91Ó°ÊÓ

A system with three independent components works correctly if at least one component is functioning properly. Failure rates of the individual components are \(\lambda_1=0.0001, \lambda_2=0.0002\), and \(\lambda_3=0.0004\) (assume exponential lifetime distributions). (a) Determine the probability that the system will work for \(1000 \mathrm{~h}\). (b) Determine the density function of the lifetime \(X\) of the system.

Jobs arriving to a compute server have been found to require CPU time that can be modeled by an exponential distribution with parameter 1/140 ms?1. The CPU scheduling discipline is quantum-oriented so that a job not completing within a quantum of 100 ms will be routed back to the tail of the queue of waiting jobs. Find the probability that an arriving job is forced to wait for a second quantum. Of the 800 jobs coming in during a day, how many are expected to finish within the first quantum?