Assistant Professor
Department of Mathematical and Statistical Sciences
University of Colorado Denver
The following is work in progress! It is a collaboration between me (in my role as a CU Denver faculty member) and friends at Greater Denver Transit.
This work combines publicly available GTFS data, other spatial data, and a mathematical optimization model (similar to the one in the Documents section below) to "propose" route frequency changes in the Denver metropolitan area under a variety of scenarios. Currently, it only considers frequency changes on existing routes. However, it may be easily adjusted to incorporate a given set of candidate routes. To give you a sense of the main source of difficulty: there are over 7,000 bus stops in the Denver metropolitan area. This induces over 49,000,000 origin-destination pairs!
George Box famously said "all models are wrong, some are useful." There are lots of assumptions in this mathematical model, most of which are "wrong." All assumptions will be thorougly explained (if and) when this work is formally published. I am a firm believer that applied math is the hardest of all maths: this work is a small step in a long, iterative process for real-world impact.
In the following maps, the different lines are color-coded and their width is proportional to their frequency. There are more lines than colors I can distinguish, so the colors may be repeated. Lines that overlap in their physical route may overlap in their rendering (again, this is work in progress). The dots represent bus stops; their size is proportional to the number of amenities within walking distance (on a logarithmic scale).
This scenario assumes no budget cut and a 60/40 ridership versus coverage budget ratio.
Ridership Service Plan. This plan optimizes for ridership subject to the constraint that at least 40% of the budget is spent on coverage. Coverage Service Plan. This plan optimizes for coverage subject to the constraint that at least 60% of the budget is spent on ridershipThis scenario assumes a 20% budget cut and a 60/40 ridership versus coverage budget ratio.
Ridership Service Plan. This plan optimizes for ridership subject to the constraint that at least 40% of the budget is spent on coverage. Coverage Service Plan. This plan optimizes for coverage subject to the constraint that at least 60% of the budget is spent on ridershipThis scenario assumes a 20% budget cut and a 70/30 ridership versus coverage budget ratio.
Ridership Service Plan. This plan optimizes for ridership subject to the constraint that at least 30% of the budget is spent on coverage. Coverage Service Plan. This plan optimizes for coverage subject to the constraint that at least 70% of the budget is spent on ridership