Sunset Airlines is reviewing its check-in procedures in anticipation of its "two for the price of one" fare promotion. Presently, a single clerk spends an average of three minutes per passenger checking luggage and issuing boarding passes. Service times have a negative exponential distribution. Passenger arrivals are Poisson distributed with anticipated mean of 15 per hour during flight operations.
a. What is the probability that an arriving passenger will be served immediately without waiting?
b. The area immediately in front of the Sunset counter can accommodate only 3 passengers, including the one being served. What percentage of the time will this area be inadequate for waiting passengers?
c. Anticipating an increase in demand, Sunset has decided to add another clerk, when passengers begin to experience an average wait time in queue of 15 minutes. Because arrival rates are monitored at the check-in counter, determine what arrival rate per hour would indicate the need for another clerk.
Average arrival rate of customers now has reached 20 per hour and Sunset Airlines must increase the capacity of its check -in system. Based on a customer survey, $15 per hour is considered the opportunity cost of waiting in queue. Clerks are paid $10 per hour and still process a passenger in three minutes. Evaluate the following check -in system alternatives to find the least expensive arrangement using total hourly costs of clerks and customers waiting in queue.
d. First, consider a multiple queue configuration with two separate waiting lines and no customer jockeying. Assuming demand is equally divided between the two clerks, what is the total hourly cost of this arrangement?
e. Consider, instead, adding one self-serve ATM (Automated Ticketing Machine) with constant service time of three minutes to help a single clerk. Assume demand is equally divided between the single clerk and the ATM. What is the total hourly costs of this arrangement if the the ATM operating costs are negligible?
f. Finally, consider a single queue arrangement witrh two clerks. What is the total hourly costs of this arrangement?