1.4 Network Models
usc-ee-den-ee555-200901-silvester section 1.4
1
1.4 Network Models
Now suppose we have a communication network of nodes. Each node is a router
and has an output buffer for each link leaving that node.
Example: 4 node network
1
3
2
4
1
3
2
4
1,2
2,1
4,3
3,4
4,1
1,4
3,1
2,3
1.4 Network Models
usc-ee-den-ee555-200901-silvester section 1.4
2
1.4.1
Traffic Matrix
Define traffic matrix of flow between source
s
and destination
d
:
{
}
sd
γ
=
Γ
in
packets per second. It is often convenient to represent this with a scale factor
outside the matrix so that the elements of the matrix represent the fraction of flow
between
s
and
d
. For our example, let us assume that the traffic pattern is uniform,
i.e. the same amount of traffic flows between any pair of nodes (not allowing a node
to talk to itself, even though they sometimes do!)
Then,
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
Γ
0
12
/
1
12
/
1
12
/
1
12
/
1
0
12
/
1
12
/
1
12
/
1
12
/
1
0
12
/
1
12
/
1
12
/
1
12
/
1
0
γ
and the total network traffic or load is just
γ
.
1.4.2
Flow Matrix
Based on the routing algorithm (or table or matrix) we can compute the flows (in
packets per second) on each link,
F
. Define
sd
ij
f
as the flow on link (
i,j
) due to [
s,d
]

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