Consider passenger arrival at the Minneapolis International Airport security check point. The passengers form a single queue. Each passenger places his or her carry-on luggage on a moving belt to be scanned by an X-ray machine. Each passenger is a customer, and the X-ray machine is the server which processes the customers in FIFO order. The arrival queue capacity is practically unlimited, so no one gets blocked from joining the queue. Moreover, all passengers must go through the security check, so no one abandons the queue. Assume that the processing time by the X-ray machine per customer is randomly varying with a mean of 5 seconds and standard deviation of 3 seconds. The interarrival time of the customers is randomly varying with a mean of 6 seconds and a standard deviation of 3 seconds. Assume general distribution for both the processing and the interarrival time. This allows the use of the queue length formula.
What is the average time spent by a passenger in the whole system?