9 Jobs arrive to a file server consisting of a CPU and two d

9 Jobs arrive to a file server consisting of a CPU and two disks (disk 1 and disk 2). Currently there are six clients, and an average of three jobs per second arrive. Each visit to the CPU takes an average of .01 second, each visit to disk 1 takes an average of .02 second, and each visit to disk 2 takes an average of .03 second. An entering job first visits the CPU. After each visit to the CPU, with probability 7/16 the job next visits disk 1, with probability 8/16 the job next visits disk 2, and with probability 1/16 the job is completed. After visiting disk 1 or 2, the job immediately returns to the CPU. a On the average, how many times does a job visit the CPU? How about disk 1? How about disk 2?

Solution

a)

average number of times a job visits the CPU = n * P(CPU)

n = number of clients

P(CPU) = probability of visiitng CPU

= 6 * 7/16

= 2.625 = 3

the average number of times job visits CPU is 3

b)

average number of times a job visits the disk 1 = n * P(disk 1)

n = number of clients

P(disk 1) = probability of visiitng disk 1

= 6 * 8/16

= 3
the average number of times job visits disk 1 is 3

c)

average number of times a job visits the disk 2 = n * P(disk 2)

n = number of clients

P(disk 2) = probability of visiitng disk 2

= 6 * 1/16

= 0.375

the average number of times job visits disk 2 is 0.375