A small diner has one employee and a counter with seating for 8 customers. The diner does not package food for takeout. Customers arrive at the diner at the rate of 20 per hour (Poisson distributed). Service times are exponentially distributed and average 24 per hour. Customers that arrive when all seats are taken do not enter the diner. What is the average number of customers waiting (average queue length)

Question

Mathematics

Yamilet Ellis

24 March, 15:11

A small diner has one employee and a counter with seating for 8 customers. The diner does not package food for takeout. Customers arrive at the diner at the rate of 20 per hour (Poisson distributed). Service times are exponentially distributed and average 24 per hour. Customers that arrive when all seats are taken do not enter the diner. What is the average number of customers waiting (average queue length)

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Liberty Ray · Answer 1

12 customers are waiting each hour to enter the diner

Step-by-step explanation:

20 customers arrive each hour to the diner. 8 customers ocuppy the seats each hour, and 12 are left waiting outside.