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When a vehicle passes through a long highway tunnel, the smoke it discharges accumulates in the tunnel. High smoke concentration has an important influence on the driver’s health and driving safety. The use of numerous jet fans to diffuse the smoke causes excessive energy consumption, so it is of significant practical value to design suitable tunnel ventilation.

The study is based on the continuum hypothesis, incompressible hypothesis, steady flow hypothesis and similar hypothesis of gas in a long highway tunnel. These hypotheses calculate the gas emissions and wind demand in a long highway tunnel given the deployment of the jet fan program.

This program selects each of the two 1120-type jet machine group and sets up 13 groups; each group has an interval of 184.5 m in the end. The analysis of air test results when the tunnel is in operation shows that CO and smoke concentrations meet the design requirements, which can provide reference for a similar engineering design later.

At present, a highway tunnel is recognized at home and abroad by means of clearance of longitudinal ventilation, which is 2,000 m. In view of this, this paper is based on the theory of longitudinal jet ventilation of a highway tunnel, whose length is more than 2,000 m, to calculate the ventilation and apply it to a tunnel’s ventilation design.

The authors propose to estimate a varying coefficient panel data model with different smoothing variables and fixed effects using a two-step approach. The pilot step estimates the varying coefficients by a series method. We then use the pilot estimates to perform a one-step backfitting through local linear kernel smoothing, which is shown to be oracle efficient in the sense of being asymptotically equivalent to the estimate knowing the other components of the varying coefficients. In both steps, the authors remove the fixed effects through properly constructed weights. The authors obtain the asymptotic properties of both the pilot and efficient estimators. The Monte Carlo simulations show that the proposed estimator performs well. The authors illustrate their applicability by estimating a varying coefficient production frontier using a panel data, without assuming distributions of the efficiency and error terms.