Question

Use the following information to answer the next few questions: An immigration agent at Ataturk airport in Istanbul, Turkey on the average could process 120 entrants during an 8 hour shift, if she was busy all the time. The number of arrivals is based on a Poisson distribution and the time to process each entrant is a random variable with an exponential distribution. On the average, an entrant arrives at her station once every 6 minutes. Determine the average number of people waiting in line.

.05

1.33

2

.09

.27

Answer 1

Answer: 1.33

Rationale:

Arrival time = 6 minutes

Arrival Rate () = 1/Arrival time

Arrival Rate () = 1/6 customers per minute

Arrival Rate () = 60/6 customers per hour

Arrival Rate () = 10 customers per hour

Service Rate (​​​​​​) = 120 customers in 8 hours

Service Rate () = 15 customers per hour

Number of customers waiting in line = Lq

Lq = 1.33

Therefore, average number of customers waiting in line = 1.33

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