Question

Use QM for Windows to solve the following problems. Click on the Waiting Lines menu options, and make sure to select the correct model (i.e. finite system size, finite population, etc, etc)

A telephone system at a help desk has the capacity to put a maximum 5 callers on hold. Assume calls come on average every 6 minutes, and it takes on average 5 minutes to assist the customer.

- What is the average wait time in minutes that a customer will be on hold?
- How many customers on average are in the system?

A consultant has 11 clients. The consultant gets on average 2 calls in an 8 hour day, and on average the consultant takes 2.5 hours to complete a call.

- What percent of the time is the consultant busy?
- What is the average time in minutes to complete service from the time the client calls until the call is completed?

A bank has 2 drive up windows. On average, customers arrive at a rate of 20 per hour, and it takes on average 4 minutes to serve the customer.

- What is the average wait time in minutes until the customer gets to the drive up window?

Answer #1

A customer service center has customers call with questions
about the use of a product. The mean arrival rate of customer calls
is 20 per hour and follows a Poisson distribution. The mean service
rate (how long it takes the call center employee to answer the
customer’s question) is 30 customers per hour (most customer
questions can be answered rather quickly) and follows an
Exponential distribution.
What is the mean (average) time in hours that a customer spends
in the...

4. Phone calls arrive at the rate of 48 per hour at the
reservation desk for Varig Airlines. a. Find the probability of
receiving three calls in a five-minute interval time. b. Find the
probability of receiving exactly 10 calls in 15 minutes. c. Suppose
no calls are currently on hold. If the agent takes five minutes to
complete the current call, how many callers do you expect to be
waiting by that time? What is the probability that none...

Ocala Software Systems operates a technical support center for
its software customers. If customers have installation or use
problems with Ocala software products, they may telephone the
technical support center and obtain free consultation. Currently,
Ocala operates its support center with one consultant. If the
consultant is busy when a new customer call arrives, the customer
hears a recorded message stating that all consultants are currently
busy with other customers. The customer is then asked to hold and
is told...

Phone calls arrive at the rate of 24 per hour at the reservation
desk for Regional Airways.
a. Compute the probability of receiving two
calls in a 10-minute interval of time.
(to 4 decimals)
b. Compute the probability of receiving exactly
12 calls in 15 minutes.
(to 4 decimals)
c. Suppose no calls are currently on hold. If
the agent takes 5 minutes to complete the current call, how many
callers do you expect to be waiting by that time?...

The customer support hotline for Bitway Computers is currently
staffed by a single technician. Calls arrive randomly at a rate of
five per hour and follow a Poisson distribution. The technician can
service calls at an average rate of seven per hour, but the actual
time required to handle a call is an exponential random variable.
The president of Bitway has received numerous complaints from
customers about the length of time they must wait “on hold” for
service when calling...

Ocala Software Systems operates a technical support center for
its software customers. If customers have installation or use
problems with Ocala software products, they may telephone the
technical support center and obtain free consultation. Currently,
Ocala operates its support center with one consultant. If the
consultant is busy when a new customer call arrives, the customer
hears a recorded message stating that all consultants are currently
busy with other customers. The customer is then asked to hold and
is told...

Problem 11-15
(Algorithmic)
Ocala Software Systems
operates a technical support center for its software customers. If
customers have installation or use problems with Ocala software
products, they may telephone the technical support center and
obtain free consultation. Currently, Ocala operates its support
center with one consultant. If the consultant is busy when a new
customer call arrives, the customer hears a recorded message
stating that all consultants are currently busy with other
customers. The customer is then asked to hold...

I need a detailed explanation with a formula
(show work) included on how to solve this
question:
Scenario
Office Equipment, Inc. (OEI) leases automatic mailing machines
to business customers in Fort Wayne, Indiana. The company built its
success on a reputation of providing timely maintenance and repair
service. Each OEI service contract states that a service technician
will arrive at a customer's business site within an average of 3
hours from the time that the customer notifies OEI of an...

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...

Scenario:
Office Equipment, Inc. (OEI) leases automatic mailing machines
to business customers in Fort Wayne, Indiana. The company built its
success on a reputation of providing timely maintenance and repair
service. Each OEI service contract states that a service technician
will arrive at a customer’s business site within an average of 3
hours from the time that the customer notifies OEI of an equipment
problem.
Currently, OEI has 10 customers with service contracts. One
service technician is responsible for handling...

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