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Title: Traffic Flow on Urban Networks with Fuzzy Information
Authors: AKIYAMA, Takamasa
SHAO, Chun-Fu
SASAKI, Tsuna
Issue Date: 28-Apr-1994
Publisher: Faculty of Engineering, Kyoto University
Journal title: Memoirs of the Faculty of Engineering, Kyoto University
Volume: 56
Issue: 2
Start page: 19
End page: 40
Abstract: Many methods of analysis of traffic on transport networks have been proposed which assume crisp travel time. Most of them are based on Wardrop's principle which says in particular “"The travel time on all routes actually used equal to and no greater than those which would be experienced by a single vehicle on any unused route.”" The principle represents a state of user equilibrium under the condition that drivers can get perfect traffic information. Though this principle reflects the definition of the crisp performance function used in traffic assignment, the drivers dynamically make decisions about route choice behaviour with their experience and given information. A method commonly used to represent such perception is stochastic traffic assignment. In the real world, however, the driver can only use fuzzy traffic information even if several types of information are available. The objective of the study is to formulate the fuzzy user equilibrium with fuzzy travel time and show the application of the techniques to an actual problem. First, a basic survey was carried out to ascertain the perception of drivers on an urban transportation network. The network includes the Hanshin Expressway and urban streets in the Osaka area. In the survey, the travel time for streets and expressways on the same O-D (Origin-Destination) are assumed to be Triangular Fuzzy Numbers (TFN). A TFN is simply defined as (Tl, To, Tr) which show the smallest value, centre of time values, and largest value respectively according to the perceived travel time T. Therefore, To is recognized to be an informed and physical travel time. Typical features of perception of travel time are summarized from the survey results. The membership function of the fuzzy number on travel time can be displayed once this database is constructed from the empirical survey. Second, the descriptive method of route choice behaviour is introduced to design the traffic assignment model. The crisp travel time for link a, Ta, is extended to fuzzy number TFa with the spread parameters described above. Two concepts of comparison among fuzzy travel times are introduced. They are the centre of gravity method and the generalized distance method based on compatibility. The former is the very simple concept that the centre of gravity point of a fuzzy number is adopted as a representative value of TFa. The latter method is based on the α-cut concept of fuzzy sets. The definition of generalized distance between fuzzy numbers is defined as the sum of successive intervals between numbers for each a value as it increases from zero to one. It is interesting that with TFNs, this can be carried out rapidly by adding the areas of the triangles in each case. Third, it is assumed that the state of user equilibrium is also generated even if fuzziness of travel time exists. Different results for user equilibrium are observed for conditions of fuzzy information when compared with those obtained under conditions of prefect information. In other words, the link performance function is extended in view of the concept of fuzzy numbers. In particular, the extension principle of fuzzy numbers allows that the comparison methods mentioned above are also valid when fuzzy travel time is applied on the route. Therefore, the fuzzified user equilibrium assignment model can be proposed with these concepts. In this section, the Fuzzified Frank-Wolfe(FFW) algorithm is introduced to obtain a fuzzy optimal solution as the solution of a conventional problem. In changing the algorithm, the modification is only to replace the crisp value of the travel time function t(x) with the representative values of the fuzzy travel time function tF(x). The fuzzified algorithm, therefore, is easily derived from a simple extension of the conventional algorithm. The results of a numerical example are presented to consider the stability of the algorithm. Different results of user equilibrium are observed when compared with those obtained under conditions of information. The relation between the width of the fuzzy travel time distribution and traffic flow is estimated on each link. It is observed that the user equilibrium flows shift according to the fuzzified link performance function. It is also mentioned that the idea can be applied to produce Fuzzy Incremental Assignment (FIA). Fourth, the application of the proposed method to a realistic problem is discussed. The information given to the drivers seems to change their perception of link travel time. In particular, this fact is usually observed when the change of the perceived width of fuzzy numbers according to the travel time information in TFN has an impact on the traffic flow on networks. Because the different definition of left and right spreads of travel time represents the change in human perception under different conditions of information, the impact can be evaluated as a change in traffic volume on the network. In conclusion, the relationship between information and traffic flow can be described by the proposed method. It becomes obvious that the traffic equilibrium flow changes according to traffic information which is available to the drivers. The results of traffic flow analysis under fuzzy information, therefore, become useful for the discussion of a future traffic information system.
URI: http://hdl.handle.net/2433/281488
Appears in Collections:Vol.56 Part 2

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