Internet DRAFT - draft-wehmuth-nmrg-sdn-model

draft-wehmuth-nmrg-sdn-model







Internet Engineering Task Force                               K. Wehmuth
Internet-Draft                                                A. Ziviani
Intended status: Informational                                      LNCC
Expires: December 23, 2017                                 June 21, 2017


          A Reference Model for Representing SDN Environments
                       draft-wehmuth-nmrg-sdn-model-00

Abstract

   Software-Defined Networks (SDNs) are multilayer systems.  In this
   context, this draft defines a graph-based reference model capable of
   properly representing such complex multilayer networks.  The defined
   reference model thus eases the management and planning of SDN
   environments.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Why modeling SDNs as multilayer networks  . . . . . . . . . .   3
   3.  How to model a SDN as a multilayer network  . . . . . . . . .   4
     3.1.  Introduction to MultiAspect Graphs  . . . . . . . . . . .   4
     3.2.  Multilayer graph (MLG) definition . . . . . . . . . . . .   4
     3.3.  Algebraic representations and structures  . . . . . . . .   5
     3.4.  MLG adjacency matrix  . . . . . . . . . . . . . . . . . .   5
     3.5.  SDN reference model . . . . . . . . . . . . . . . . . . .   8
   4.  Conclusion  . . . . . . . . . . . . . . . . . . . . . . . . .   9
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   9
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   7.  Informative References  . . . . . . . . . . . . . . . . . . .   9
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  10

1.  Introduction

   Software-Defined Networks (SDNs) are inherently multilayer systems.
   In addition to the traditional layers associated with the separated
   data and control planes, other layers can be considered to support
   structures, such as hierarchical controllers, structured interaction
   between applications, use of Network Functions Virtualization (NFV)
   on SDN environments, among others.  It is important to properly
   represent such a complex structure in a convenient way that allows
   modeling and analysis of a SDN environment with a single object.

   In this context, we propose the use of a theoretical graph framework
   [Wehmuth2016], capable of modeling multilayer complex networks, for
   representing SDN environments.  This framework is capable of
   representing complex networks containing an arbitrary (finite) number
   of layers, thus allowing the representation of SDN systems with any
   number of associated layers.  In this framework, if desired, the
   usual SDN layers can be divided into sub-layers allowing the creation
   of more detailed and structurally rich SDN reference models.
   Therefore, this framework is capable of modeling various distinct SDN
   architectures, such as ForCES [RFC3746], SDN systems adherent to
   [RFC7426], [draft-irtf-sdnrg-pop-00], or any other layered networking
   architecture.  Further, the considered framework has the property of
   guaranteeing that any model created in it is necessarily equivalent
   (isomorphic) to a directed graph.  Therefore, all knowledge available
   for directed graph analysis can be directly applied to representation
   based on this framework.  Additionally, the graph theoretical
   knowledge can be extended in the framework in order to allow for
   results based on advanced aggregation of layers that are present on
   the represented models.





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   Since SDN reference models created using the proposed framework are
   guaranteed to be equivalent to directed graphs, they can be
   represented in their canonical compact form, or by means of matrices
   usually employed for graph representation (e.g., adjacency matrices).
   Further, well-known graph algorithms can be applied directly to the
   representation based on the considered framework, allowing for the
   straightforward computing of distances among objects on a SDN system,
   the evaluation of the flow capacity of any given path on the system,
   the finding of structurally relevant objects or edges in the system
   (i.e. centrality evaluation), the construction of flow matrices, or
   any other operation possible for directed graphs.

   The proposed SDN reference model fully reflects the complexity of SDN
   systems, while also allowing the straightforward usage of the model
   as a directed graph.  Moreover, the fact that the whole network
   structure can be represented by a single mathematical object greatly
   contributes to the consistency of the obtained results.  Therefore,
   the proposed framework can be useful either in an offline
   environment, where it can be used for system design and simulation of
   what-if scenarios, or as an online environment deployed, for
   instance, in the SDN controller(s), allowing for real-time evaluation
   of the structural properties of the whole system network.  The
   proposed reference model for representing SDN environments thus
   contributes to the management and planning of these environments.

2.  Why modeling SDNs as multilayer networks

   Since SDNs are intrinsically layered systems, it is natural to model
   it as a multilayer network.  Moreover, the usage of such a model has
   the advantage of clearly exposing the SDN layered structure.  In a
   multilayer model, not only the natural layers visible on a SDN are
   clearly represented, but also, if desired, it is possible to divide
   each SDN layer into a set of sub-layers.  In this way, structures
   such as hierarchical distributed control architectures, where
   multiple controllers with distinct hierarchy can be allocated to
   distinct control sub-layers.  In this manner, not only the
   topological structure of the controllers is clearly modeled, but
   also, their hierarchical structure.  Further, structures that may
   sometimes be attached to a SDN system, such as NFVs, can be modeled
   in layers specifically reserved for them, making the whole structure
   clear.

   Moreover, by modeling a SDN as a multilayer network, it becomes
   possible to take advantage from the body of knowledge already
   established in graph theory for analyzing the SDN structure.






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3.  How to model a SDN as a multilayer network

3.1.  Introduction to MultiAspect Graphs

   A MultiAspect Graph (MAG) is a graph generalization introduced in
   [Wehmuth2016] that is shown to be equivalent to a directed graph.  In
   this generalization, the set of vertices, layers, time instants, or
   any other independent features are considered as an aspect of the
   MAG.  For instance, a MAG is able to represent multilayer or time-
   varying networks, while both concepts can also be combined to
   represent a multilayer time-varying network and even other higher-
   order networks.  Since the MAG structure admits an arbitrary (finite)
   number of aspects, it hence introduces a powerful modeling
   abstraction for networked complex systems.

3.2.  Multilayer graph (MLG) definition

   We propose to model SDN systems by using a Multilayer Graph (MLG)
   model, that is a particular case of a MultiAspect Graph~(MAG)
   [Wehmuth2016], in which the vertices and layers are the key features
   (i.e., aspects) to be represented by the model.  Formally, a MAG can
   be defined as an object H=(A,E), where E is a set of edges and A is a
   finite list of sets, each of which is called an aspect.  In our case,
   for modeling a MLG, we have two aspects, namely vertices and layers,
   i.e. |A|=2.  For the sake of simplicity, this 2-aspect MAG can be
   regarded as representing a MLG with an object H = (V, E, L), where V
   is the set of vertices, L is the set of layers, and E is a subset of
   (V X L X V X L), that is the set of edges.  As a matter of notation,
   we denote V(H) as the set of all vertices in H, E(H) the set of all
   edges in H, and L(H) the set of all layers in H.

   An edge e in E(H) is defined as an ordered quadruple e = (u, la, v,
   lb), where u,v in V(H) are the origin and destination vertices, while
   la, lb in L(H) are the origin and destination layers, respectively.
   Therefore, e = (u, l_a, v, l_b) should be understood as a directed
   edge from vertex u at layer la to vertex v at layer lb.  If one needs
   to represent an undirected edge in the MLG, both (u, l_a, v, l_b) and
   (v, l_b, u, l_a) should be in E(H).

   An edge e= (u, la, v, lb) in our model may be classified into four
   classes depending on its characteristic:

   o  Intralayer edges connect two vertices in a same layer, e is in the
      form of e =(u, la, v, la)$, where u and v are distinct;

   o  Interlayer edges connect the same vertex in two distinct layers, e
      is in the form of e=(u, la, u, lb), where la and lb are distinct;




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   o  Mixed edges connect distinct vertices in distinct layers, e is in
      the form of e=(u, la, v, lb)$, where u and v are distinct and $la
      and lb$ are distinct;

   o  Intralayer self-loop edges connect the same vertex in the same
      layer, e is in the form of e=(u, la, u, la).

   Further, we define a composite vertex as an ordered pair (u, la),
   where u in V(H)$ and l_a in L(H).  The set VL(H) of all composite
   vertices in a MLG H is given by the Cartesian product of the set of
   vertices and the set of layers, i.e. VL(H) = V(H) X L(H)$. As a
   notation note, a composite vertex is represented by the ordered pair
   that defines it, e.g. (u, l_a), where u in V(H) and la in L(H).

3.3.  Algebraic representations and structures

   In this section, we discuss ways to properly represent a MLG using
   our proposed model.  Similarly to static graphs, a MLG can be fully
   represented by an algebraic structure, like the MAG structure from
   which our MLG model is derived.  In this work, we adopt matrix-based
   representations, in particular the adjacency matrix.

   In order to illustrate such representations, we use the MLG W
   presented in Figure 1.

3.4.  MLG adjacency matrix

   Since every MAG has a directed graph that is equivalent to it, the
   same holds for our MLG model, since it is a particular specialized
   case of a MAG.  Consequently, it follows that the MLG can be
   represented by an adjacency matrix.  For the sake of standardization
   and without loss of generality, we define that in a MLG the first
   aspect represents the vertices (i.e. the objects that compose the SDN
   system) and the second aspect represents the layers of the
   represented system.

   In the more general environment represented by a MAG, a companion
   tuple is used in order to properly identify and position each
   composite vertex of the equivalent graph in the adjacency matrix.
   Since the case we present in this work is restricted to MAGs with 2
   aspects, it follows that the companion tuple is reduced to a pair,
   which in the first entry has the number of vertices and the second
   entry has the number of layers.  For instance, considering the MLG
   example of Figure 1, the companion tuple associated with its
   adjacency matrix is (10,3), since there are 10 vertices and 3 layers.
   The function of the companion tuple is only to ensure that the order
   by which the composite vertices are placed in the adjacency matrix is
   the one shown in Figure 2.  Since in the case where the number of



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   aspects is restricted to 2 this placement can be easily achieved, in
   this work we do not further mention the companion tuple.

   To get the MLG adjacency matrix, we only need to consider that each
   composite vertex (u,la) can be thought of as a vertex in a directed
   graph.  This directed graph has |V| * |L| vertices and, as a
   consequence, its adjacency matrix has |V| * |L| * |V| * |L| = |V|^2
   * |L|^2 entries.  Since the non-zero entries of this matrix
   correspond to the edges of the MLG, further analysis show that this
   matrix is usually sparse and can therefore be stored in an efficient
   way.

       +---+     +---+                     +---+
       | A |     | A |                     | A |
       | 1 +-----+ 2 |                     | 3 |
       |   |     |   |                     |   |
       +-+-+     +-+-+                     +-+-+      Application Layer
   ......|.........|.........................|.........................
         |         |                         |
    +----+---------+----+           +--------+---------+
    |                   |           |                  |
    |        C1         +-----------+        C2        |
    |                   |           |                  |
    +-+--+---------+----+           +---+----------+---+
      |  |         |                    |          |  Control Layer
   .../..|.........|....................|..........|...................
     /   |         |                    |          |  Data Layer
    /  +-+-+     +-+-+                +-+-+      +-+-+
    |  | D |     | D |                | D |      | D |
    |  | 1 +-----+ 3 |                | 4 +------+ 5 |
    |  |   |     |   |                |   |      |   |
    |  +-+-+     +-+-+                +---+      +---+
    |    |         |
    |    |         |
    |    |  +---+  |
    |    +--+ D |  |
    +-------+ 2 +--+
            |   |
            +---+

                           Figure 1: SDN Example

   Figure 2 shows the adjacency matrix obtained for the illustrative MLG
   W shown in Figure 1.  From Figure 2, we highlight that the adjacency
   matrix form of the MLG has interesting structural properties.






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   +-                                                         -+
   |0 1 1 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D1
   |1 0 1 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D2
   |1 1 0 1 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D3
   |0 0 1 0 1 0 0 0 0 0|0 0 0 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0|D4
   |0 0 0 1 0 0 0 0 0 0|0 0 0 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0|D5 Data
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|C1 Layer
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|C2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A1
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A3
   |...................|...................|...................|
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D1
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D3
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D4
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D5 Ctrl
   |1 1 1 0 0 0 0 0 0 0|0 0 0 0 0 0 1 0 0 0|0 0 0 0 0 0 0 1 1 0|C1 Layer
   |0 0 0 1 1 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 0 1|C2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A1
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|A3
   |...................|...................|...................|
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D1
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D3
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D4
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|D5 Apps
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|C1 Layer
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 0 0 0 0|C2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 0 1 0|A1
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 1 0 0 0 0|0 0 0 0 0 0 0 1 0 0|A2
   |0 0 0 0 0 0 0 0 0 0|0 0 0 0 0 0 1 0 0 0|0 0 0 0 0 0 0 0 0 0|A3
   +-                                                         -+
    D D D D D C C A A A D D D D D C C A A A D D D D D C C A A A
    1 2 3 4 5 1 2 1 2 3 1 2 3 4 5 1 2 1 2 3 1 2 3 4 5 1 2 1 2 3

          Data                Control             Apps
          Layer               Layer               Layer

                       Figure 2: SDN Matrix Example

   First, each one of the ten vertices (identified as D1, D2, D3, D4,
   D5, C1, C2, A1, A2 and A3) of the MLG W clearly appears as a separate
   entity in each of the three layers (l0 - Data, l1 - Control, and l2 -
   Applications) that compose the MLG W.  Second, the main block
   diagonal contains the entries corresponding to the intralayer edges
   of each layer.  In these blocks, the entries corresponding to the



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   intralayer edges of the MLG carry value 1.  Finally, the entries at
   the off-diagonal blocks correspond to the interlayer edges.  The
   eight interlayer edges present at the MLG W are indicated by the
   value 1 on the off-diagonal blocks.  Further, we remark that all
   these structural properties derive from the order adopted for
   representing the vertices and layers present in the MLG and can be
   readily verified in the matrix form in a quite convenient way.

3.5.  SDN reference model

   From the MLG definition, it follows that a MLG can represent
   multilayer networks with an arbitrary (finite) number of layers.  At
   a first glance, this would be enough to represent a multilayer
   system, such as a SDN.  However, additional definitions can be made
   in order to provide a clear description of a SDN.  For instance, a
   SDN reference model could benefit from an adequate name structure for
   its layers.

   We start by naming the four basic layers considered in this work as
   Ld for the data layer, Lc for the control layer, La for the
   application layer, and Ln for the NFV layer.  Further, each basic
   layer can be defined in a number of sub-layers, yielding Ld1 to Ldj
   for data plain layers, Lc1 to Lck for control plan layers, La1 to Lam
   for application layers and Ln1 to Lni for NFV layers.  In this way,
   the total number of layers in the SDN model is given by |L| = j + k +
   m + i.  Note that not all layers need to be necessarily represented.
   For instance, a simple SDN with 1 data plan layer, 1 control plan
   layer, 1 application layer, and no NFV layer, can be modeled by a 3
   layer MLG, where j = k = m = 1 and i = 0.

   We remark that since a MLG is equivalent to a directed graph, all
   extensions usually applied to graphs, such as edge weights and
   vertices weights can be directly applied to MLGs, and also, all
   algorithms known for directed graphs can be directly applied to MLG.

   In addition to the traditional directed graph algorithms, it is
   possible to construct algorithms that use the full information
   present on the MLG and deliver aggregated results (e.g. results for
   vertices; disregarding layers).  By using these algorithms, the
   results do not consider the artifacts generated by the traditional
   aggregation operation.  This means, for instance, that aggregated
   paths are calculated using only paths that are actually present on
   the MLG.








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4.  Conclusion

   In this work, we presented a SDN reference model based on MLGs, which
   are a special case of a MultiAspect Graph (MAG).  In particular, a
   MLG is a MAG with exactly 2 aspects, named vertices and layers.
   Since the MLG has a fix number of aspects, it can be constructed with
   a simpler structure than a MAG.

   We show that a MLG can properly represent a SDN system and that since
   the MLG inherits the basic properties of a MAG, in particular, the
   equivalence (isomorphism) to directed graphs, the knowledge present
   in the theory of directed graphs can be applied to our proposed
   reference model for representing SDN environments.  This makes our
   model a convenient way of representing a SDN, by both expressing it
   as a multilayer system, while also providing a well established
   theoretical ground and available algorithms to build analytics.

5.  IANA Considerations

   This memo includes no request to IANA.

6.  Security Considerations

   Similarly to [RFC7426], this document does not propose a new network
   architecture or protocol and therefore does not have any impact on
   the security of the Internet.  However, security in SDN environments
   is discussed in the literature, e.g. in [SDNSec], [SDNSecSrv], and
   [SDNSecOF].

7.  Informative References

   [Wehmuth2016]
              Wehmuth, K., Fleury, E., and A. Ziviani, "On
              MultiAspect graphs", Theoretical Computer Science Vol.
              651, pp. 50-61, DOI 10.1016/j.tcs.2016.08.017, October
              2016.

   [SDNSecOF]    
              Kloti, R., Kotronis, V., and P. Smith, "OpenFlow: A
              Security Analysis", 21st IEEE International Conference
              on Network Protocols (ICNP) pp. 1-6, October 2013.
                 
   [SDNSecSrv]  
              Scott-Hayward, S., O'Callaghan, G., and S. Sezer, "SDN
              Security: A Survey", In IEEE SDN for Future Networks
              and Services (SDN4FNS), pp. 1-7, 2013.





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   [SDNSec] 
              Kreutz, D., Ramos, F., and P. Verissimo, "Towards
              Secure and Dependable Software-Defined Networks", In
              Proceedings of the second ACM SIGCOMM workshop on Hot
              Topics in Software Defined Networking, pp. 55-60, 2013.

   [I-D.irtf-sdnrg-pop]
              Tian, Y., "Programming Model for Protocol Oblivious
              Forwarding SDN Networks", draft-irtf-sdnrg-pop-00 (work in
              progress), January 2017.

   [RFC3746]  Yang, L., Dantu, R., Anderson, T., and R. Gopal,
              "Forwarding and Control Element Separation (ForCES)
              Framework", RFC 3746, DOI 10.17487/RFC3746, April 2004,
              <http://www.rfc-editor.org/info/rfc3746>.

   [RFC7426]  Haleplidis, E., Ed., Pentikousis, K., Ed., Denazis, S.,
              Hadi Salim, J., Meyer, D., and O. Koufopavlou, "Software-
              Defined Networking (SDN): Layers and Architecture
              Terminology", RFC 7426, DOI 10.17487/RFC7426, January
              2015, <http://www.rfc-editor.org/info/rfc7426>.



Authors' Addresses

   Klaus Wehmuth
   LNCC
   Avenida Getulio Vargas, 333
   Petropolis, RJ  25651-075
   Brazil

   Phone: +55 24 2233-6000
   Email: klaus@lncc.br


   Artur Ziviani
   LNCC
   Avenida Getulio Vargas, 333
   Petropolis, RJ  25651-075
   Brazil

   Phone: +55 24 2233-6199
   Email: ziviani@lncc.br









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