Consider the example in Fig. 1, with link failure probabilities
and flow allocations as labeled (p and f respctively). A unit
demand needs to be routed from s to t with P = 1
4 and partial
protection requirement q. In [17], a simple partial protection
scheme called 1 + q protection was developed, which routes
the primary demand on one path and the partial protection
requirement onto another edge-disjoint path. After any failure
along the primary path, the partial protection requirement is
met. This is shown in Fig. 1a with the solid line carrying the
primary flow of 1 and the dotted line carrying the protection
flow of q. However, in this example the maximum failure
probability is exceeded for the 1 + q routing: after a failure,
the flow drops below the unit demand between s and t with a
probability of 1
2 (because the failure of either of the primary
links would drop the demand below its full capacity). A
naive alternative would be to simply allocate another path for
protection, which would be identical to the 1+1 full protection
scheme (shown in Fig. 1b), and utilize 4 units of capacity. After
any failure, the full demand of 1 is maintained; thus, the user
will face no downtime, which meets and exceeds the maximum
probability of failure requirement of 1
4 .