Question 2 [30 points]: A computer system S can be decomposed into three subsystems: processor, memory, and I/0. S has a failure rate equal to A failures/sec. The processor accounts for a fraction fp of the total failures, the memory accounts for a fraction fm of the total failures, and the I/0 subsystem accounts for a fraction fi/o of the total failures. (Note that fp+fm+f/o 1) (a) [7.5 points] What is the reliability improvement index (RII) of system S if the factors Pp, Pm, and Pi/o, respectively (i.e., the failure rates are reduced)? (b) [4.5 points] Compute the RII assuming that fp 0.25, fm 0.35, and fi/o 0.4 failure rates of the processor, memory, and I/0 subsystem are improved by and Pp 2, Pm-3, and Pi/o .5 (c) [7.5 points] Assume that there is a cost to improve the reliability of each of the subsystems. This cost is not the same for each subsystem. Assume the following notation Cp: cost per unit of reliability improvement for the processor. So, the cost of improving the reliability of the processor by a factor of Pp is Cp xPp Cm: cost per unit of reliability improvement for the memory subsystem. So, the cost of improving the reliability of the memory by a factor of Pm is Cm x Pm. Ci/o: cost per unit of reliability improvement for the I/O subsystem. So, the cost of improving the reliability of the I/0 subsystem by a factor of Pi/o is Ci/o x Pi/o Give an expression for the metric K defined as the total improvement cost divided by the RIII. (d) [4.5 points] Consider the numerical values of item (b) above and compute K when Cp-$5000, Cm $10,000, and Ci/o - $25,000. (e) [6 points] Describe how K varies as the improvement factors vary. Question 2 [30 points]: A computer system S can be decomposed into three subsystems: processor, memory, and I/0. S has a failure rate equal to A failures/sec. The processor accounts for a fraction fp of the total failures, the memory accounts for a fraction fm of the total failures, and the I/0 subsystem accounts for a fraction fi/o of the total failures. (Note that fp+fm+f/o 1) (a) [7.5 points] What is the reliability improvement index (RII) of system S if the factors Pp, Pm, and Pi/o, respectively (i.e., the failure rates are reduced)? (b) [4.5 points] Compute the RII assuming that fp 0.25, fm 0.35, and fi/o 0.4 failure rates of the processor, memory, and I/0 subsystem are improved by and Pp 2, Pm-3, and Pi/o .5 (c) [7.5 points] Assume that there is a cost to improve the reliability of each of the subsystems. This cost is not the same for each subsystem. Assume the following notation Cp: cost per unit of reliability improvement for the processor. So, the cost of improving the reliability of the processor by a factor of Pp is Cp xPp Cm: cost per unit of reliability improvement for the memory subsystem. So, the cost of improving the reliability of the memory by a factor of Pm is Cm x Pm. Ci/o: cost per unit of reliability improvement for the I/O subsystem. So, the cost of improving the reliability of the I/0 subsystem by a factor of Pi/o is Ci/o x Pi/o Give an expression for the metric K defined as the total improvement cost divided by the RIII. (d) [4.5 points] Consider the numerical values of item (b) above and compute K when Cp-$5000, Cm $10,000, and Ci/o - $25,000. (e) [6 points] Describe how K varies as the improvement factors vary