A Local Bank Has a Single Drive-In Teller Window

question 26

Essay

A local bank has a single drive-in teller window.Customers arrive at the drive-in window following a Poisson distribution at an average rate of 20 per hour.Assume that service is provided at the drive-in window at a rate of 30 customers per hour and that service time follows an exponential distribution.Moreover,assume that the population size is infinite and the queue length is unrestricted.To determine the efficiency of operations,the bank wishes to examine several queue operating characteristics.
a.What is the utilization rate of this service system?
b.What is the average number of customers in line?
c.What is the average time that each customer spends in the queue?
d.What is the average time that each customer spends in the system?
e.What is the probability that the drive-in window will be idle?

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Definitions:

Contra-Asset

A contra-asset account is an asset account where the account balance is a negative amount. It's used to offset the value of the asset account it is associated with, such as accumulated depreciation.

Cash Register Tapes

Physical or electronic records produced by cash registers, detailing each transaction made within a business.

Cash Short

A situation where the recorded amount of cash does not match the actual amount of cash available, often indicating errors or theft.

Cash Over

A situation where the amount of cash on hand is more than what was expected or reported, often requiring investigation.