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Question Number 112359 by udaythool last updated on 07/Sep/20

$$\mathrm{Suppose}\mathrm{a}\mathrm{job}\mathrm{consists}\mathrm{of}\mathit{n}\mathrm{tasks}$$$$\mathrm{each}\mathrm{of}\mathrm{which}\mathrm{takes}\mathrm{time}\mathit{t}$$$$\mathrm{seconds}.\mathrm{Thus}\mathrm{if}\mathrm{there}\mathrm{are}\mathrm{no}$$$$\mathrm{failuers}\mathrm{the}\mathrm{sum}\mathrm{over}\mathrm{all}\mathrm{computed}$$$$\mathrm{nodes}\mathrm{of}\mathrm{the}\mathrm{time}\mathrm{taken}\mathrm{to}$$$$\mathrm{execute}\mathrm{tasks}\mathrm{at}\mathrm{that}\mathrm{node}\mathrm{is}\mathit{n}\mathit{t}.$$$$\mathrm{Sppose}\mathrm{also}\mathrm{that}\mathrm{the}\mathrm{probability}$$$$\mathrm{of}\mathrm{a}\mathrm{task}\mathrm{failing}\mathrm{is}\mathit{p}\mathrm{per}\mathrm{job}\mathrm{per}$$$$\mathrm{second}\mathrm{and}\mathrm{when}\mathrm{a}\mathrm{task}\mathrm{fails}\mathrm{the}$$$$\mathrm{overhead}\mathrm{of}\mathrm{management}\mathrm{of}\mathrm{the}$$$$\mathrm{restart}\mathrm{is}\mathrm{such}\mathrm{that}\mathrm{it}\mathrm{adds}10\mathit{t}$$$$\mathrm{seconds}\mathrm{to}\mathrm{the}\mathrm{total}\mathrm{execution}$$$$\mathrm{time}\mathrm{of}\mathrm{the}\mathrm{job}.\mathrm{What}\mathrm{is}\mathrm{the}\mathrm{total}$$$$\mathrm{expected}\mathrm{execution}\mathrm{time}\mathrm{of}\mathrm{the}$$$$\mathrm{job}?$$

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