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UW-Madison ECE 539 - Fuzzy Dynamic Traffic Assignment Model

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Fig.4 Fuzzy Addition IllustrationFig.3 Membership function for fuzzy sets of perceived link travel timeTable 1. Link InformationTable 2. Distinctive Features of Two ScenariosTable 3. Parameters of Stochasticity for Each LinkTable 4. Results for Scenario #1Table 5. Results for Scenario #2Fuzzy Dynamic Traffic Assignment ModelAbstractTraffic assignment is a popular topic in Transportation Engineering and has received much attention since 1950s’. Stochasticity and dynamic are two characteristics of traffic assignment. Since drivers always have no perfect information about traffic conditions, they choose their route based on perceived travel time. Traditional traffic assignment model can only capture the stochasticity and dynamic features of traffic assignment and cannot represent the fuzziness of driver’s perception over travel time. Thus, we presented a fuzzy dynamic traffic assignment model in this paper. By the definition of fuzzy link travel time and fuzzy path travel time, we use fuzzy shortest path algorithm to find the group of fuzzy shortest paths and assignment traffic to each of them proportionally to their memberships. We also compare the results of our proposed model with those from traditional Stochastic Dynamic Traffic Assignment (SDTA) model and it turns out that our model can generate more reasonable solution than SDTA.1. Introduction and Motivation2-1 Traffic AssignmentAccording to Meyer and Miller, there are four major stages in Urban Transportation Modeling System (UTMS)[1]. After the first three steps (Trip Generation, Trip Distribution, Modal Split), the urban area will be divided into different zones and traffic flow (OD demand) will be generated between any two zones, as shown in Fig.1.Traffic Assignment (also referred as Route Choice by many researchers) is the last and crucial step of UTP and it will try to assign traffic flows between each origin-destination pair to actual links through the given road networks, as shown in Fig.2 (only one O-D pair was shown in this figure). Since the most important thing drivers care about is the travel time from origin to destination, the goal of traffic assignment is to achieve minimum travel time for every driver by assigning appropriate traffic flows to each link of the networks. 2-2 Traffic Assignment MethodsStarting from mid-1950s, many methods have been developed trying to solve the traffic assignment problem. In 1952, Wardrop proposed his first principle [2] that is the foundation for later traffic assignment solutions. This principle requires for used routes between a given origin-destination pair that the route cost equals the minimum route cost, and that no unused route has a lower cost. This principle was also referred as User Equilibrium (UE) by many researchers: in a user-equilibrated network no user can improve his travel time (cost) by unilaterally changing routes[2]. Although efficient algorithms can be formulated by using Wardrop’s first principle, his principle assumes a very unrealistic situation: all drivers are supposed to have perfect information and knowledge of the traffic conditions, which is not the case in real life circumstances. In real world, it is almost impossible for drivers to have perfect 1information on current traffic conditions. Therefore, drivers choose their route from origin to destination based on their perceived travel time rather than actual travel time. Another disadvantage of this principle is that it only considers the static case in which all traffic conditions, like traffic flow, speed, link travel time, etc., are presumed to be constant over all the time periods. However, in practice, all traffic conditions may changeover time frequently. 1 2 3 5 6 7 1 2 3 4 5 Z11 Z12 Z45 400 200 Fig. 1 Zone layout in Urban Area origin O destination D Fig. 2 Traffic Assignment Illustration 400 Traffic will go from Origin O to Destination D 1 2 3 4 5 6 7 (Z11) (Z45) In order to capture the stochastic and dynamic characteristics of traffic assignment problem, various traffic assignment models have been developed over the past several decades. In 1971, Dial described a flow-independent logit model for network loading [3]. Daganzo and Sheffi formulated a stochastic user-equilibrium route choice model in 1977[4]. Detailed reviews of these models were prepared by Boyce et al in 1988 [5]. At the same time, other practitioners focused on the dynamic feature of traffic assignment. Yagar, Hurdle, Merchant and Nemhauser were among the first to consider dynamic models for congested traffic networks[6]. Using optimal control theory, Ran and 2Shimazaki established traffic assignment models over a multiple origin-destination (O-D)networks[7] in 1989. Later on, Ran and Boyce integrated both the stochastic and dynamic traffic assignment models into one Stochastic Dynamic Route Choice Model (SDRCM) using Variational Inequality (VI) method in 1996[6]. Although these stochastic dynamic models can reflect the stochasticity and dynamic of traffic condition quite well, drivers’ perception of travel time cannot be simulated reasonably using these models. Hence, in 1987, Mirchandani and Soroush proposed a static probabilistic model in which driver’s perception over travel time was represented by actual travel time plus perceived error that follows a Gamma distribution [8]. In 2001, Liu and Ban extended Mirchandani’s model from static case into dynamic case [9]. However, using probabilistic distribution to simulate driver’s perception is questionable by intuition. Because driver’s perception of travel time, for example, “Beltline is fast,” “University Ave. is congested now,” is actually a linguistic term that has no equivalent exactly defined expression, a few researchers applied fuzzy logic into driver’s perception.Vincent Henn developed a fuzzy route choice model using fuzzy number ranking in 2000 and his model is somewhat similar to logit model mentioned above [10]. However, Henn only considered static case in his paper.For the purpose of reflecting stochastic and dynamic features of traffic conditions and driver’s perception over travel time more realistically, we propose a Fuzzy Dynamic Traffic Assignment (FDTA) model in this paper. We first formulate the fuzzy perceived link travel time and fuzzy perceived path travel time in Section 2 and 3. Fuzzy shortest path algorithm will be


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