The study of accessibility - the ease of reaching destinations - by public transport has made huge advances thanks to the availability of standardized, routable transit schedule data.The General Transit Feed Specification (GTFS) has provided researchers with a vast trove of machine-readable data allowing for highly detailed spatio-temporal modelling of scheduled transit operations.Yet it is well established that in the real-world schedules are imperfect - vehicles often run late, get bunched, miss transfers, arrive too full for anyone to board, and otherwise behave in predictably unpredictable ways. Schedule data alone cannot possibly account for this distinctly stochastic component of much transit service, which to date has been considered separate from accessibility analysis under the umbrella of ``reliability''. This dissertation takes the perspective that transit service is reliably unreliable and will continue to be so until humans are taken out of the equation. Detailed observations of actual service can be used to construct more realistic models for estimating travel times and thus accessibility via transit.Chapter 2 introduces a novel method of converting a detailed GPS record of transit fleet locations into a retrospective GTFS package. This backward-looking "schedule'' format allows the same tools developed for schedule-based GTFS analysis to be applied in Chapter 3 to a more accurate depiction of actual transit accessibility. The findings indicate that models of transit accessibility based on schedule data alone tend to produce substantial overestimates of accessibility and systematic spatial errors by failing to account for normal irregularities in service provision. Chapter 4 points toward a way of better suiting available GTFS analysis tools to actual transit service by addressing the problem of imperfect information in modelled route choice. The travel time implications for a large minority of trips are shown to be substantial. Transit accessibility research has come a long way in the last decade and has a long way yet to go. Models based on schedule data alone should give way in many cases to models based on service as actually provided, acknowledging that schedules may guide but rarely constrain the transit services that passengers actually use every day.