Along a transit line, vehicle traffic and passenger traffic are jointly subject to variability in travel time and vehicle load hence crowding. The paper provides a stochastic model of passenger physical time and generalized time, including waiting on platform and in-vehicle run time from access to egress station. Five sources of variability are addressed: (i) vehicle headway which can vary between the stations provided that each service run maintains its rank throughout the local distributions of headways; (ii) vehicle order in the schedule of operations; (iii) vehicle capacity; (iv) passenger arrival time; (v) passenger sensitivity to quality of service. The perspective of the operator, which pertains to vehicle runs, is distinguished from the user's one at the disaggregate level of the individual trip, as in survival theory. Analytical properties are established that link the distributions of vehicle headways, vehicle run times, passenger wait times, passenger travel times, and their counterparts in generalized time, in terms of distribution functions, mean, variance and covariance. Many of them stem from Gaussian and log-normal approximations.