Consider using multipath routing such that a demand requiring a total service
rate of R is split equally among M diverse paths (of equal cost). Assume that
if one of the M paths fails, it is required that a fraction P of the original total
service rate still be achievable, where 0≤P≤1. (a) How large must M be such
that no explicit protection capacity is required for the demand (i.e., the working capacity of the M−1 surviving paths is sufficient)? (b) Assume that M
is smaller than this threshold. If protection is provided by utilizing the M−1
surviving paths, where the working capacity of these paths is now supplemented by protection capacity, what is the total amount of protection capacity that is required? (c) Again, assume that supplemental protection capacity
must be deployed. If all of this protection capacity is deployed along a diverse
( M+1)st path, how much protection capacity is required?