Orders are arriving rapidly! Since you believe that the quality of your customer service is one of the most important aspects of Bobbie’s Bobbles that will determine whether it is successful or not, you have decided to handle all orders yourself. Suppose that the time between orders is exponentially distributed with a rate of 10 per hour. You process the orders one-at-a-time and, out of fairness, on a first-come- first-serve basis. The time that it takes you to process each order is exponentially distributed with rate μ. (a)Assuming that orders continue to arrive indefinitely, what kind of model can you use to analyze the long-run behavior of your system of processing incoming orders of Bobbles? (b) Suppose that you want to process orders fast enough such that the long-run expected number of orders in your system (including any order you are processing along with any orders waiting to be processed) is at most 5. What is the minimum value for μ (in terms of orders per hour) that you need to process in order to achieve this goal? (c) Nowsupposethatyouwanttoconsideradifferentperformancemeasure. In particular, suppose that you want to work fast enough such that the long-run expected time that an order needs to wait in line (before you start processing it) is at most 6 minutes. What is the minimum value for μ (in terms of orders per hour) that you need in order to achieve this?
Orders are arriving rapidly! Since you believe that the quality of your customer service is one of the most important aspects of Bobbie’s Bobbles that will determine whether it is successful or not, you have decided to handle all orders yourself.
Suppose that the time between orders is exponentially distributed with a rate of 10 per hour. You process the orders one-at-a-time and, out of fairness, on a first-come- first-serve basis. The time that it takes you to process each order is exponentially distributed with rate μ.
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(a)Assuming that orders continue to arrive indefinitely, what kind of model can you use to analyze the long-run behavior of your system of processing incoming orders of Bobbles?
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(b) Suppose that you want to process orders fast enough such that the long-run expected number of orders in your system (including any order you are processing along with any orders waiting to be processed) is at most 5. What is the minimum value for μ (in terms of orders per hour) that you need to process in order to achieve this goal?
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(c) Nowsupposethatyouwanttoconsideradifferentperformancemeasure. In particular, suppose that you want to work fast enough such that the long-run expected time that an order needs to wait in line (before you start processing it) is at most 6 minutes. What is the minimum value for μ (in terms of orders per hour) that you need in order to achieve this?
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