PROBLEM #$4$: Simulation $(25$ points$)$

A reference librarian works alone at an information desk in one of the Welland Public Library branches for a certain period each Tuesday morning.

Simulate the arrival times of ten library patrons, and the service times for them.

Assume that there is one patron waiting at the information desk when the librarian arrives on the particular Tuesday morning that you will model.

Create one row for each patron, showing the following information:

Simulated$$interarrival time

Arrival time

When the librarian will begin servicing the patron's request for information

Simulated service time

When the librarian will finish servicing the patron's request.

How much time the patron will have had to wait for service

How much time the librarian was idle, which is to say, not servicing a library patron

Count of the number of patrons waiting at each step.

Be sure to make each row depend on the previous row in an appropriate way.

Summarise your simulation with the following information:

Total time that patrons had to wait.

Total time that the librarian was idle.

Average patron wait time.

Total idle time as a fraction of total service time.