## 2 Materials and Methods  
### Modelling with PTV Vissim  
The method of model building in the PTV Vissim software is described in the articles [21; 22]. To carry out the analysis, as a case study of the impact of heavy goods vehicles on the urban transport network, a model was implemented that reflects the existing state in the example of the port city of Gdynia. Traffic caused by cars and HGVs mainly characterises the modelled area. Over the past few years, the city has also been encouraging residents to use public transport. Thus, there are bus lanes for public transport vehicles in the modelled section. To demonstrate the scale of the traffic volume on the road network from the model obtained from the local road administrator, Figure 1 shows the distribution of traffic on the roadway near the port areas.  
The traffic volume in the sections in the port area is approximately 3500 vehicles per hour. The maximum intensity is up to 4000 vehicles per hour. It should be noted that the main flyover connecting the north and south of the city has only two lanes. There are some ramps and ascents in the third lane. Figure 1 shows the traffic flow around the port area.  
The existing condition of the modelled network was compared to the increased volume of heavy goods vehicle traffic, resulting from travel to and from the port from 10% to 100% more HGVs. The model aimed to check the periods in which the freedom of movement would remain within the range, regarding operational reliability. Particular operating reliability limits for individual states were determined based on the existing state model.  
To perform the described analysis, a simulation model was created using the PTV Vissim tool [23; 24; 25]. This model was implemented with data from the Gdynia Road and Greenery Authority in Gdynia and manually calculated data. The data come from the TRISTAR Intelligent Traffic Control System. Additionally, measured manually was the peak hours data to calibrate the model with the exact generic structure of the vehicles. Figure 2 shows example cars at one of the intersections.  
An example of a transport network based close to the port area is the city of Gdynia. Road sections included in the model were Estakada Kwiatkowskiego with several junctions.  
neighbourhood and is denoted by \(N_{G}(v)\) or \(N(v)\). The close neighbourhood of this vertex is defined as \(N_{G}(v)\cup\{v\}\) and denoted by \(N_{G}[v]\) or \(N[v]\). The other primary essential parameter for graphs is the degree of vertex \(v\in V\), which is defined as the number of vertices in \(N_{G}(v)\) and denoted by \(deg(v)\). Additionally, a set \(D\subseteq V(G)\) is a dominating set of graphs, \(G\), for any \(v\in V(G)\), where either \(v\in D\) or \(N_{G}(v)\cap D=\emptyset\). At the same time, the minimum cardinality of a dominating set of graphs, G, is called a domination number of G and is denoted as \(\gamma(G)\). Furthermore, a set \(X\subseteq E(G)\) is called the edge-dominating set of graph \(G\) if every edge not in \(X\) has a neighbour in set \(X\). The cardinality of a minimum-edge-dominating set is called the edge-domination number of a graph, \(G\), and is denoted by \(\gamma^{\prime}(G)\).  
Essential to these definitions, we define a bondage-connected number \(b_{c}(G)\) of nonempty graph, \(G\), as the minimum cardinality among all sets of edges \(E\) for which \(\gamma(G-E)>\gamma(G)\) and graph \(G-E\) are connected [26].  
Bearing in mind the above definitions, we can further define the basic critical parameters of the transport network under consideration, such as [26]:  
* Number of critical nodes described by a domination number;
* Number of critical edges described by an edge-domination number;
* Topological (structural) vulnerability of transport network described by a bondage-connected number;
* Node-bottlenecks of transport network described by dominating set;
* Arc-bottlenecks of transport network described by an edge-dominating set.