Predicting road travel times Luis Campos (with Dan Elliott) 10 th INFRADAY Conference, Berlin, 07 Oct 2011
Predict road travel time to prioritise investments Different factors affect The Highways Agency was travel time interested in measuring the Road network relative contribution of each investments of the main factors affecting road conditions to travel time. Road delays Measure the impact of different changes to road conditions/layout Road management on average delays strategies Help prioritise future investments The Highways Agency wanted assess the impact of past road network investments and road management strategies on 2 Frontier Economics average delays.
An empirical model to predict road travel times Different models, of “specific” changes to At any moment, travel time is affected by a “representative” roads variety of factors 400 350 Average travel time (in seconds) 300 250 ? 200 150 100 50 0 1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321 341 361 381 401 421 441 461 481 501 521 541 561 581 601 621 641 661 15 minute intervals over one week period Most empirical analysis relied on simple Road conditions are constantly changing “before and after” comparisons. across the network. ● Comprehensive model that reflects the particular features of and Bespoke model the actual traffic flow behaviour on the HA road network. 3 Frontier Economics
Conceptual challenge – finding a simple descriptive formula A simple formula needs to capture the complex Illustrative example: interaction between flow and speed dynamics of traffic behaviour, given: ● the large number of factors affecting travel times and: ● how these factors vary across the network and over time; ● how these factors interact; and ● how road delays are likely to persist over time and propagate over the network. Illustrative example: impact of an accident depends on Illustrative example: disruptions in one section affect travel times across the network initial traffic conditions Impact of accidents on journey time Impact of a sudden increase in journey time (simulation using model parameters) (additional 200 seconds) 800 500 450 700 Average journey time (in Average journey time (in Road section 400 600 350 Congested road 500 seconds) seconds) 300 400 250 Accident 200 300 Upstream road section 150 Non congested 200 d 100 100 50 0 0 0 5 10 15 20 25 30 35 40 45 50 55 60 65 75 80 85 90 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 70 15 minute intervals 15 minute intervals 4 Frontier Economics
Time-series non-linear descriptive formula ( ) * J a b P b N b F b W b I b R J it i 1 i it n 2 i it 1 3 i it 4 i it 5 i it 6 i it it 1 Weather conditions, incidents, Density road works, etc. 5 Frontier Economics
Practical challenge – parameter estimation We collated an impressive dataset of We used what we knew about “data rich” road sections to infer more than 190 million records, but: what the likely parameters for the “data poor” road sections was ● despite the richness of this dataset, we found gaps in the data for a Data for > 2,500 sections, over significant number of road sections 2 years, 15 min. frequency and so: ● we were unable to directly traffic conditions over time road features across sections estimate the average impact of 1 st stage 2 nd stage changes to road conditions on Road section time-series Network level cross- travel time in these road data section data sections. parameter parameter ● To construct a fully dynamic model we 3 rd stage estimates estimates had to find an indirect way of Weighted average obtaining these estimates. ● We used this approach to improve the estimates on all the road sections, even on “data rich” road sections. More generally ● The objective was to improve the forecast power of the model, which can be different from maximising the “in-sample” fit. 6 Frontier Economics
Practical challenge – prediction power Using a statistical model to make Illustrative example: unstable predictions predictions is not straightforward ● A statistical model is, by its very Predicted vs. actual journey time nature inaccurate. ● Inaccurate parameters, when 1500.0 combined with strong dynamic 1000.0 Average journey time (in seconds) 500.0 features, can result in very unstable 0.0 0 1 2 3 4 5 6 7 8 -500.0 predictions. -1000.0 -1500.0 ● Minor errors can spread over the -2000.0 -2500.0 network and persist over time, Distribution of estimated -3000.0 leading to large prediction errors in Hours parameter across road sections Actual journey time Predicted journey time subsequent periods. ● We constrained the estimation to Predicted vs. actual journey time (after constraints) ensure the model generated stable predictions, e.g.: 1500.0 ● used log-linear model 1000.0 Average journey time (in seconds) 500.0 ● restricted the parameters 0.0 0 1 2 3 4 5 6 7 8 -500.0 associated with , , J N P -1000.0 it 1 1 it it n -1500.0 -2000.0 -2500.0 -3000.0 Hours Actual journey time Predicted journey time 7 Frontier Economics
The National Delay Model What is the relative contribution of different factors for delays? What is the How is travel expected impact time expected to of adding a new change after lane on a road to several the average The NDM incidents? travel time? should answer… How do changes How long is the in road conditions impact on an in one section accident affect average expected to last? travel time across the network? 8 Frontier Economics
An easy-to-use tool of travel time prediction… The NDM measures the impact on road delays of changes to the road conditions and/or road layout by comparing the average journey time on a selected set of road sections before and after those changes, i.e. comparing a base case with a scenario case . Inputs Outputs ● Choose the base case: ● period considered; and ● roads considered. ● travel time (average, relative contributions, profile over time) ● Insert the changes to road conditions and/or road layout to ● reliability (number of periods, vehicle-hours) include in the scenario. 9 Frontier Economics
…to help the HA prioritise its investments The quantification of the relative impacts of different incidents/events over time and across the network has obvious implications on the type of intervention the HA should be investing on to reduce delays. Reduce the impact of accidents on road or Reduce the impact of rain on road delays delays ● Strong impact on travel time. ● Low impact on travel time. ● Relatively rare. ● Relatively frequent (in England!). 10 Frontier Economics
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