A material handling station in a production area fills requests for more parts. On average, $15$ requests for part fulfillment arrive every hour. This arrival rate is Poisson distributed. The time for one technician to make a parts delivery averages $6$ minutes. The service time is exponentially distributed. There are currently three technicians working in the station. Find:

$=\backslash$lambda $=$ M $=$

a$.$ System utilization

b$.$ The average number of requests in line that have yet to be started

c$.$ The average time a request waits in line before being started

d$.$ How much time would a request wait to be started if one of the technicians is out sick?