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QUESTION 1 (Queing Analysis) A movie theater ticket booth has a mean arrival rate of 5...

QUESTION 1 (Queing Analysis) A movie theater ticket booth has a mean arrival rate of 5 persons every minute and the service rate is 6 persons per minute. Assuming that arrivals are Poisson distributed and service times are exponentially distributed, and that steady-state conditions exist, calculate the following characteristics of this queuing system applying the FIFO M/M/1 model: a) Utilization ratio (or traffic intensity) b) The average number of people in the system c) The average length of the queue (average number of people in the queue) d) Average waiting time of each customer in the system e) Average waiting time of each customer in the queue f) Percent of the time that the server is idle g) Roughly sketch (or plot) Pn (the probability that there are n persons in the queue) against n. h) List all the characteristics (assumptions) of the FIFO M/M/1 queuing model.

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