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This paper attempts to assess the parking reliability with taking into account drivers' travel choice behaviors under various traffic conditions. Apart from the well-known travel-time reliability, a parking reliability is newly defined as the probability that the drivers' average searching time for parking is less than a given threshold. This is particularly important under conditions of shortage of parking spaces in urban areas. A Monte Carlo simulation approach, which incorporates a combined trip distribution and assignment model with explicit elastic demand function, is proposed to estimate the two reliability measures of road network (i.e. travel-time and parking reliabilities). A numerical example is used to illustrate the applications of the reliability measures and the proposed approach.