A financial institution is evaluating the need for additional drive-up windows at a branch that currently ...

A financial institution is evaluating the need for additional drive-up windows at a branch that currently has only one drive-up window. Employees working in that branch have gathered data about activity during their busiest times, which are the times of concern for keeping patrons satisfied with customer service. Data shows that patrons arrive at an average rate of 20 per hour and that the average time to complete any one patron’s business at the drive-up window is two minutes.

Assume single-channel waiting line with Poisson arrivals, exponential service times, and a first-come, first-served queue discipline

Apply the single-channel waiting line model to the given situation to determine the following:

1.  Probability that the system is idle because no patrons are in the system

2.  Average number of patrons in the waiting line at one time

3.  Average number of patrons in the system at one time

4.  Average time in minutes a patron spends in the waiting line

5.  Average time in minutes a patron spends in the system.

6.  Probability that an arriving patron will have to wait for service