A distributed storage system operates continuously for 100 days. Failures occur on days 10, 25, and 80, with recovery times of 1, 4, and 1 hours, respectively. What is the availabi... A distributed storage system operates continuously for 100 days. Failures occur on days 10, 25, and 80, with recovery times of 1, 4, and 1 hours, respectively. What is the availability of this system, expressed as a percentage? Read more

Steps to Solve

1. Calculate total operating time in a year

Since the system is designed to operate 24/7, we calculate the total number of hours in a year:

$$ \text{Total hours} = 365 \text{ days} \times 24 \text{ hours/day} = 8760 \text{ hours} $$

2. Calculate total downtime due to 1-hour incidents

There were 3 incidents, each lasting 1 hour. So the total downtime for these incidents is:

$$ 3 \text{ incidents} \times 1 \text{ hour/incident} = 3 \text{ hours} $$

3. Calculate total downtime due to 2-hour incidents

There were 2 incidents, each lasting 2 hours. So the total downtime for these incidents is:

$$ 2 \text{ incidents} \times 2 \text{ hours/incident} = 4 \text{ hours} $$

4. Calculate total downtime

Add up the downtime from all the incidents:

$$ \text{Total downtime} = 3 \text{ hours} + 3 \text{ hours} + 4 \text{ hours} = 10 \text{ hours} $$

5. Calculate total uptime

Subtract the total downtime from the total operating time:

$$ \text{Total uptime} = 8760 \text{ hours} - 10 \text{ hours} = 8750 \text{ hours} $$

6. Calculate availability

Divide the total uptime by the total operating time:

$$ \text{Availability} = \frac{\text{Total uptime}}{\text{Total operating time}} = \frac{8750}{8760} $$

7. Convert to percentage and round

Multiply the availability by 100 to express it as a percentage, and round to four decimal places:

$$ \text{Availability percentage} = \frac{8750}{8760} \times 100 \approx 99.8858% $$