Micro-simulation of learning and adaptation in activity-travel choice

1. Micro-simulation of learning and adaptationin activity-travel choice

2. Background and Objectives (1) • Activity based models of travel demand aim to predict: • which activities are conducted • when • where • for how long • transport mode • Examples of existing activity-based models: • Albatross (operational on a national scale) • Aurora (under development) • Bhat 1999 • Bowman and Ben-Akiva • PCATS

3. Background and Objectives (2) • Existing models implicitly assume that activity-travel patterns are static • Adaptation refers to a choice to change an existing pattern in response to changed conditions in the environment, household, life cycle of the individual • Learning follows from the fact that individuals have limited knowledge of their environment (locations and routes) • Adaptation and learning means that activity patterns are in a constant state of change

4. Background and Objectives (3) • The objective is to develop a micro-simulation system of dynamics of activity-travel choice

5. Approach • Micro-simulation: • Individuals are individually represented as agents • The scheduling and implementation of activities are simulated in space and time • High resolution of space and time • Components of agents: • An activity-based model: Aurora • Spatial cognition: Belief networks and Bayesian learning • Social interaction: Social networks and communication

6. Bayes theorem Where: Pr(xj | Y) the belief that X = xj given finding Y Pr(Y | xj) the probability of Y given X = xj. Pr(xj) the a-priori belief that X = xj

7. Bayes theorem: Example • Pr(yes) = 0.3 • Pr(Y | xj) • Pr(yes | Y = no) = 0.2 x 0.3 / (0.2 x 0.3 + 0.9 x 0.7) = 0.087 • Pr(yes | Y = yes) =0.8 x 0.3 / (0.8 x 0.3 + 0.1 x 0.7) = 0.774

8. Advantages of the Bayesian learning approach • Learning is incremental so that at any moment in time beliefs are defined as a set of probability distributions • The probabilities have a ready interpretation as beliefs that certain locations/routes have certain attribute values • Utilities can be redefined as expected utilities as the criterion for choice • The probabilities can be used to define an entropy measure of the expected information gain that can be obtained from certain activities and trips

9. Information gain measure (1) • The information quantity of the finding that a cell i has a value xij on some variable Xi is: Bits • The expected amount of information required for identifying the value of a cell is defined as a weighted sum of this measure across values of Xi:

10. Information gain measure (2) • The info(i) after some observation Yiis: • The expected info(i) beforesome observation is: • The expected information gainis: info(i,) – info(i)

11. Spatial Search • Information gathering can be modeled as the choice of a route that maximizes the information gain within a given acceptable distance

12. Individual’s observations (1) • Sensitiveness of an observation is a function of: • The distance from the cell • The nature of the variable observed • Transport mode • Link type • The purpose of the trip

13. Individual’s observations (2) • Zero sensitiveness is defined as (n is nof levels of y): • Pr(yk | xj) = 1/nk, j • And maximum sensitiveness as: • Pr(yj | xj) = 1 en Pr(yk | xj) = 0, kjj

14. Individual’s observations (3) • Sensitiveness in general as: • Where • jk are observation-bias parameters determining the probability of Y = yk given X = xj •  is an observation-sensitiveness parameter

15. A spatial belief network: Variables (1) • Structural type • Inner city • High density urban • Low density urban • Rural • Relationship with road network • Nearby link of main road • Nearby link of local road • No relationship

16. A spatial belief network: Variables (2) • Main Landuse • Industry • Housing • Shops • Etc. • Availability of facilities for activity A • Attractiveness for activity A • High • Medium • Low • Zero

17. Land use Neighbor of i Type i Network i Observation N Land use i Observation L Facilities i for A Observation F Attraction i for A Observation A A spatial belief network: Structure

18. Social Networks • The probability that A is a social contact of B is a function of: • Overlap in action space between A and B • Overlap in socio-economic space between A and B • Unobserved factors • Definition: A is a social contact of B iff • Beliefs/preferences of B are conditionally dependent on beliefs/preferences of A

19. Communication • A social contact can be modeled as a link between belief networks of A and B • A conditional probability table defines the social contact: • Partial adjustment, biased adjustment of beliefs/preferences • Attribute specific impact • A symmetrical impacts • Information gain of the social contact

20. Conclusion • Project is still in an early stage of conceptualization • Simulation studies will be conducted to test the validity of the ideas • Data collections are needed to estimate parameters of belief- network model and social-network model • The Aurora, Belief-network and Social-network model need to be implemented as methods of agents