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