probability theory
Bank of America has a single drive-in teller window in a busy location in New York City. The number of customers arriving at the window in any interval of length t (minutes) is Poisson with mean t/3.
The service time is exponentially distributed with mean 4 minutes.
1) Find the theoretical distribution of the interarrival times.
2) Find the theoretical distribution of the arrival time of the Nth customer.
3) Simulate four working hours (9am – 1pm) and find the following:
• average inter-arrival time
• average service time
• server utilization (proportion of time the teller is busy)
• number of customers that had to wait
• their average waiting time (applied only to those who had to wait).
Provide histograms for the number of customers arriving each hour along with the theoretical Poisson distribution graph, inter-arrival times along with the corresponding theoretical distribution and the service times with the corresponding theoretical distribution.
You can use Matlab for simulation
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