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Part A: Customer Support - Amazon Customer Service
Calls requiring product installation support arrive at the customer support every 3 minutes (exponential distribution). The time it takes to troubleshoot the problem over the phone is exponentially distributed with a mean of 6 minutes. IT support staff are paid an average of $25 an hour. The lost time for the care provider making the call to have the issue resolved is valued at $70 an hour. Based on a cost analysis, what is the optimal number of servers?
Note/Hint: This task required to compute total cost of waiting. While computing total cost consider number of servers and the most appropriate queuing operating characteristic(s). Following is the hints to find total cost:
Total cost = Wait cost + Server cost
Server cost = Number of servers * Server fee
Wait cost = avg number of entity/entities waiting in the queue/system * cost of waiting
time in queue/system
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