Direct Network Reliability Calculation
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This chapter is a collection of several direct methods for calculating network reliability. These methods are good for small networks having not more than 8–10 elements subject to failure. The most straightforward is network state enumeration method. It allows obtaining network UP/DOWN probability in an explicit form. More elegant and efficient are the methods based on using network structural parameters—the so-called minimal path and minimal cut sets. Knowing these parameters allows us to construct rather accurate upper and lower bounds on network reliability. For very reliable networks in which node/edge failure reliability tends to zero, very good results are obtained by using so-called Burtin-Pittel approximation. We present it in Sect. 3.5. Network reliability as a function of the number of failed elements is an important characteristic of so-called resilience, see Sect. 3.6. The chapter is concluded by introducing so-called dynamic reliability which is network reliability behaviour in time. This is obtained by replacing element static reliability p by survival probability \(1-G(t)\) depending on time t.
KeywordsMin cuts Min paths Reliability bounds B-P approximation Network resilience Dynamic reliability
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