## 3 The Model of Freight Unit Flow at a Container Terminal
### Model Notation Method  
As mentioned previously, model notation was based on the graph method. A subgraph of any freight unit handling stage can be defined as  
\[K^{m}(\gamma^{m};\xi^{m}),\]  
where  
\(\gamma^{m}\)--change in the waiting time for operation start, determined by the probability density function \(f(t)\); and  
\(\xi^{m}\)--decision variable describing the consequence operation implementation. The freight unit handling process after the completed waiting time for the operation to start is defined by the vertex:  
\[W^{m}(\xi^{n}),\]  
where  
\(\xi^{m}\)--is a decision variable describing the consequence of waiting for operation implementation. Another freight unit handling process possible after completing an operation defined by the subgraph is described by the vertex:  
\[W^{r}(\xi^{r}),\]  
where:  
\(\xi^{r}\)--decision variable describing the consequence of operation implementation. Notation of a state example in tree form is described below. A definition of the state of technical inspection after accepting a freight unit at a container terminal via road transport is presented below. A place where the process is implemented is usually a position marked within the terminal--a parking place for road vehicles arriving with a container for unloading or transshipment. Freight unit technical condition is assessed after the vehicle with a freight unit enters the terminal or after other processes are completed (e.g., parking or document inspection). It involves checking the container (potential damage) and seal condition and weighing the freight unit. The graph of the freight unit road entrance technical condition inspection system can be defined as  
\[K^{d}\left(\gamma^{d};\xi^{d}\right),\]  
where  
\(\gamma^{d}\)--time variable of freight unit road entrance technical condition inspection determined by the probability density function \(f(t^{d})\);  
\(\xi^{d}\)--decision variable describing the consequence of freight unit road entrance technical condition inspection. After the technical condition of the freight unit is inspected, it can be called to the next process stages described previously. The freight unit road entrance technical inspection \(U^{d}\left(\gamma^{d};\xi^{d}\right)\), consists of four main subprocesses:  
- waiting at a technical condition inspection station,  
- freight unit technical inspection,  
- waiting at a weighing station,  
- freight unit weighing. The process of freight unit waiting for a technical inspection can be described as a path in the subgraph  
\[K^{w1}\left(\gamma^{w1};w^{w1}\right),\]  
where  
\(\gamma^{w1}\)--decision variable of waiting for the freight unit road entrance technical inspection,\(n^{w1}\)--variable characterizing the probability of an unproductive move during the freight unit waiting for a technical inspection at the road entrance. Another freight unit handling process possible after the completed waiting time for the technical inspection is defined by the vertex:  
\[W^{w1}\left(\xi^{w1}\right),\]  
where  
\(\left(\xi^{w1}\right)\)--decision variable describing the consequence of a freight unit waiting for a technical inspection at the road entrance. \[\xi^{w1}=\left\{ \begin{array}{c}0-unit\;\;forwarded\;\;to\;\;technical\;\; inspection\\ 1-unit\;\;withrawn\;\;from\;\;further\;handling\;\;at\;\;a\;\;terminal\end{array} \right.\]  
The process of freight unit road entrance technical inspection can be described as a path in the subgraph  
\[K^{d1}\left(\gamma^{d1};n^{d1}\right),\]  
where  
\(\gamma^{d1}\)--time variable of freight unit road entrance technical inspection execution time,  
\(n^{d1}\)--variable characterizing the probability of an unproductive manipulation during freight unit road entrance technical inspection. Technical inspection involves a visual check of the side and rear walls, as well as the doors and locking mechanisms of a freight unit. This leads to identifying possible damage (e.g., torn sheathing, indentation, deformation). The condition of corner cubes and customs seals (if any) is also inspected.