Agents at the security gate at the Hurtsfield County Regional Airport are able to check passengers and process them through the security gate at the rate of 52 per hour (Poisson distributed). Passengers arrive at the gate throughout the day at the rate of 45 per hour (Poisson distributed).
a. Determine the average waiting time and waiting line.
b. The passenger traffic arriving at the airport security gate varies significantly during the day and flight takeoffs tend to cluster making the passenger traffic very heavy at specific times while at other times there is little or no passenger traffic through the security gate. At the times leading up to flight takeoffs passengers arrive at a rate of 125 per hour (Poisson distributed). Develop and solve a waiting line system that can accommodate this increased level of passenger traffic.