The following four questions follow this scenario. Assume an M/M/1 queue model w

Question

The following four questions follow this scenario. Assume an M/M/1 queue model with unlimited arrivals and FIFO queue discipline. Stacey is a high school student in a big city. Her summer vacation is coming up and she is thinking about opening an ice cream stand to make some money for a good cause. Stacey is wondering if it will be sufficient to have only one employee at the ice cream stand at any time. If so, she and her friend Mark could take turns. Stacey has done some basic research the previous summer by observing some ice cream shops in the city and also by talking to some potential customers. She expects to see about 25 customers an hour. She estimates that it would take her an average of 2 minutes to serve each customer. Customers would be served in a First in First Out (FIFO) manner. Her research further suggests that if there is a line of more than 4 people then some customers will “balk”. In addition, if customers have to wait more than 6 minutes to get their order filled they are not likely to come back.

What formula or equation would you use to compute average percentage of time the server is busy?

Explanation / Answer

The correct answer is Option B - p = / µ

Option A is used for calculating probability of zero customers in the system.

Option C is used for calculating probability of nth customer in the system.

Ws is used to calculate Average time spent in the system, including service

Wq is used to calculate Average waiting time in line

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