Question

A Security Pacific Bank branch has opened up a drive through teller window. There is a single service lane, and customers in their cars line up in a single line to complete bank transactions. The average time for each transaction to go through the teller window is exactly four minutes. Throughout the day, customers arrive independently and largely at random at an average rate of ten customers per hour.

What is the probability that a customer gets to complete his/her transaction within 5 minutes?

Answer #1

The First American Bank of Rapid City has one outside drive-up
teller. It takes the teller an average of 4 minutes to serve a bank
customer. Customers arrive at the drive-up window at a rate of 12
per hour. The bank operations officer is currently analyzing the
possibility of adding a second drive-up window, at an annual cost
of $20,000. It is assumed that arriving cars would be equally
divided between both windows. The operations officer estimates that
each minute’s...

Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 24 customers
per hour or 0.4 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 36 customers per hour, or 0.6
customers per minute. Determine the probabilities...

Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 30 customers
per hour or 0.5 customers per minute. In the same bank waiting line
system, assume that the service times for the drive-up teller
follow an exponential probability distribution with a service rate
of 36 customers per hour, or 0.6...

Problem 11-04 (Algorithmic)
Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 24 customers
per hour or 0.4 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 36 customers per hour, or 0.6
customers per minute....

Problem 15-3 (Algorithmic) Willow Brook National Bank operates a
drive-up teller window that allows customers to complete bank
transactions without getting out of their cars. On weekday
mornings, arrivals to the drive-up teller window occur at random,
with an arrival rate of 18 customers per hour or 0.3 customers per
minute. In the same bank waiting line system, assume that the
service times for the drive-up teller follow an exponential
probability distribution with a service rate of 30 customers per...

Exponential/Poisson
Megacity Bank operates a drive-up teller window that
allows customers to complete bank transactions without having to
get out of their car. Megacity Bank waiting line times follow an
exponential distribution with a service rate of 36 customers per
hour.
A.What is the probability that the time to service is 1 minute
or less? (show your formula with the numbers plugged in, as well as
the answer. You may use the e^(-λ) table, an advanced calculator or
excel to...

A bank is designing a new branch office and needs to determine
how much driveway space to allow for cars waiting for drive up
teller service. The drive up service will have three tellers and a
single waiting line. At another branch of the bank in a similar
setting, the average service time for drive up tellers is 4 minutes
per customer and average arrival rate is 36 customers per hour. It
is expected that the new bank will have...

The National Bank of Germany is opening a new bank teller.
Management estimates that customers will arrive at the rate of 10
per hour. The teller who will staff the window can serve customers
at the rate of one every four minutes.
Assuming Poisson arrivals and exponential service, find:
Average number of customers in the system.
Average time in the system.
Average waiting time in the line.
Average number of customers in the line.
Utilization of the teller.

1. Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 6 customers
per hour or 0.1 customers per minute. Also assume that the service
times for the drive-up teller follow an exponential probability
distribution with a service rate of 54 customers per hour, or 0.9
customers per minute. Determine the...

An automatic roller coaster ride takes a constant time of 2.5
minutes to complete a ride. Customers arrive at the facility every
2.75 minutes (exponentially distributed). Report answers to 4
decimal places.
a. Determine the average waiting time in the queue (in
minutes).
b. The local bank drive-through teller window can serve a
customer at an average of 4.5 minutes per customer (exponentially
distributed). Customers arrive in their cars at a rate of 12 per
hour (poisson distributed). Determine the...

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