Question

Customers arrive at a post ofﬁce with a single server. Fifty percent of the customers buy...

Customers arrive at a post ofﬁce with a single server. Fifty percent of the customers buy stamps, and take 2 minutes to do so. Twenty percent come to pick up mail and need 3 minutes to do so. The rest take 5 minutes. Assuming all these times are deterministic and that the arrivals form a Poisson process with a rate of 18 per hour, compute the expected number of customers in the post ofﬁce in steady state.

Expected number of customers in the Post office in steady state = 13.3

Explanation:

Fifty percent of the customers take 2 minutes, Twenty percent need 3 minutes and rest take 5 minutes.

Therefore,

Average service time = 0.50*2 + 0.20*3 + 0.30*5 = 3.1 minutes.

Average service rate = = (1/3.1)*60 = 19.3548 customers per hour.

Mean arrival rate = = 18 per hour.

Expected number of customers in the post ofﬁce in steady state =

=13.2861

Expected number of customers in the system = 13.3

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