Question: Queuing Problem (7 larks). The student cafeteria in C3 building has one employee. Student arrivals follow a Poisson distribution with arrival rate of 15 students

Queuing Problem (7 larks). The student cafeteria in C3 building has one employee. Student arrivals follow a Poisson distribution with arrival rate of 15 students per hour. The service time is exponentially distributed and the employee spends on average 3 minutes to serve each student. Assume that students are served in the order they arrive. Answer the following questions and show your detailed calculation steps. Round to 2 decimal places. 1. What is the service rate and what is the arrival rate? (1 mark) 2. Calculate the percentage of time the employee is busy. (1 mark) 3. Calculate the average number of students waiting in line. (1 mark) 4. Calculate the average waiting time in line. (1 mark) 5. How much time on average do students spend in the cafeteria? (1.5 marks) 6. When a student arrives to the cafeteria, what is the probability for him to find 3 or more students in the system? (1.5 marks)

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