Question: Problem 1. A small grocery store has two checkout counters that are always open to serve customer…

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Jun 13, 2022

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Question: Problem 1. A small grocery store has two checkout counters that are always open to serve customer…

by | Jun 13, 2022 | Questions & Answers


Problem 1. A small grocery store has two checkout counters that are always open to serve customers. The average checkout time per customer is 2 minutes per server. Suppose customers arrive to the checkout at a Poisson rate of 2 in 3 minutes. Calculate the average time that a customer spends in checkout for the following two policies: (a) All customers form a single line, and the customer at the front of the line goes to the first free counter (randomly picked if both happen to be free). (b) Customers pick one of the two lines to join randomly (i.e, with probability 0.5) and go to that lines counter (c) What is the maximum possible arrival rate for the above two policies if the customer checkout time is to be no more than 10 minutes?

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Problem 1. A small grocery store has two checkout counters that are always open to serve customers. The average checkout time per customer is 2 minutes per server. Suppose customers arrive to the checkout at a Poisson rate of 2 in 3 minutes. Calculate the average time that a customer spends in checkout for the following two policies: (a) All customers form a single line, and the customer at the front of the line goes to the first free counter (randomly picked if both happen to be free). (b) Customers pick one of the two lines to join randomly (i.e, with probability 0.5) and go to that line's counter (c) What is the maximum possible arrival rate for the above two policies if the customer checkout time is to be no more than 10 minutes?

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