Abstract
Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties.
Highlights
Day-to-day (DTD) traffic assignment model seems to be the most widely used approach in existing literatures to describe traveler’s individual route switching behavior, and the corresponding network traffic dynamic evolution at an aggregate level
Property I: Under the conditions of Assumptions I and II, if travelers are assumed to be risk averse, their perceived systematic disutility has a larger value than the perceived mean route travel time, this disutility is positively associated with their perceived travel time variation ranges
Property II: Under the conditions of Assumptions I and II, if travelers are risk prone, their perceived systematic disutility has a smaller value than the perceived mean route travel time, which is negatively associated with the perceived travel time variation ranges
Summary
Day-to-day (DTD) traffic assignment model seems to be the most widely used approach in existing literatures to describe traveler’s individual route switching behavior, and the corresponding network traffic dynamic evolution at an aggregate level. The DTD models previously introduced have addressed the integration of past experiences or other information sources to estimate the perceived mean travel time They do not address the updating of travel time uncertainty, nor consider travelers’ risk-taking behaviors in the route choice processes. According to the learning rule governed by Bayesian theorem, these two studies only address the updating of the inherent within-day travel time uncertainty, but do not address the updating of day-to-day travel time uncertainty which is caused by the inter-day fluctuation of traffic flow They have not considered travelers’ risk-taking behaviors in the context of route choice. This paper makes some efforts to examine the effects of travel time uncertainties and travelers’ risk attitudes on traffic flow evolution and other dynamic system properties, convergence, stability and irreversibility.
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