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Bounded rationality and irreversible network change

A network change is said to be irreversible if the initial network equilibrium cannot be restored by revoking the change. The phenomenon of irreversible network change has been observed in reality. To model this phenomenon, we develop a day-to-day dynamic model whose fixed point is a boundedly rational user equilibrium (BRUE) flow. Our BRUE based approach to modeling irreversible network change has two advantages over other methods based on Wardrop user equilibrium (UE) or stochastic user equilibrium (SUE). First, the existence of multiple network equilibria is necessary for modeling irreversible network change. Unlike UE or SUE, the BRUE multiple equilibria do not rely on non-separable link cost functions, which makes our model applicable to real-world large-scale networks, where well-calibrated non-separable link cost functions are generally not available. Second, travelers’ boundedly rational behavior in route choice is explicitly considered in our model. The proposed model is applied to the Twin Cities network to model the flow evolution during the collapse and reopening of the I-35 W Bridge. The results show that our model can to a reasonable level reproduce the observed phenomenon of irreversible network change.
 
 

Modeling the day-to-day traffic evolution process after an unexpected network disruption

Although various approaches have been proposed for modeling day-to-day traffic flow evolution, none of them, to the best of our knowledge, have been validated for disrupted networks due to the lack of empirical observations. By carefully studying the driving behavioral changes after the collapse of I-35W Mississippi River Bridge in Minneapolis, Minnesota, we found that most of the existing day-to-day traffic assignment models would not be suitable for modeling the traffic evolution under network disruption, because they assume that drivers’ travel cost perception depends solely on their experiences from previous days. When a significant network change occurs unexpectedly, travelers’ past experience on a traffic network may not be entirely useful because the unexpected network change could disturb the traffic greatly. To remedy this, in this paper, we propose a prediction–correction model to describe the traffic equilibration process. A “predicted” flow pattern is constructed inside the model to accommodate the imperfect perception of congestion that is gradually corrected by actual travel experiences. We also prove rigorously that, under mild assumptions, the proposed prediction–correction process has the user equilibrium flow as a globally attractive point. The proposed model is calibrated and validated with the field data collected after the collapse of I-35W Bridge. This study bridges the gap between theoretical modeling and practical applications of day-to-day traffic equilibration approaches and furthers the understanding of traffic equilibration process after network disruption.
 
 

Indifference Bands for Route Switching

The replacement I-35W bridge in Minneapolis saw less traffic than the original bridge though it provided substantial travel time saving for many travelers. This observation cannot be explained by the classical route choice assumption that travelers always take the shortest path. Accordingly, a boundedly rational route switching model is proposed assuming that travelers will not switch to the new bridge unless travel time saving goes beyond a threshold or “indifference band”. To validate the boundedly rational route switching assumption, route choices of 78 subjects from a GPS travel behavior study were analyzed before and after the addition of the new I-35W bridge. Indifference bands are estimated for both commuters who were previously bridge users and those who never had the experience of using the old bridge. This study offers the first empirical estimation of bounded rationality parameters from GPS data and provides guidelines for traffic assignment.

 
  Selected publications
1.   Di X, Liu H X, Zhu S, et al. Indifference bands for boundedly rational route switching[J]. Transportation, 2015: 1-26.
2.   Di, X., He, X., Guo, X., and Liu, H.* (2014) Braess Paradox under the Boundedly Rational User Equilibria (BRUE), Transportation Research Part B, 67, 86-108.
3.   Di, X., Liu, H., Ban, X., Yu, J.W. (2014) On the Stability of a Boundedly Rational Day-to-day Dynamic, Networks and Spatial Economics, DOI: 10.1007/s11067-014-9233-y.
4.   Di, X., Liu, H.*, Pang, J.S., and Ban, X. (2013) Boundedly Rational User Equilibria (BRUE): mathematical formulation and solution sets, Transportation Research Part B, 57, 300-313.
5.   He, X. and Liu, H.* (2012) Modeling the day-to-day traffic evolution process after an unexpected network disruption, Transportation Research Part B, 46(1), 50-71.
6.   Guo, X. and Liu, H.* (2011) Bounded Rationality and irreversible network changes, Transportation Research Part B, 45(10), 1606-1618.
7.   Guo, X., & Liu, H. (2011). Day-to-day dynamic model in discrete-continuum transportation networks. Transportation Research Record: Journal of the Transportation Research Board, (2263), 66-72.
8.   Zhu, S., Levinson, D., Liu, H., and Harder, K., (2010) The Traffic and Behavioral Effects of the I-35W Mississippi river Bridge Collapse, Transportation Research Part A, 44(10), 771-784.
9.   He, X., Guo, X., and Liu, H. (2010) A link-based day-to-day traffic assignment model, Transportation Research Part B, 44(4), 597-608.
10.   Danczyk, A., He, X., & Liu, H. X. (2010). Uncovering the Perceived Cost Evolution in the Avoidance Phenomenon after the I-35W Bridge Collapse.
11.   Zhu, S., Levinson, D. M., & Liu, H. (2009). Measuring winners and losers from the new I-35W Mississippi River Bridge. Available at SSRN 1743613.