Question: When a vehicle arrives at the base for maintenance, it must be delivered to the one and only customer Service Entry Point (SEP), which is

When a vehicle arrives at the base for maintenance, it must be delivered to the one and only customer Service Entry Point (SEP), which is located at the western end of the base. Here, the one and only customer service representative (CSR) receives and inspects the vehicle; during the inspection the CSR assesses each vehicle for the type of maintenance that is required and then assigns the vehicle to a particular maintenance shop. Once the assessment is completed, the vehicle is moved to its assigned maintenance shop.

Your data search has revealed the following information:

  1. The SEP is open for business 8 hours a day six days a week.
  2. Approximately 40 vehicles arrive daily at the customer SEP. The arrival pattern follows a Poisson distribution. Assume vehicles arrive only when the SEP is open for business.
  3. On average, the CSR requires 10 minutes to receive, inspect, and assign a repair shop. Service time follows an exponential distribution.
  4. Service occurs on a first come first served basis.

COL Boyd has determined that adding a second server at the one SEP requires an investment of $68,000 to expand the building to accommodate the second server. He does not have that amount of money in his budget. However, he has found an abandoned building on the eastside of the base that could be rehabilitated for only $8,000. This building could only accommodate one CSR. If he decides to rehab the abandoned building and place a server there, COL Boyd would have two SEPs with one CSR at each. In this case, assume that vehicles randomly and uniformly select which SEP to enter; also assume that each server services a vehicle in an average of 10 minutes. Under this scenario determine the average wait time in line, the average wait time in the system, the average length of the queue, and the average length of time spent in the system. Determine all times in minutes, rounding to at least six significant digits.

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