Question

A customer plans to checkout at a grocery store but finds all 5 cashiers busy serving other customers. There are no other customers when this person arrives, and they will be served as soon as someone finishes. All customer arrival and service times are independent and exponentially distributed.

a) What is the probability that this customer will not be the last customer to depart?

b) If the average service time per cashier is 4 minutes, what is the average time this customer will spend in the store?

c) If the average arrival rate is 3 customers/minute, on average how many customers will be in the system?

Answer #1

A customer plans to checkout at a grocery store but finds all 5
cashiers busy serving other customers. There are no other customers
when this person arrives, and they will be served as soon as
someone finishes. All customer arrival and service times are
independent and exponentially distributed.
a) What is the probability that this customer will not be the
last customer to depart?
b) If the average service time per cashier is 4 minutes, what is
the average time...

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