# 2 Methods

UTA provided time point data for all trips on the UVX system during the summer of 2019. During this period, the TSP requesting threshold was set at three different levels:

• June 10 through July 12 and after August 12: 2 minute threshold
• July 15 through July 26: no TSP
• July 30 through August 9: TSP always requested

We calculated the headway between successive UVX trips at each stop, as well as the cumulative dwell time of all stations along the route to that point. To control for omitted variables, we limited our analysis to the periods between 7 AM and 8 PM when the system runs at a 6-minute headway. Time points within these periods are considered “AM Peak” if occurring between 7 and 9 AM, or “PM Peak” between 4 and 6 PM. We also discard timepoints in south Provo where UVX runs on a one-way circulating loop.

Standard statistical tests — such as the student’s $$t$$-test or ordinary least squares regression models — are designed to ascertain the significance of a statistic at the mean of the distribution. In this application, we are less concerned with the mean deviation in headway, and are instead interested in whether TSP is able to reduce the lateness of buses that already have substantial deviation from their programmed headway. Further, a bus that is delayed from its intended headway may shorten the subsequent headway due to “bunching.” Consequently, we employ conditional quantile regression to estimate the effect of TSP requesting threshold on headway deviation at multiple percentiles of the distribution. This is done with the quantreg package for R