Consider a closed system in which 4 terminals submit jobs to a computer system. Each terminal submits jobs according to a Poisson process with a rate λ = 1 job every 2 seconds. Once a terminal submits a job it cannot submit another job until its submitted job is complete. The computer system has 2 CPUs which can each handle one job at a time. There is also a buffer for holding one additional job. A terminal is not allowed to submit a job if both CPUs and the buffer are occupied. In this case, the job will be blocked. The speed of the processors can be controlled in order to save power. If there are one or two jobs in the computer system, the processors that are occupied each operate at a speed of 500 MHz (million cycles per second). If there are three jobs in the computer system, each processor operates at a speed of 1 GHz (billion cycles per second). The length of a job is exponentially distributed with an average job length of 500 million cycles. (Hint: Find the service rates in units of jobs per second).

(a) Draw the state diagram for the system, clearly labeling transition rates.

(b) Find the steady-state probabilities for the number of jobs in the computer system (consisting of the CPUs and buffer).

(c) Find the expected number of customers in the system.

(d) Find the expected time that a job waits in the buffer before receiving service.

(e) Find the total system utilization.

(f) Find the probability that an arriving job to the computer system is blocked