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Investigation of passenger flight delays with statistical physics has been less focused by previous researchers. We consider the flights as special particles, and take quasi-thermodynamic variables to describe their van der Waals - like gaseous equations. Improved from our former model, we download data of 6 more years (2015–2020) with 20 original ones (1995–2014), and redefine pressure as two average number of departure/arrival flights per airport in a given day. Therefore, we enact an empirical gaseous constant R , and get a new kind of “delayor gases” as the daily average delays per flight at all airports. The approach could be applied to passenger flights of any other countries and different complex systems.

The scale-free features widely concerned by previous weighted network models seemed to not be the best choice to describe the link weight distributions of passenger air transportation networks. In this paper, by introducing an exponent α to the weight evolution rule of the earliest weighted model, and considering the spatial constraints of two-dimensional distances on linking probability, we have conducted rigorous analyses leading to the exponentially truncated power-law distribution for weights: P ( w ) = A ⋅ w − α ⋅ e − B w 1 − α , where A and B are parameters, α < 1. The theoretical expression is consistent with the empirical results of the American domestic passenger flight records from 1995 to 2020. The model would be applicable to different air transportation systems and to problems in other fields.