Side_1_360

Obviously, the actual handling and post-process-

ing of measurement data depends on the ultimate

usage of the measurement data and must be

planned carefully. Hence, there are many

options, and the analyses presented in this sec-

tion merely illustrate some of the possibilities.

4 A Conceptual Model for IP

Measurements

4.1 Introduction

There is an increasing need to define network

level performance parameters precisely. For

instance service level agreements must state

exactly what is being measured. This situation is

currently being addressed by the IETF working

group IP performance metrics (IPPM) [Pax-

son96] [RFC2330] and ITU-T [I.380]. This

chapter presents a conceptual model for IP mea-

surements [Viken2000] that allows precise defi-

nitions of network level performance parame-

ters. The foundation of the model is simple well-

defined operations and functions on sets of

events. The conceptual model presented is

appropriate for packet-switched networks but the

nomenclature in this chapter is for IP networks.

The model will be used to give precise defini-

tions of previously loosely defined concepts.

4.2 Network Topology

Graph theory is used to describe the topology of

a given network domain. The topology of a net-

work domain is modeled by a directed8)graph

G= (V, E) where V= {1, 2, ..., n} and EV×V

are the set of nodes and directional links, respec-

tively.

Vdenotes the set of nodes that represent the

routers, switches and hosts in the network

domain and the outside world. The set of nodes,

V, can be divided into four subsets:

• Idenotes the set of ingress nodes, IV, that
  consists of nodes where packets enter the net-
  work domain.


• Odenotes the set of egress nodes, OV, that
  consists of nodes where packets leave the net-
  work domain.


• Xdenotes the set of external nodes, XV,
  that consists of nodes that symbolize the out-
  side world of the network domain.


• Mdenotes the set of internal nodes, MV,
  that consists of nodes that are neither external,
  ingress nor egress nodes.

Note that a node, n∈V, can be both an ingress

and an egress node, consequently I∩O Φ.

E, EV×V, represents the set of directional

links that connect the nodes. A directed link,

l∈E, has certain properties like transmission

capacity and propagation delay. The propagation

delay is mainly determined by the physical dis-

tance to the next remote node.

Note that the entire network, a given network

domain or any chosen part of a network can be

represented by this notation, see example in Fig-

ure 4.1 (for simplicity the directed links are not

shown but only indicated by arrows). For related

work on graph-based models of large networks,

see e.g. [Calvert97].

4.3 Paths

A packet that enters the network domain,

G=(V, E), follows a certain path, π(i,j)k, from

node i∈Vto node j∈V. Index kindicates that

there are several possible paths from node ito

node j. π(i,j)kis defined by the sequence of nodes

Method Central processing7) Local “off line” Local “real-time”

A 22.3 / 446 /446 22.3 / 446 / 446 22.3 / 446 / 446

B 22.3 / 446 / 44.6 22.3 / 44.6 / 44.6 2.2 / 44.6 / 44.6

C 22.3 / 446 / 11.2 22.3 / 11.2 / 11.2 0.6 / 11.2 / 11.2

D 22.3 / 446 / 0.00002 22.3 / 0.00002 / 0.00002 0.000001 / 0.00002 / 0.00002

Table 3.3 Data volumes
(locally/exported/centrally)
[Gbytes]

7)Assume that raw packet traces are deleted after the post-processing has been performed.

8)Parallel directed links from node A to node B cannot be represented by this notation. That is, they

are represented as one link.

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