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Question: 2. Customers arrive to a single-server queue according to a Poisson process with mean rate...

Question:
2. Customers arrive to a single-server queue according to a Poisson process with mean rate 10 per hour. Customer service times have an exponential distribution with a mean of 5 minutes.
Find:
a. average number of customers in queue
b. average number of customers in queue and being served

Answer:
2. (a) 25/6 (b) 5.0

Professor gave answer, but I would like to see the steps on how to get the answer.

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Answer #1

Mean arrival rate, = 10 per hour = 1/6 per minute

Average customers served per unit time, = 1/5 per minute

a) Average number of customers in queue =

= 25/6

b) Average number of customers in queue and being served =

= (1/6) / (1/5 - 1/6)

= 30/6

= 5

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