Side_1_360

LSPs that will be established is given in Figure

14 a). Increasing the k-factor is the same as

increasing the influence from control and

switching on network costs. An increase in the

costs related to control and switching will make

the establishment/cross-connection of LSPs

profitable.

The costs related to control, switching and trans-

mission, as well as the total network cost as

functions of number of LSPs are given in Figure

14 b). Establishing or cross-connecting LSPs

means a splitting of one LSP into two where one

of them is cross-connected through the switch.

The resulting sum of transmission bandwidth

required for these two LSPs will always be

greater than or equal to the bandwidth of the

LSP that is split. Cross-connecting an LSP

implies that less traffic is switched and less con-

trol activities would be involved. This leads to

lower switching and control cost when the num-

ber of LSPs is increased. The minimum total

cost for the reference case with the weight factor

set to 1.0 is obtained when there are 406 LSPs

established. The cost contributions from trans-

mission, switching and control are given, and

they seem to counterbalance each other for an

increasing number of LSPs in such a way that

the total cost is hardly influenced by the number

of LSPs established.

A set of curves for the relative total cost for a

selected number of control/switching weight fac-

tors are depicted in Figure 14 c). The relative

costs are found by dividing the total cost ob-

tained by the minimum total cost for the relevant

weight factor value k. As seen from the curves,

a larger number of LSPs are found as the better

solutions (minimum relative cost) when greater

weight is placed on control/switching cost. The

shapes of the curves are explained by this effect.

In one respect, these curves show the “good-

ness” of the solution found compared to alterna-

tive solutions. For instance, in case k= 1.0, hav-

ing only 50 LSPs gives a total cost that is

approximately 15.5 % greater than the better

solution having 406 LSPs.

During the calculations, the bigger LSPs will be

cross-connected first. This is clearly shown by

the results in Figure 14 d). One rationale for this

is that splitting an LSP into two LSPs might lead

to less additional need for bandwidth when

larger LSPs are considered, as the amount of

traffic load (number of micro flows and their

characteristics) influences the needed bandwidth.

This is recognised as the scale effect observed

through the effective bandwidth measure.

7.2 Case Variations

Some variations of the reference case have been

examined:

• Single class of service (all traffic flow types
  are assigned to the same CoS value);


• Higher demand (double demand of reference
  case);


• Lower demand (one tenth demand of refer-
  ence case).

Similar results as depicted in Figure 14 can be

obtained for these as well, allowing us to iden-

tify the LSP network solution with the lowest

cost together with some sensitivity results. Fig-

ure 15 contains some observations from these

case variations.

As seen from Figure 15 a), reducing demands

to one tenth, the number of LSPs for the corre-

sponding weight factors is reduced. The flows

with reduced demands are smaller than for the

reference case, and when splitting the LSPs the

relative required capacity for the replacing LSPs

is increased, because of the effective bandwidth

and call blocking probability.

The total costs of the better network solutions

for the four cases are given in Figure 15 b). As

expected, increasing the demands leads to higher

cost, while reducing the demands leads to lower

cost. For the other cases, minor changes to the

total cost are found. Related to the costs in Fig-

ure 15 b), the relative cost when a minimum

number of LSPs and a maximum number of

LSPs are established are given in Figure 15 c).

To a certain extent, these values indicate the

potential savings in finding the appropriate LSPs

Figure 14 Results for
reference case: a) Number of
LSPs; b) Network cost;
c) Total cost relative to mini-
mum total cost; d) Average
LSP capacity as a function
of number of LSPs

1.4

1.3

1.2

1.1

1.0

50 250 450

Number of LSPs

c)

Relative cost

4.6

3.0

1.9

0

50 250 450

Number of LSPs

d)

Average VP capacity

(^30)
Mvit/s
160
120
80
40
0
50 250 450
Number of LSPs

b)

Cost

Million

450

350

250

150

50

0.01 1 10 1000

Weight factor, k

a)

Number of LSPs

total

control

switching

transmission

k=10

k=1.0

k=0.5 kk=0=0.1