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More Basics: Graph Theory and Modeling Language

Graph theory and the Unified Modeling Language (UML) standardized modeling language are two ancillary topics that one often encounters when first approaching new communications technologies such as MPLS. Although these two areas are not essential to the MPLS domain knowledge, understanding the basics can enhance one's knowledge in the area.

Graph Theory

Graph theory is a branch of mathematics that uses diagrams called graphs as mathematical models to help simplify complex problems. Pictorially, a graph can be drawn as a finite number of small circles linked together by lines. Each small circle is called a vertex, and the collection of all the dots in the graph is called a set of vertices. The links—the lines that connect the circles—are called the edges. Each edge connects two vertices. Graph theory is a common technique frequently used for describing communication networks. There is also additional terminology that one can learn if one wishes to delve deeper into this discipline. For example, the valence of any vertex in a graph model is the number of edges that meet at a point. Additionally, a graph is a connected graph if for each pair of its vertices there is at least one path of edges connecting the two vertices.

Figure 1–27 on the next page is a common graph model used in explaining MPLS; it is called the "fish" network. Obviously, it is called this because of its shape. This connected graph has several properties that make it applicable for discussing basic routing concepts.

Figure 1–27 The "fish" network model.

Figure 1–28 shows a (slightly unbalanced) fish model that demonstrates how routes can be set up in a network. This model can be used to simulate and model traffic flows for setting up applications such as TE. Conventional IP routing would most likely set up a route from C to D to G for traffic that is being sent from host H1 to host H2. The routing protocols running on these nodes would create forwarding information bases that would direct the packets along this route using the SPF, longest destination address match algorithm. MPLS can use a TE application and constraint-based signaling and label distribution (such as RSVP-TE or CR-LDP) to set up an LSP tunnel from C to E to F to G as an alternative route. The overall network resources are now more evenly utilized as alternate paths that would be under-utilized in the IP routing only case begin carrying the MPLS traffic.

Figure 1–28 IGP and MPLS route model.

that would direct the packets along this route using the SPF, longest destination address match algorithm. MPLS can use a TE application and constraint-based signaling and label distribution (such as RSVP-TE or CR-LDP) to set up an LSP tunnel from C to E to F to G as an alternative route. The overall network resources are now more evenly utilized as alternate paths that would be under-utilized in the IP routing only case begin carrying the MPLS traffic.

To further specify, document, and design networks, modeling languages are often used. The standardized modeling language, UML, has come to the forefront as the most commonly used tool for this purpose. Before MPLS applications such as TE can be designed, modeling languages must be typically employed to do the top-level network engineering that is required. The first step in modeling a network is to understand the traffic, what resources are required, and where the bandwidth needs to be placed. After the network engineering has been modeled, the use of Internet technologies such as MPLS can be successfully configured and deployed.

Unified Modeling Language (UML)

Understanding the role of MPLS in a network is a complex enough activity that there is a need for standardized modeling. UML has become the premier industry-standard language for network modeling. The Object Management Group (http://www.omg.org) adopted UML as a standard in November 1997, and it has been in popular use since then.

UML comprises a number of graphical elements that are combined to form various types of diagrams. UML can be used for a variety of modeling needs. These include models for the initial process, class and object modeling, modeling of system components, and even distribution and further development modeling. The most important UML diagrams are the class diagram (CD), the object diagram, the use case diagram, the state diagram, the sequence diagram, the collaboration diagram, the component diagram, and the deployment diagram.

When one delves deeper into MPLS design and implementation, these various types of UML diagrams are often encountered.

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