Table 4 Overview of the core equations used in the model

Arrival distribution of the passenger at the airport [min]

μ = 89; σ = 26

\( p(x)=\frac{1}{\sigma \sqrt{2\pi }}{e^{-\frac{1}{2}\left(\frac{x-\mu }{\sigma}\right)}}^2 \)

Duration Check-in [min]

μ=58; σ= 25

Deposition of personal belongings at the security control [min]

a = 0; b = 81

mode=21

\( p(x)=\left\{\begin{array}{c}\frac{2\left(x-a\right)}{\left(b-a\right)\left(c-a\right)}\kern2em for\ x\in \left[a,c\right]\\ {}\frac{2\left(b-c\right)}{\left(b-a\right)\left(b-c\right)}\kern1.75em for\ x\in \left[c,b\right]\\ {}0\kern6.25em else\end{array}\right. \)

Security check of person and luggage [min]

a = 2; b = 169

mode = 43

Receiving of personnel belongings at the security control [min]

a = 0; b = 260

mode= 22

Duration Passport control [s]

a = 50; b = 60

\( p(x)=\left\{\begin{array}{c}\frac{1}{\left(b-a\right)}\kern2.5em for\ a\le x\le b\\ {}0\kern7.5em else\end{array}\right. \)

Calculation of delay times in the airport terminal [m/s]

v = 1.34

dv = 0.26

\( t=\frac{s}{v} \)

\( dt=\sqrt{{\left(\frac{1}{v}\right)}^2\ast {ds}^2+{\left(\frac{s}{v^2}\right)}^2\ast {dv}^2} \)