  Buses are known to be an unstable system, and as a result they struggle to
stay on schedule and/or to maintain regular headways. In current practice,
transit agencies add significant slack to the schedule and hold buses until
their scheduled departure time at certain stations along the route. These
practices can smooth out small disruptions but are not robust to large
disruptions. Various headway-based strategies have been proposed but these also
rely on holding buses and therefore reduce their average pace. Transit signal
priority (TSP) is commonly used to reduce the signal delay that buses
experience but the potential for signals to serve as an additional control
agent to enhance bus reliability has not been systematically evaluated. We are
especially interested in evaluating conditional signal priority (CSP), in which
buses send priority requests only when a condition is met. A mathematical model
based on Brownian motion is proposed for bus systems with a schedule where
pairing is not a concern and is used to develop formulas for the expectation
and variance of steady state deviation. Simulation is used to confirm these
findings and to evaluate the case of bus systems operated by headway where
pairing is a concern. The analytical and simulation results show that CSP can
be used not just to accelerate buses but to improve their reliability. CSP is
as good as TSP in some scenarios and better in others. In all scenarios it is
better for other traffic because it sends fewer priority requests.
