In a server farm such as that used by Amazon or eBay, a single failure does not cause the entire system to crash. Instead, it will reduce the number of requests that can be satisfied at any one time.

a. If a company has 10,000 computers, each with an MTTF of 35 days,

and it experiences catastrophic failure only if 1/3 of the computers fail, what is the MTTF for the system?

b. If it costs an extra $1000, per computer, to double the MTTF,

would this be a good business decision? Show your work.

c. Figure 1.3 shows, on average, the cost of downtimes, assuming that the cost is equal at all times of the year. For retailers, however, the Christmas season is the most profitable (and therefore the most costly time to lose sales). If a catalog sales center has twice as much traffic in the fourth quarter as every other quarter, what is the average cost of downtime per hour during the fourth quarter and the rest of the year?

 Figure 1.3

Application Brokerage service Energy Telecom Manufacturing Retail Health care Media Cost of downtime per hour $4,000,000 $1,750,000 $1,250,000 $1,000,000 $650,000 $400,000 $50,000 Annual losses with downtime of 0.5% (43.8 h/year) 1% (87.6 h/year) $350,400,000 $153,300,000 $109,500,000 $87,600,000 $56,900,000 $35,000,000 $4,400,000 $175,200,000 $76,700,000 $54,800,000 $43,800,000 $28,500,000 $17,500,000 $2,200,000 0.1% (8.8 h/year) $35,000,000 $15,300,000 $11,000,000 $8,800,000 $5,700,000 $3,500,000 $400,000