# Analyze the timesharing system of Exercise 33.6 using the convolution method with N = 3 users….

Analyze the timesharing system of Exercise 33.6 using the convolution method with N = 3 users.

Determine the distribution of the CPU queue length.

Exercise 33.6

For the system of Exercise 33.5, answer the following:

a. What is the bottleneck device?

b. What is the minimum average response time?

c. What is the maximum possible disk A utilization for this configuration?

d. What is the maximum possible throughput of this system?

e. What changes in CPU speed would you recommend to achieve a response time of 10 seconds with 25 users? Would you also need a faster disk A or disk B?

f. Write the expressions for asymptotic bounds on throughput and response time.

Exercise 33.5

For a timesharing system with two disks (user and system), the probabilities for jobs completing the service at the CPU were found to be 0.80 to disk A, 0.16 to disk B, and 0.04 to the terminals. The user think time was measured to be 5 seconds, the disk service times were 30 and 25 milliseconds, and the average service time per visit to the CPU was 40 milliseconds. Using the queueing network model shown in Figure 32.8, answer the following for this system:

a. For each job, what are the visit ratios for CPU, disk A, and disk B?

b. For each device, what is the total service demand?

c. If disk A utilization is 60%, what is the utilization of the CPU and disk B?

d. If the utilization of disk B is 10%, what is the average response time when there are 20 users on the system?