Traffic Flow on Urban Networks with Fuzzy Information

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

A network mobility indicator using a fuzzy logic approach

This paper introduces a methodology to assess the mobility of a road transport network from the 3 network perspective. In this research, the mobility of the road transport network is defined as the 4 ability of the road transport network to connect all the origin-destination pairs within the network with 5 an acceptable level of service. Two mobility attributes are therefore introduced to assess the physical 6 connectivity and the road transport network level of service. Furthermore, a simple technique based 7 on a fuzzy logic approach is used to combine mobility attributes into a single mobility indicator in 8 order to measure the impact of disruptive events on road transport network functionality. 9 The application of the proposed methodology on a hypothetical Delft city network shows the ability of the technique to estimate variation in the level of mobility under different scenarios. The method allows the study of demand and supply side variations on overall network mobility, providing a new tool for decision makers in understanding the dynamic nature of mobility under various events. The method can also be used as an evaluation tool to gauge the highway network mobility level, and to highlight weaknesses in the network

Resilience Assignment Framework using System Dynamics and Fuzzy Logic.

This paper is concerned with the development of a conceptual framework that measures the resilience of the transport network under climate change related events. However, the conceptual framework could be adapted and quantified to suit each disruption’s unique impacts. The proposed resilience framework evaluates the changes in transport network performance in multi-stage processes; pre, during and after the disruption. The framework will be of use to decision makers in understanding the dynamic nature of resilience under various events. Furthermore, it could be used as an evaluation tool to gauge transport network performance and highlight weaknesses in the network. In this paper, the system dynamics approach and fuzzy logic theory are integrated and employed to study three characteristics of network resilience. The proposed methodology has been selected to overcome two dominant problems in transport modelling, namely complexity and uncertainty. The system dynamics approach is intended to overcome the double counting effect of extreme events on various resilience characteristics because of its ability to model the feedback process and time delay. On the other hand, fuzzy logic is used to model the relationships among different variables that are difficult to express in numerical form such as redundancy and mobility

Traveller Behaviour: Decision making in an unpredictable world

This paper discusses the nature and consequences of uncertainty in transport systems. Drawing on work from a number of fields, it addresses travellers’ abilities to predict variable phenomena, their perception of uncertainty, their attitude to risk and the various strategies they might adopt in response to uncertainty. It is argued that despite the increased interest in the representation of uncertainty in transport systems, most models treat uncertainty as a purely statistical issue and ignore the psychological aspects of response to uncertainty. The principle theories and models currently used to predict travellers’ response to uncertainty are presented and number of alternative modelling approaches are outlined. It is argued that the current generation of predictive models do not provide an adequate basis for forecasting response to changes in the degree of uncertainty or for predicting the likely effect of providing additional information. A number of alternative modelling approaches are identified to deal with travellers’ acquisition of information, the definition of their choice set and their choice between the available options. The use of heuristic approaches is recommended as an alternative to more conventional probabilistic methods

Fuzzy linear assignment problem: an approach to vehicle fleet deployment

This paper proposes and examines a new approach using fuzzy logic to vehicle fleet deployment. Fleet deployment is viewed as a fuzzy linear assignment problem. It assigns each travel request to an available service vehicle through solving a linear assignment matrix of defuzzied cost entries. Each cost entry indicates the cost value of a travel request that "fuzzily aggregates" multiple criteria in simple rules incorporating human dispatching expertise. The approach is examined via extensive simulations anchored in a representative scenario of taxi deployment, and compared to the conventional case of using only distances (each from the taxi position to the source point and finally destination point of a travel request) as cost entries. Discussion in the context of related work examines the performance and practicality of the proposed approach

A bi-level model of dynamic traffic signal control with continuum approximation

This paper proposes a bi-level model for traffic network signal control, which is formulated as a dynamic Stackelberg game and solved as a mathematical program with equilibrium constraints (MPEC). The lower-level problem is a dynamic user equilibrium (DUE) with embedded dynamic network loading (DNL) sub-problem based on the LWR model (Lighthill and Whitham, 1955; Richards, 1956). The upper-level decision variables are (time-varying) signal green splits with the objective of minimizing network-wide travel cost. Unlike most existing literature which mainly use an on-and-off (binary) representation of the signal controls, we employ a continuum signal model recently proposed and analyzed in Han et al. (2014), which aims at describing and predicting the aggregate behavior that exists at signalized intersections without relying on distinct signal phases. Advantages of this continuum signal model include fewer integer variables, less restrictive constraints on the time steps, and higher decision resolution. It simplifies the modeling representation of large-scale urban traffic networks with the benefit of improved computational efficiency in simulation or optimization. We present, for the LWR-based DNL model that explicitly captures vehicle spillback, an in-depth study on the implementation of the continuum signal model, as its approximation accuracy depends on a number of factors and may deteriorate greatly under certain conditions. The proposed MPEC is solved on two test networks with three metaheuristic methods. Parallel computing is employed to significantly accelerate the solution procedure