Session 20 Joel P. Franklin
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This document summarizes research investigating the use of a theoretical random bottleneck model to predict travel time variability and mean lateness. The model was tested on traffic data from Stockholm highways. While the bottleneck model reproduced some aspects of variability over time, it did not predict as accurately as a static approach and had issues related to scale. However, with improved random traffic demand data, the bottleneck model could provide better forecasts of travel time reliability in the future.
Session 20 Joel P. Franklin
- 1. Congestion and Travel Time Reliability: Comparing a Random Bottleneck to Empirical Data Joel P. Franklin Kungliga Tekniska Högskolan
- 2. Overview Investigate the Role of Travel Time Variability in Costs/Benefits Estimation Case of Interest: Future demand is known Traveler preferences are known Future travel time variability is unknown What tools can we use to predict future variability?
- 3. Background Travel Time Variabilty Matters to Travelers It Matters in a Particular Way – Implications for Measurement Lateness matters more than Earliness i.e. standard deviation can be misleading We can assume people try to optimize departure time Hence, total costs are a mixture of: Early departure from previous activity* Travel time in itself* Expected late arrival to next activity: ”Mean Lateness”* *Given optimized departure time
- 4. What does our congestion look like? Hour of Day (morning) Bergslagsvägen, Inbound
- 5. How does it vary? Hour of Day (morning) Bergslagsvägen, Inbound
- 6. What features are important to us? Take a person who wants to arrive on-time 20% of the time Value of Lost Time at Home : 1/hr Value of Lost Time at Work : 5/hr Additional Cost of Travel Time : 1/hr Where: ”mean lateness” is the average time late Mean Travel Time – predicted by standard demand models Mean Lateness …?
- 7. Theoretical Framework (Fosgerau & Karlström, 2009) Chosen Departure Time Preferred Arrival Time Actual Arrival Time 1 5 1 / 5 Marginal Utilities CDF of Travel Time Area = Mean Lateness
- 8. How do those features vary? Mean Time / Freeflow Time Bergslagsvägen, Inbound
- 9. Results Static Approach (for comparison): Scale is 50% low Looping pattern is absent (mostly) No Peak at Shoulders Effect: Role of Variability is understated by about 50% Difference in Variability at Times of Day is Lost Conclusion: May need a Dynamic approach Results of Static Approach Centralbron, Inbound
- 10. Research Question How well can a random bottleneck model predict mean lateness? Why? Could be a very simple way to forecast improvements in travel time variability Incorporates time-dependent congestion dynamics
- 11. Bottleneck Approach Fixed capacity Demand surpasses capacity at time ”0” Demand later subsides below capacity For an arrival at t: Queue Length measured by ”Q(t)” Queue Time measured by ”q(t)” Time of Day 0 Q(t) q(t) t
- 12. Random Bottleneck Demand in each period is random Queue time ”q” is random, depending on random variation in demand up to time ”t” Time of Day 0 Q(t) q(t) t
- 13. Procedure Selected Stockholm Highway Segments: Example shown here: Centralbron—Northbound Observed Delay Distributions by 15-Min Periods Simulate Bottleneck Delay Distributions Started with observed flow by 15-minute periods Simulate random deviations in each period, using exponential distribution Also tested log-normal, poisson, negative-binomial Manually Calibrate for Capacity, Random Dispersion Compute Optimal Expected Lateness by 15-Min Periods Also, Mean and Standard Devation
- 14. Results Observed Travel Times (Segment) Random Bottleneck Travel Times (Point) Centralbron, Northbound Centralbron, Northbound
- 15. Results Bottleneck Approach: Looping effect exaggerated Peaks not separated No peaks at shoulders Scale different by nature (point delay vs. link delay) Centralbron, Northbound 9:00 16:45
- 16. Main Conclusions Dynamic approach of the bottleneck reproduces the cyclical behavior behind ”mean lateness” Scale issues need to be better-calibrated Maximum Capacity Freeflow Travel Time Random Characteristics of Traffic Demand Pure Bottleneck may be too simple E.g. Demand just under capacity gives zero delay Overall : The Bottleneck doesn’t give better predict than a static approach (yet) But better random-demand data can give better forecasts
- 17. Other Observations Under the Random Bottleneck Model: Mean Lateness tracks very closely with Standard Deviation For facilities that truly operate as a bottleneck, standard deviation (multiplied by a constant) may be a good approximation to mean lateness Mean Flow Mean Travel Time Std. Dev. Travel Time Mean Lateness Mean Lateness / Std. Dev.
- 18. Future Directions Mixed congestion models: Uncongested volume-to-capacity relationship of static models Congested time-dependency of bottleneck models Data on traffic volume variations: Needed to appropriately simulate randomness Potential Source: California highway data (day-to-day flows and travel times) Theoretical Exploration of Bottleneck Model Why do Standard Deviation and Mean Lateness often track so closely?