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Research on multimodal accessibility under uncertain travel time has become a significant issue. Existing studies on accessibility lack a direct integration of multi-source data accessibility evaluation methods. This paper develops a multimodal random accessibility model (MR model). Multi-source data is integrated with a built-in joint calculation method of walking time, waiting time, and transit time while considering the effects of both the travel time budget in the time dimension and distance friction parameter in the spatial dimension. Taking Beijing as an example, accessibility generally shows a downward trend from the center of the city to the suburbs, especially along the subway lines, and there is a positive correlation between traffic flow and accessibility. The low-accessible high-flow area is mainly distributed in areas away from the city center and at the end of subway lines. These results could help transport planners formulate more reasonable public transport planning policies. [ABSTRACT FROM AUTHOR]