Question 3 The following questions concern simple applications of queueing theory: a If an M/M/1 queue in a server has task arrivals at a rate of 30 per second and serves at a rate of 50 per second, how many tasks are in the system (waiting and being served) on average? b In part (a), how many tasks are being served, on average? c What is the utilization of an M/M/1 queue in a server that has four tasks waiting on average? Question 4: A certain program takes 26.67 seconds to run on 3 processors and 16 s to run on 7 processors. Find the execution time on one processor, the fraction of the program that can be parallelized, the theoretical execution time on an infinite number of processors, and P1/2. Question 5: Evaluate the average gate capacitance of, and power dissipated by, a processor with the following properties Gate oxide thickness 14 nm Gate length = 65 nm Gate area (65 nm)x(65 nm) . Permittivity of free space = 8.85 x 10e-12 Farads/m . Relative permittivity of SiO2-3.9 -Rail-to-rail voltage = 1.1 V Clock frequency = 3.6 GHz Switching probability 1.0 Number of transistors per die = 1-3 x 1 0e9