Networking Reference

In-Depth Information

number of failures per year and downtime for repair of 14 days. Suppose that a reli-

ability improvement budget is sufficient for purchasing two redundant edges only,

which can be placed as shown in
Figure 10.5B
H
. The performance measure used

for assessing the networks is the maximum throughput flow reliability.

Interestingly, the network with the highest probability of 200 units throughput

flow on demand is the network in
Figure 10.5F
,
R
f
5

81.5%. For comparison, the

network in
Figure 10.5H
is characterised by a probability of 200 units throughput

flow on demand
R
f
5

42.7%. Smaller than 81.5% probabilities of the required

throughput flow, correspond to the networks in
Figure 10.5B
(53.1%),

Figure 10.5C
(70.4%),
Figure 10.5D
(70.4%) and
Figure 10.5E
(66.7%).

The reason for the superior throughput flow reliability of the network shown

in
Figure 10.5F
becomes clear if a connection is made with the topic related to

the number of disjoint
st
paths in a network, discussed in Chapter 3. (Two paths

are edge-disjoint if they do not share common edges.) The number of disjoint

paths for the network shown in
Figure 10.5F
is three. These are the paths (s,4,
t
),

(s,2,
t
) and (s,3,5,
t
). In contrast, the rest of the networks have only two disjoint

paths. The extra disjoint path provides extra resilience of the network shown in

Figure 10.5F
against simultaneous edge failures and this explains its superior

performance.

Repairable flow networks from different application areas impose particular

constraints that need to be addressed during the design of discrete-event solvers.

In production networks for example, oil and gas production networks, only the

edges/components are unreliable. The nodes are notional (perfectly reliable) and

are used only to define the topology of the network. Furthermore, the links in pro-

duction networks are directed links because, as a rule, no reversal of flows or

back flows are permitted. In contrast, in computer networks both, the nodes

(representing routers) and the edges (representing communication lines) are

unreliable.

Furthermore, parametric studies showed that flow networks with meshed topol-

ogy have a superior throughput flow reliability on demand, compared to networks

with tree topology. The reason is the alternative paths provided by the mesh topol-

ogy. For networks with tree topology, such alternative paths are missing and failure

of any edge results in the loss of the entire flow through the edge.

10.4 Investigating the Link Between Network Topology and

Network Performance by Using Conventional

Reliability Analysis

In some cases, inferences about the link between flow network topology and flow

network performance can be made by using a standard system reliability analysis.

Let us consider the repairable flow networks with redundancy shown in

Figure 10.6
, which have different topologies but contain the same number of com-

ponents. The same number of components selected for the competing topologies