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This paper attempts to assess the transit service reliability with taking into account the interaction between network performance and passengers' travel choice behaviors. Besides the well-known schedule reliability, a waiting-time reliability is newly defined as the probability that the passengers' average waiting time is less than a given threshold. A Monte Carlo simulation approach, which incorporates a stochastic user equilibrium transit assignment model with explicit capacity constraints and elastic frequencies, is proposed to estimate the above two reliability measures of transit service. A numerical example is used to illustrate the applicability of the reliability measures and the proposed approach.