11.9 Suppose a high-performance computer (HPC) processes jobs which arrive according to a Poisson process with rate λ = 6 per day. We assume that all jobs require some time to complete and this time is uniformly distributed between 2 and 3 h. The HPC will process the jobs in the order they are received, and the jobs will be processed continuously as long as there are any in the queue. Calculate the expected proportion of time the HPC is busy.