A statistical method for estimating predictable differences between daily traffic flow profiles

It is well known that traffic flows in road networks may vary not only within the day but also between days. Existing models including day-to-day variability usually represent all variability as unpredictable fluctuations. In reality, however, some of the differences in flows on a road may be predictable for transport planners with access to historical data. For example, flow profiles may be systematically different on Mondays compared to Fridays due to predictable differences in underlying activity patterns. By identifying days of the week or times of year where flows are predictably different, models can be developed or model inputs can be amended (in the case of day-to-day dynamical models) to test the robustness of proposed policies or to inform the development of policies which vary according to these predictably different day types. Such policies could include time-of-day varying congestion charges that themselves vary by day of the week or season, or targeting public transport provision so that timetables are more responsive to the day of the week and seasonal needs of travellers. A statistical approach is presented for identifying systematic variations in daily traffic flow profiles based on known explanatory factors such as the day of the week and the season. In order to examine day–to-day variability whilst also considering within-day dynamics, the distribution of flows throughout a day are analysed using Functional Linear Models. F-type tests for functional data are then used to compare alternative model specifications for the predictable variability. The output of the method is an average flow profile for each predictably different day type, which could include day of the week or time of year. An application to real-life traffic flow data for a two-year period is provided. The shape of the daily profile was found to be significantly different for each day of the week, including differences in the timing and width of peak flows and also the relationship between peak and inter-peak flows. Seasonal differences in flow profiles were also identified for each day of the week.