Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according...

Q5. During peak hours, customers arrive at the cashier check-out queue in a local supermarket according to a Poisson process with an average rate of 120 customers per hour. There are four cashiers serving the check-out, and they provide identical service to customers. The time to service any customer by any of the cashier is exponentially distributed with a mean of 20 seconds. If all the cashiers are busy, customers join in a single queue on arrival.

(a) Compute the probability that an arriving customer have to wait in the queue for an available cashier;
(b) Suppose the supermarket opens at 10am, and Peter arrives at the cashier check-out at 10.02am. What assumptions are needed to approximate the probability that Peter do not have to queue.

Pls explain with workings. Thxs

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Expert Solution

During peak hours, customers arrive at the cashier check-out queue in a local supermarket according to a Poisson process with an average rate of 120 customers per hour.

Colby Messinger answered 1 year ago

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