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University Financial Inc. (UFI) recently hired an employee to produce various reports for reporting requests from internal teams and their clients. At the beginning,
University Financial Inc. (UFI) recently hired an employee to produce various reports for reporting requests from internal teams and their clients. At the beginning, the new employee receives an average of nine reporting requests per hour, which follows a Poisson distribution. The new employee follows FCFS discipline to produce reports for reporting requests. The employee is capable of producing a report every five minutes on average. Assume that the service time is distributed exponentially. a) What is the employee utilization? b) How many reporting requests would you expect to see that are waiting in line? c) What is the average time in minutes a report request spends in the system (i.e. both waiting in line or being produced)? d) What is the probability that more than three reporting requests are either waiting in line or being produced? Later, both internal teams and clients realize the value of data-driven reports in their daily decision- making. The number of reporting requests has dramatically increased, and the company receives an average of 30 reporting requests per hour. University Financial Inc. hired three more employees to work on the reports. (i.e. four employees in total work on the reports at University Financial Inc.). Assume the service time of each employee is identical and distributed exponentially at one report every five minutes. e) How many reports would the company expect to see waiting in line or being produced?
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