Consider a system with a single CPU server in a steady-state condition where jobs arrive at rate per second. Jobs are processed using the FCFS scheduling policy. Each job requires average S seconds of service time.

(a) What is the server CPU utilization in this system? Express your answer in terms of and S.

(b) Let N denote the average number of jobs in this system and let T be the average amount of time a job spends in the system before departing. Given that jobs arrive at random points in time, a newly arriving job would find the average number of jobs in the system equal to N. With FCFS discipline, an arriving job has to wait for the completion of all of the jobs before it in the system. Ignoring the amount of service a job in the system may have already received and assuming that each of these jobs would require S seconds of average service time, give an expression for the average turnaround time T in terms of S and N.

(c) By Littles Law, N = T. Using this law, find the expression for N in terms of the server utilization .

(d) What is the value of N when = 1? What is its value when = 0.5?