On a Typical Monday, an Average of 8 Customers Per

question 66

Essay

On a typical Monday, an average of 8 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is five minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find:
a) The average time in the line.
b) The average number in the line.
c) The average time in the system.
d) The average number in the system.
e) The probability that the bank is empty.
f) If the business is considering adding a second teller (who would
work at the same rate as the first) to reduce the waiting time
for customers. She assumes that this will cut the waiting time in
half. If a second teller is added, find the new answers to parts (a)
to (e).

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Definitions:

Capacity Expansion

The process of increasing the production capabilities of a facility or system to meet expected demand increases.

Total Cost Comparisons

The process of comparing the overall costs of different alternatives or options in order to make a decision that minimizes costs while achieving desired outcomes.

Preventive Maintenance

A plan that involves routine inspections, servicing, and keeping facilities in good repair to prevent failure.