ITPEC IP April 2025 Question 16
There is a web system that is composed of two (2) web servers and one (1) database server as shown in the figure. When the availability of each Web server is 0.8 and the availability of the Database server is 0.9, which of the following is the availability of this system rounded off to two (2) decimal places? Here, if at least one (1) of the two (2) Web servers are operating and the Database server is operating, it is considered that the system is operating. Also, a fault occurs randomly on each server.
Explanation
0.86 — reduce the two Web servers in parallel to one block, then multiply by the Database server in series.
- •One Web server fails: 1 − 0.8 = 0.2
- •Both Web servers fail: 0.2 × 0.2 = 0.04
- •Web tier works (at least one server up): 1 − 0.04 = 0.96
- •Whole system, Web tier and Database server both needed: 0.96 × 0.9 = 0.864, rounded 0.86
Answer (c)
Why not others:
- •(a) 0.04 — the probability that both Web servers are down, a failure rate of one tier, not the availability
- •(b) 0.58 — 0.8 × 0.8 × 0.9 = 0.576: treats all three servers as in series, as if both Web servers had to be running
- •(d) 0.96 — the availability of the Web tier alone, forgetting to multiply by the Database server
Key rule: Series: multiply the availabilities; parallel: 1 − the product of the unavailabilities. Reduce each parallel group to one block first.
System Component · AI-written, may contain errors
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