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
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
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
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