If n computers are interconnected and the availability of each computer is needed to maintain a service provided using distributed computing involving these computers, what is the probability that the service will not be available at any time, assuming that no other components in the distributed system will fail?
In this exercise we will use a simplified mathematical model to analyze failures in a distributed system. Explain your answers.
Suppose each computer in has a probability of p of failing at any time.
All n computers need to be functioning in order for the service to be available. The probability that each system is functioning is 1 – p.
The probability that all n systems are functioning is ( 1 – p)n , the probability that the service is available.
The probability that the service is not available is the complement, or
1 – ( 1 – p)n
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