Consider two machines that operate in parallel. Each machine processes jobs at a rate of 5 jobs per hour (i.e., µ = 5 jobs/hour). Jobs arrive to the machines at a rate of 8 jobs per hour (i.e., λ = 8 jobs/hour). When jobs arrive, they wait in a single queue and are processed by the first machine that becomes available. There is again randomness in both job processing times and inter-arrival times. The standard deviation of processing times is 6 minutes; the standard deviation of inter-arrival times is 15 minutes.
(a) What is the average utilization of each machine?
(b) On average, what is the throughput (in terms of number of jobs per hour)?
Use the G/G/m approximation to answer the following:
(c) On average, how long does a job spend waiting to get processed, E(Wq)?
(d) On average, how long does a job spend in the system (time in the queue + time in process), E(W)?
(e) On average, how many jobs are in the queue, E(Nq)?
(f) On average, how many jobs are in the system (number of jobs in the queue + jobs in process), E(N)?
(g) Compare your answers for this problem to those you obtained for problem 2). Explain briefly the differences.