Final answer:
The question asks for the average number of customers waiting in a queue at an airport with multiple service lines, requiring the use of a queueing theory model. Given the provided arrival and service rates, as well as the lines available, additional information or the use of an M/D/n queueing theory model is necessary to calculate the exact number.
Step-by-step explanation:
Calculating the Average Number of Customers in Queue
The question involves the concept of queues, specifically in a scenario where demand and service rates are variable and there are multiple servers. Given that there are nine lines for arriving passengers at the airport, and the arrival rate is 120 passengers per hour, which is one passenger every 30 seconds, we can start analyzing the situation.
Each passenger takes on average 4 minutes to process by a worker. This gives us a service rate of 15 passengers per hour for each line. However, to calculate the average number of customers waiting in the queue, we would need a queueing theory model that takes into account the coefficient of variation for arrival and service times, and the fact that there are multiple servers. One such model that could be applied here is the M/D/n (Poisson arrivals, deterministic service times, 'n' servers) queue model, which is not fully described by the information given. Nevertheless, the question appears to require additional information or assumptions to provide an accurate calculation of the average number of customers waiting in the queue.
Without the necessary formula or more specific constraints, we cannot provide an exact numerical answer. It would also be appropriate to use a queueing theory calculator or software equipped with the M/D/n features to obtain a precise answer.