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16.04.2021 • 
Mathematics

Pete's Market is a small local grocery store with only one checkout counter. Assume that shoppers arrive at the checkout lane according to a Poisson probability distribution, with an arrival rate of 13 customers per hour. The checkout service times follow an exponential probability distribution, with a service rate of 20 customers per hour. It is the manager's service goal to limit the waiting time prior to beginning the checkout process to no more than five minutes. After reviewing the waiting line analysis of his store, the manager of Pete's Market wants to consider one of the following alternatives for improving service. Option 1: Hire a second person to bag the groceries while the cash register operator is entering the cost data and collecting money from the customer. With this improved single-server operation, the service rate could be increased to 30 customers per hour. (Note: Although we hire one more person, it is still an M/M/1 queueing system, Because we do not operate a second counter but only hire a person to help with the first cashier counter, the service rate of the cashier improves.) What are the arrival and service rates in Option 1

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