Public transport companies are in need of systems to keep track of their passenger traffic, both for stock scheduling purposes or as a key to share ticket sale revenues in regions offering multiservice means of transport.
Estimating tram passengers
On behalf of Ruter AS, the common management company for public transport in the Oslo region, NR has developed a method for estimating tram passengers on all trips based on passenger counts from a subset of trips.
The method predicts the number of passengers entering and leaving the tram at every stop on any line, and thereby implicitly deduces the number of passengers who stay on the tram between successive stops as well. Basic predictions are made at stop level for every single trip, and all types of aggregated quantities can therefrom be calculated by summing over individual stops of interest, replacing estimates by real counts wherever available. From this high-resolution level of information, aggregated measures such as annual totals over all lines or line-wise passenger growth from one year to another are easily derived. All estimates are given with a quantified uncertainty.
One model for entering the tram and another for leaving
The method consists of one statistical model for the number of passengers entering the tram, and another model for passengers leaving the tram. The latter is modelled as a proportion of passengers currently on the tram, thus ensuring consistency in the predictions. The basic structure of the models characterizes the systematic variation in the passenger data, with multi-layer seasonality over day, week and year, and typically with similarities between stops. The method is fitted to data from Oslo, but is general in nature, and thus potentially portable to other regions and similar means of transport.