Travel Time Perception and Learning in Traffic Networks Roger B. Chen UIC Seminar, May 19, 2008

Introduction The study of user decisions (interactions) in traffic networks has two motivations: Scientific: Traffic systems are examples of socio- economic systems. Practical: We desire the ability to devise strategies and policies for managing traffic systems. Microscopic Decisions Macroscopic Properties Collectively Varying levels of Information and Technological Capabilities User Interactions Consequences guiding systems towards more socially desirable paths and system states

Background Assumed equilibrium under various user behaviors Interdependence Between User Behaviors and Network Performance Assumed equilibrium under various user behaviors User Equilibrium Stochastic User Equilibrium Day-to-day adjustment processes of travelers Stochastic Process “Tatonnement” Process Simulate network response, user response, or both Mathematical Programming (Sheffi 1984) (Cascetta and Cantarella 1989, 1991, 1996) (Freitz et al. 1994) Analytical Laboratory Experiments Real Users Simulated Network Performance Mahmassani and Herman; Helbing et al. 2001, 2002

Background Behavioral Decision Theory Integration of Travel Experiences and Learning Behavioral Decision Theory “Gestalt Characteristics” Integration of Experiences (Transportation) Weighted Average of Travel Times Myopic Adjustment Departure Time Weighted Average of Travel Times and ATIS Updating of Travel Time and Uncertainty Only salient experiences count (Ariely et al. 2000) (Horowitz 1982) (Mahmassani and Chang 1980, 1996) (Ben-Akiva, de Plama and Kaysi 1982) Kaysi 1991; Jha, Peeta, and Madanat 1998,

Research Objectives Simulation Model the interdependence between user decisions and system performance. Simulation Experiments: Updating of perceived travel times Timing of Learning: Starting and Stopping Extend Past Studies: Further consider travel time learning Triggering Mechanisms Perceived Uncertainty Capturing their effects on network performance Simulation Learning may be costly, and not occur continuously.

Attitudes and Perceptions Modeling Framework Environment Agent-Based Simulation Framework Te,d Traffic Network d=d+1 Experienced Travel Time on day d Integrating Travel Time δd Learning/ Updating? Route Choice Travel Time Updating Triggering Mechanism yes Perceived Travel Time no yes Te1 Te2 Tp Te3 Switch Routes? Decision Mechanisms no Experienced Travel Times Attitudes and Perceptions Triggering Mechanism User

Mean Updated Travel Time Travel Times Experienced Travel Time Perceived Travel Time Gaussian Error Due to Perception Objective Travel Time Same Variance Error Due to “not knowing” The performance of the system Mean Updated Travel Time

Bayesian Updating Updating the Mean Updating the Variance Sample Size Weighted Average Prior Mean Mean of the sample Sample Variance With Every New Experience, Updated Variance Decreases Confidence Increases with the Number of Experiences Inverse of Variance is a Measure Of Confidence As Confidence Increases, New Experiences have less Impact

Trigger Mechanisms Unrealistic Learn Selectively Condition Description Number of Days Difference in Experienced Travel Times Confidence of Updated Travel Time Update at every Mn-th day Unrealistic Update if an experienced travel time is relatively “salient” Learn Selectively Update until confidence for all routes reaches a desired level Similar to New Users becoming Commuters

Route Switching Travel Time “Savings” Threshold [0,1] Perceived Best Travel Time on Day d Users will choose the “Best” Path (assumption)

Test Network Links near the centre have smaller capacities compared with links on the border 7 8 9 6 4 5 1 2 3 link tmin capacity b E 1 20 360 0.1 0.95 2 12 3 15 240 0.12 4 180 0.15 5 6 10 150 7 8 9 30 11 O-D Routes Demand 1-8 6 60 1-9 2 40 9-8 10 1-5 1 5-8 1-4 4-8 7 OD Pairs Link Cost Function

Given Objective Travel Time Simulation Procedure Perceived Mean Initialize Perceived Variance Calculate Link Flows d = d+1 Initial Route Choice Determine Objective Travel Times n = n+1 n = N? Given Objective Travel Time Draw Experienced Travel Time no Switch Routes? Choose Best Route Update? yes Bayesian Rules Update Perceived Travel Time

Traffic System States Convergence Oscillating Non-Convergence

Varying Inter-Update Periods WHY? Lower initial uncertainty perception (β=0.5) may delay convergence. β = variance per unit of time High initial uncertainty perception (β=5.0), updating may not decrease uncertainty fast enough for convergence. Lower usage levels show greater propensity towards convergence compared to high levels. As the number of days between updates increases…(all else being equal) Optimum Point? Also, the number of updates to reach convergence decreases. the number of days until convergence decreases then increases; As the number of days between updates increases, sample (DS) gets BIGGER Mean will stabilize more rapidly Variance will decrease more rapidly However, number of days until convergence does not decrease monotonically

Differences in Experienced and Updated Travel Times All other factors equal OD Pair 2 Travel Times =0.07 Not a UE Increasing Tolerance of Differences before UPDATING Increasing Propensity towards Convergence =0.90

Differences in Experienced and Updated Travel Times All other factors equal OD Pair 3 Travel Times =0.07 Same Trend – Different OD Pair =0.90

Terminating Based on Confidence OD Pair 2 Travel Times Not a UE λnd = 0.05 Increasing Confidence to Terminate Updating Decreases Propensity towards Convergence λnd = 0.90

Conclusions for Route Choice Dynamics Individuals’ perception of travel times and mechanisms for updating them greatly affect convergence. Perceived confidence in the updated travel times is an important factor and should not be ignored. The results also show that there are system-wide properties common to all cases regardless of triggering mechanism. The results call into question some of the behavioral assumptions invoked in stochastic and deterministic equilibrium assignment models. Travel Time Perception and Updating Affects Convergence Should Not Be Ignored System-wide properties common to all cases Calls into questions behavioral assumptions in UE and SO Assignment Models

Extensions and Future Studies Consider Different Learning Types and Risk Perform Laboratory Experiments to Provide Empirical Insight Estimate Parameters in Learning Model Chen and Mahmassani 2008 forthcoming Interdependency between User Decisions and System Performance Empirical Data on Route Choice Econometrically Estimating the Weights for Travel Time Updating