A single public health worker is inoculating children against measles at a local clinic. An average of 5 children per hour are expected to arrive. He serves the children at a rate of 6 per hour. You may assume that the coefficient of variation of the time between arrivals and the service times are both 1, i.e., CVaCVa = 1 and CVpCVp = 1.
a) For the inoculation system, find (SHOW YOUR WORK)
i. the load factor of the health worker
ii. the average time spent by a child in the system in minutes
iii. the average number of children in the system
b) At what rate must children be served in order to reduce the average time spent in the system to 30 min? (children/hr)
iv. the average number of children in line