At an airport, Company needs to check in three flights that leave at the same ti

Question

At an airport, Company needs to check in three flights that leave at the same time. For each of the three flights, 100 passengers will arrive randomly over the next two hours. There are 2 employees assigned to each flight and each employee can help a passenger on average in 2 minutes, with a standard deviation of 2 minutes. How long would passengers have to wait, on average, if these three flights were pooled such that each passenger could check in at each of the six employees?

PLEASE show calculation

ANSWERS:

Approximately 0.01 minutes

Explanation / Answer

Arrival rate is 100 passengers over two hours (120 minutes), say 120/100=1.2 minutes per passenger or 100/120 passengers per minute.

Average Service rate is 2 minutes per passenger or 1/2 passenger per minute and there are six employees (2 for each flight, 3flights=2*3).

Applying the formula for M/M/6 queue Having arrival per hour and service per hour

The minimum value (close to above calculations) is 0.01 minutes

Parameter Value M/M/s Arrival rate(lambda) 50 Service rate(mu) 30 Number of servers 6

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