Use the following information to answer the next 2 questions (problems 9 & 10).

Question

Use the following information to answer the next 2 questions (problems 9 & 10). Suppose an additional immigration officer is added to the process so that now there are two immigration officers each able to process (serve) IS passengers per hour. Also, assume that the arrival rate for passengers is now 20 per hour. Answer the following questions: On average, how many passengers are in the system, this includes those who are waiting for service and those being processed? {Fractional answers are acceptable because we are dealing with averages) On average, how many minutes do passengers spend in the immigration process-this includes wait time plus service (processing) time?

Explanation / Answer

Let a=arrival rate and s=service rate

a = 20 = 1/3 passengers per hour

s = 2 x15 = 30 passengers per hour

No. of customer in the system = a^2 / s (s-a)

= 20^2 / 30 (30-20)

= 4 / 3

= 1.3 = 2 customers

Expected waiting time in the system = 1 / (s - a)

= 1 / 30-20

= 1/10

Converting into minutes = (1/10) x 60

= 6 minutes

Passenger spends 6 minutes in the migration process.

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