A Practical O-D Matrix Estimation Model Based On Fuzzy Set Theory For Large Cities

Estimation of the origin-destination trip demand matrix (O-D) plays a key role in travel analysis and transportation planning and operations. Many researchers have developed different O-D matrix estimation methods using traffic counts, which allow simple data collection as opposed to the costly traditional direct estimation methods based on home and roadside interviews. In this paper, a new fuzzy O-D matrix estimation model (FODMEM) is proposed to estimate the O-D matrix from traffic count. A gradient-based algorithm, containing a fuzzy rule based approach to control the estimated O-D matrix changes, is proposed to solve FODMEM. Since link data only represents a snapshot situation, resulting in inconsistency of data and poor quality of the estimated O-D's, the proposed method considers link data as fuzzy values that vary within a certain bandwidth. An equilibrium based fuzzy assignment method is proposed to assign the estimated O-D matrix, which causes the assigned volumes to be fuzzy numbers. The shortest path algorithm of the proposed method is similar to the Floyd-Warshall algorithm, and we call it the Fuzzy Floyd-Warshall Algorithm (FFWA). We introduce a new fuzzy comparing index to compare and estimate the distance between the assigned and observed link volumes and the model is formulated based on this index. FODMEM is implemented in Mashhad city in Iran. Real data obtained from Mashhad Comprehension Transportation Study (MCTS) are used in this study and results are presented to show high capability of FODMEM to estimate O-D matrix in large networks. INTRODUCTION Obtaining the origin-destination (O-D) matrix by conventional methods takes a considerable amount of time, money, and manpower, while gathering traffic volume data for the links of the transportation network is easy. Recently, a variety of analytic models has been developed to establish O-D trip matrices based on traffic counts along with other information. Although O-D matrix estimation models from traffic counts are different in formulation, they are similar in that their implementation is extremely difficult in largescale networks. Another important problem is the inconsistency among link-count data that results in poor quality of the estimated O-D's and even nonconvergence of the solution algorithm. Data inconsistency occurs due to diverse reasons, such as counting error and the deriver's behaviour. Some researchers tried to solve this problem by using a set of "Fuzzy Weights" for each piece of inconsistent data (Xu and Chan 1993). They considered the link counts as imprecise values, so they proposed to survey link volumes more than once and computed fuzzy weights for every set of link counts. The traffic assignment methods utilized in the above O-D estimation models, such as equilibrium and proportional based, consider the user's route choice as a crisp and precise process. Some research has demonstrated that the common equilibrium based assignment methods cannot correctly reproduce real traffic volumes. It is indicated that real assigned traffic flow might not certainly converge to the userequilibrium. In other words, travel times used in routes have salient differences from the lowest route travel time (Jan and Ridwan 1994). As a result, it should be realized that common equilibrium and stochastic assignment models do a poor job of accounting for imprecision and uncertainty in the user's route choice behavior. Recently, some assignment models based on fuzzy theory have been proposed, but these models have not been widely used in the O-D estimation problem. Some researchers proposed a fuzzy inference based assignment algorithm in the O-D matrix estimation problem (Harikishan and Partha 1998). They applied an entropy model previously developed in the upper level of the O-D estimation problem. In this paper, we use a new fuzzy approach to propose equilibrium based O-D matrix estimation model. We implement this model in Mashhad City, one large city in Iran. This model has a bi-level structure, and the fuzzy approach is applied in both the upper and lower levels. Proceedings 23rd European Conference on Modelling and Simulation ©ECMS Javier Otamendi, Andrzej Bargiela, José Luis Montes, Luis Miguel Doncel Pedrera (Editors) ISBN: 978-0-9553018-8-9 / ISBN: 978-0-9553018-9-6 (CD) THE PROPOSED FUZZY O-D MATRIX ESTMATION MODEL (FODMEM) Here, we propose the fuzzy O-D matrix estimation model (FODMEM). The model is formulated as an optimization problem. The objective function tries to minimize the fuzzy distance between the assigned and observed link volumes based on a new fuzzy index c I1 : ( ) ( ) ∑       − = ∈ A a a c x I q Z ˆ 1 2 ~ ˆ 1 2 1 min (1) ( ) q assign x t s = ~ . . (2) : q Trip demand matrix ( ) q assign : Fuzzy traffic assignment  : The observed links set The observed link volume is defined as a fuzzy value: ( ) R L x x x x ˆ , ˆ , ˆ ˆ = (3) where x̂ is the crisp value of observed link volume, and ( ) l L x x β − = 1 ˆ ˆ and ( ) r R x x β + = 1 ˆ ˆ are the lower and upper boundaries. l β and r β are experimental values and represent the degree of imprecision in link counts, which can be obtained based on expert knowledge or observation of daily traffic variation of each link in a specific time period. The assigned fuzzy link volumes x ~ is formulated as below: ( ) R L x x x x , , ~ = (4) where x ~ is the fuzzy link volume, x is the assigned link volume, and ( ) l L x x α − = 1 and ( ) r R x x α + = 1 are the lower and upper boundaries. The parameter r α is the link degree of saturation, and l α is an experimental value. These parameters can be specified through different approaches, such as interviewing, using expert knowledge or simulation. ( ) a c x I ˆ 1 is the proposed fuzzy comparison index between the fuzzy observed link volume a x ~ ˆ and the fuzzy assigned link volume a x ~ in link a . This index is computed as below: ( ) ( ) ( ) ∞ ≤ ≤ ∞ − − + − − = c a R a L a a L a R a a c I x x x x x x x I 1 1 , ˆ ˆ ˆ ~ ˆ (5)