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A Small Diner Has One Employee and a Counter with Seating

question 69

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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 time a customer spends waiting?


Definitions:

Compulsive Craving

An uncontrollable and intense desire for a particular substance or experience, often associated with addiction.

Addiction

Compulsive drug craving and use, despite adverse consequences.

Psychological Dependence

A condition where an individual feels emotionally or mentally attached to a substance or behavior, often leading to an insatiable craving for it.

Tolerance

The diminishing effect with regular use of the same dose of a drug, requiring the user to take larger and larger doses before experiencing the drug’s effect.

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