Side_1_360

4.5.2 Sets of Events Observed on a Link
Events that have occurred on a certain link
l=(n,k)∈Eare described by the following
three subsets, see Figure 4.3:

• R*(n,k)(t 1 , t 2 ) = {p|p∈Sn(t 1 , t 2 ) ∧(n, k) ∈
  lnk(p)} represents the set of packets sent into
  the link l= (n, k) ∈Efrom node n∈Vin the
  time window [t 1 , t 2 >.


• S*(n,k)(t 1 , t 2 ) = {p|p∈Rk(t 1 , t 2 ) ∧(n, k) ∈
  lnk(p)} denotes the set of packets received
  from the link l= (n, k) ∈Eby node k∈Vin
  the time window [t 1 , t 2 >.


• X*(n,k)(t 1 , t 2 ) = {p|p∈Sn(t 1 , t 2 ) ∧p∉Rk(t 1 , t 2
  
  
  • prop. delay) ∧(n, k) ∈lnk(p)} is the set of
    packets lost on the link l= (n, k) ∈Ebecause
    of transmission errors in the time window
    [t 1 ,t 2 }.
  
  
  
  

Note that packets in transit cannot be observed.

4.6 Unidirectional Network Level

Performance

Using the conceptual model, unidirectional net-

work-level performance parameters can be pre-

cisely described. This section illustrates the use

of the model to describe packet loss.

4.6.1 Unidirectional Packet Loss for

Individual Packets

A packet travelling through a network domain

can be lost in a node or on a link, as shown in

Figure 4.4.

Table 4.1 shows the representation of packet loss

for individual packets.

Consider a packet, p, travelling along a path,

pth(p), from node ito node j. The packet can be

lost at an intermediate node or on a link in the

end-to-end path. Thus, the indicator variable of

end-to-end loss of packet p, I(p), is the sum of

the indicator variables of each intermediate node

and link along the path, pth(p).

Node n

X*(n, k) (t 1 , t 2 )

R*(n, k) (t 1 , t 2 ) S*(n, k) (t 1 , t 2 )

Link (n, k) Node k Figure 4.3 Sets of events

observed on a link

Node n-1 Node n

Packet

loss on link

Packet loss in node

Figure 4.4 Unidirectional

packet loss

Description Definition

I(p, n),indicator variable for loss of packet p (4.1)

in node n.

I*(p, l),indicator variable for loss of packet p (4.2)

on link l= (n–1, n).

I*(p,l)=

1 p∈X*l(t 1 ,t 2 )

0 p∉X*l(t 1 ,t 2 )

⎧

⎨

⎪

⎩⎪

I(p,n)=

1 p∈Xn(t 1 ,t 2 )

0 p∉Xn(t 1 ,t 2 )

⎧

⎨

⎪

⎩⎪

Table 4.1 Representation of

unidirectional packet loss