Queuing Model$)$ A single public health worker is inoculating children against measles at a local clinic. An average of $8$ children per hour is expected to arrive according to a Markovian process. He serves the children at a rate of $10$ per hour. Assume that the service process is also approximately a Markovian process.

$($a$)$ For the $$inoculation system$,$ find:

i$)$ the utilization of the health worker.