Network Reliability Analysis

1
Network Reliability Analysis

• Assume failure events of separate components are
  statistically independent.
• Algorithm based on simple laws of calculating
  probabilities of compound events
• PU ? VPU PV
• Availability(U and V) Availability(U)
  Availability(V)
• PU ? VPU PV - PU PV
• For small unavailability values -
• Unavailability(U and V) ? Unavailability(U)
  Unavailability(V)
• Working on unavailability is easier and usually
  accurate enough.

2
Application of the Algorithm

• A network with parallel links
• Equivalent to a single-link network of equivalent
  availability (union prob.)
• Or equivalent unavailability of product of two
  individual unavailabilities
• A network with serial links
• An availability equal to the product of two
  individual availabilities
• Equivalent to a single combined link with added
  unavailability

A
B
e.g. 2x 99 ? 99.99
A
B
C
e.g. 99 x 99 ? 98
3
A Network Example

• What is the reliability between A and B?

99
B
99.9
99
99
99.9
99.9
A
E
99.9
C
99.9
99.9
99
D
4
An Equivalent Network

• Red trail across top add unavailability
• .01.01.001.01.031 ? 96.9
• Next simplify E-C links

B
99.9
99.9
A
E
99.9
C
99.9
99.9
99
D
5
Further Deduction

• Unavailability for E-C links
• (.001.01.001) x .001.000012 ? 99.9988
• Next Combine the lower path
• Unavailability for green path
• .001.000012.001.002012
• Final result
• Availability(A,B) 99.994

B
99.9
99.9
A
E
99.9988
C
6
Reliability of Rings

• E.g., a ring with 200 nodes, links all with 99
  availability
• Nodes A and B separated by 100 links, the
  availability will be 1-(1-0.99100) 2 0.599.
• For large networks, more than 1 ring will be
  required to achieve good availability.

B
A ring with 200 nodes
A
7
Southern Cross Cable System

• 240 Gbits capacity (by 2003)
• Owned by Telecom NZ, Optus, MCI WorldCom
• Outsourced to Alatec and Fijitsu
• Designed to have network availability of 99.999.
• If one cable network breaks, full redundancy
  (self-healing) is immediately available via
  alternative pathways.