The importance of travel time reliability in traffic management, control, and network design has received a lot of attention in the past decade. In this paper, a network travel time distribution model based on the Johnson curve system is proposed. The model is applied to field travel time data collected by Automated Number Plate Recognition (ANPR) cameras. We further investigate the network-level travel time reliability by connecting the network reliability measures such as the weighted standard deviation of travel time rate and the weighted skewness of travel time rate distributions with network traffic characteristics (e.g., the network density). The weighting is done with respect to the number of signalized intersections on a trip. A clear linear relation between the weighted average travel time rate and the weighted standard deviation of travel time rate can be observed for different time periods with time-varying demand. Furthermore, both the weighted average travel time rate and the weighted standard deviation of travel time rate increase monotonically with network density. The empirical findings of the relation between network travel time reliability and network traffic characteristics can be possibly applied to assess traffic management and control measures to improve network travel time reliability.