The cafeteria line in the university student center is a self-serve facility in

Question

The cafeteria line in the university student center is a self-serve facility in which students select the items they want and then form a single line to pay the cashier. Students aive at a rate of about four per minute according to a Poisson distribution. The single cashier takes about 12 seconds per customer, following a negative exponential distribution. a) The probability there are more than two students in the system is 0.512 (round your response to three decimal places). The probability there are more than three students in the system 0.410 (round your response to three decimal places). The probability there are more than four students in the system-0328 round your response to three decima,places b) The probability that the system is empty is 0.2 (round your response to one decimal place). c) Before reaching the cashier, the average student have to wait 0.8 minutes (round your response to one decimal place) d) The expected number of students in the queue is 3.2 students (round your response to one decimal place). e) The average number of students in the system is 4 students (enter your response as a whole number). f) A second cashier is added and works at the same pace. Assume customers wait in a single line and go to the first available cashier The probability that the two server system is empty is 0.429 (round your response to three decimal places) The average waiting time for the two server system isminutes (round your response to three decimal places)

Explanation / Answer

formulas in excel

f) W = 0.2381 min

rest all answers are correct and can be seen using above excel formulation

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lambda mu c utilization % idle W L Wq Lq P0 4 5 2 0.8 0.2 0.23809524 0.952380952 0.038095238 0.152380952 0.42857143 4 5 1 0.8 0.2 1 4 0.8 3.2 0 0.2 0.2 0.8 1 0.16 0.36 0.64 2 0.128 0.488 0.512 ` 3 0.1024 0.5904 0.4096 4 0.08192 0.67232 0.32768 5 0.065536 0.737856 0.262144

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