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

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 2 years ago

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