Jobs arrive to a file server consisting of a CPU and two disks (disk 1 and disk 2). With probability 13/20, a job goes from CPU to disk 1, and with probability 6/20, a job goes from CPU to disk 2....

Jobs arrive to a file server consisting of a CPU and two disks (disk 1 and disk 2). With probability 13/20, a job goes from CPU to disk 1, and with probability 6/20, a job goes from CPU to disk 2. With probability 1/20, a job is finished after its CPU operation and is immediately replaced by another job. There are always 3 jobs in the system. The mean time to complete the CPU operation is .039 second. The mean time to complete the disk 1 operation is .18 second, and the mean time to complete the disk 2 operation is .26 second.

a Determine the steady-state distribution of the number of jobs at each part of the system.

b What is the average number of jobs at CPU? Disk 1? Disk 2?

c What is the probability that CPU is busy? Disk 1? Disk 2?

d What is the average number of jobs completed per second by CPU? Disk 1? Disk 2?