Consider a grocery store between the hours of 6 and 8pm on a weeknight. Suppose two checkout lanes are typically open, each checkout can handle customers with any number of items, and each checkout has a dedicated employee. It has been observed that checking out takes a mean of 1.5 minutes per customer and that this is approximately normally distributed with a standard deviation of .3 minutes. The mean amount of time between customer arrivals at the checkouts is 1 minute and can be approximated by an exponential distribution. A: Model the scenario where a single queue is used to feed both checkout lanes (similar to the bank example with two tellers). What is the average flow time of a customer? B: Model the scenario where each checkout lane has its own separate queue, and assume that half of the customers go to queue 1 and the rest go to queue 2. What is the average flow time of a customer in this setup? Hint: Split the customer arrivals in half (i.e., double ??) and model just a single queue leading to a single checkout lane. The second queue- checkout lane will have identical performance. C: Which system works better? Why?
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Consider a grocery store between the hours of 6 and 8pm on a weeknight. Suppose two checkout lanes are typically open, each checkout can handle customers with any number of items, and each checkout has a dedicated employee. It has been observed that checking out takes a mean of 1.5 minutes per customer and that this is approximately
normally distributed with a standard deviation of .3 minutes. The mean amount of time between customer arrivals at the checkouts is 1 minute and can be approximated by an exponential distribution.
A: Model the scenario where a single queue is used to feed both checkout lanes (similar to the bank example with two tellers). What is the average flow time of a customer?
B: Model the scenario where each checkout lane has its own separate queue, and assume that half of the customers go to queue 1 and the rest go to queue 2. What is the average flow time of a customer in this setup? Hint: Split the customer arrivals in half (i.e., double ??) and model just a single queue leading to a single checkout lane. The second queue- checkout lane will have identical performance.
C: Which system works better? Why?
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