Based on Driver Perceived Travel Time of Network Links. Scientia Iranica. 2011;18(2): 190-197.

Miralinaghi M, Shafahi Y, Anbarani RS. A Fuzzy Network Assignment Model Based on User Equilibrium Condition. Scientia Iranica. Transaction A, Civil Engineering. 2015;22(6): 2012-2023.

Zadeh LA. Fuzzy Sets. Information and Control. 1965;8(3): 338-353.

Ozkok B, Albayrak I, Kocken H, Ahlatcioglu M. An Approach for Finding Fuzzy Optimal and Approximate Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems With Mixed Constraints. Journal of Intelligent and Fuzzy Systems. 2016; 1-10.

Urgen Zimmermann HJ. Fuzzy Set Theory and Its Applications (3rd Edition). Boston, Dordrecht, London: Kluwer Academic Publishers; 1996.

Yang R, Wang Z, Heng PA, Leung KS. Fuzzy Numbers and Fuzzification of the Choquet Integral. Fuzzy Sets and Systems. 2005;153(1): 95-113.

Guven A. Trafik Yönetiminde Kuadratik Programlama Uygulaması. Master thesis. Istanbul Kultur University; 2011. Turkish.

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