Question

Students arrive at the Administrative Services Office at an average of one every 15 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times.

**a.** What percentage of time is Judy idle?
**(Round your answer to 1 decimal place.)**

Percentage of time %

**b.** How much time, on average, does a student spend
waiting in line? **(Do not round intermediate calculations.
Round your answer to the nearest whole number.)**

Average time minutes

**c.** How long is the (waiting) line on average?
**(Round your answer to 2 decimal places.)**

Average length of the waiting line
customers

**d.** What is the probability that an arriving
student (just before entering the Administrative Services Office)
will find at least one other student waiting in line? **(Do
not round the intermediate calculations. Round your answer to 2
decimal places.)**

Probability %

Answer #1

This is a M/M/1 system problem:

Arrival rate (l) = 4 students per hour

Service rate (m) = 6 students per hour

No of servers (s) = 1

Average utilization (p) =l/m = 4/6 = 0.667

a) Idle time = 1- utilization time = 1-p = 0.333 or 33.33%

b) The average time in the line, in minutes (Wq) = p * 1/(m-l) = 0.667 * (1/2) = 0.3335 hr = 0.3335 * 60 =20.01 mins

c) The average number of students waiting in the line (Lq) = p*l / (m-l) = (0.667*4)/ (6-4) = 2.668/2 = 1.334 students = 1.33 students

d) The probability that there are 1 or more people the system = 1 – 0.333(1 + 0.667) = 1 – 0.333 (1.667) = 1- 0.555 = 0.4451 = 44.51%

Students arrive at the School Office at an average of one
student every 15 minutes, and their requests take on average 10
minutes to be processed. The service counter is staffed by only one
clerk, Linda Jones, who works eight hours per day and gets
paid $75 per day.
a) On average, how many students go to the School Office per
day?
b) How much time, on average, does a student spend waiting in
line?
c) How many minutes a...

Agan Interior Design provides home and office decorating
assistance to its customers. In normal operation, an average of 2.7
customers arrive each hour. One design consultant is available to
answer customer questions and make product recommendations. The
consultant averages 10 minutes with each customer.
Compute the operating characteristics of the customer waiting
line, assuming Poisson arrivals and exponential service times.
Round your answers to four decimal places. Do not round
intermediate calculations.
Lq =
L =
Wq = ____minutes
W...

Agan Interior Design provides home and office decorating
assistance to its customers. In normal operation, an average of 3.2
customers arrive each hour. One design consultant is available to
answer customer questions and make product recommendations. The
consultant averages 12 minutes with each customer.
Compute the operating characteristics of the customer waiting
line, assuming Poisson arrivals and exponential service times.
Round your answers to four decimal places. Do not round
intermediate calculations.
Lq =
L =
Wq = minutes
W = minutes...

Exercise 11.2.5 Customers arrive at Bunkey’s car wash service at
a rate of one every 20 minutes and the average time it takes for a
car to proceed through their single wash station is 8 minutes.
Answer the following questions under the assumption of Poisson
arrivals and exponential service.
(a) What is the probability that an arriving customer will have
to wait?
(b) What is the average number of cars waiting to begin their
wash?
(c) What is the probability...

At CDE dental office, on average, 30 patients arrive every hour
and are processed at the same rate. Patients wait in line for
registration. On average, it takes 5 minutes for registration, not
including waiting time. A dentist’s assistant sees a patient after
registration and assigns the patient to one of the two tracks, one
for routine cleanings and another for major treatments. On average,
the dentist's assistant spends 20 minutes with each patient. On
average, 2/3 (or 66.67%) of...

On average, 90 patrons arrive per hour at a hotel lobby
(interarrival times are exponential) waiting to check in. At
present there are five clerks, and patrons wait in a single line
for the first available clerk. The average time for a clerk to
service a patron is three minutes (exponentially distributed).
Clerks earn $10 per hour, and the hotel assesses a waiting time
cost of $20 for each hour that a patron waits in line. If needed,
round your...

Please answer the entire problem!
Problem 15-25 (Algorithmic)
Burger Dome sells hamburgers, cheeseburgers, French fries, soft
drinks, and milk shakes, as well as a limited number of specialty
items and dessert selections. Although Burger Dome would like to
serve each customer immediately, at times more customers arrive
than can be handled by the Burger Dome food service staff. Thus,
customers wait in line to place and receive their orders. Suppose
that Burger Dome analyzed data on customer arrivals and concluded...

An insurance company has one adjuster in the branch office.
People with claims against the company are found to arrive in a
Poisson fashion during an 8 to 5 workday. Determine the hourly
service and arrival rates using an 8-hour workday. The amount of
time that the adjuster spends with a claimant is exponentially
distributed. Claimants are processed in the order of their
arrival.
You are the manager of this branch and you wanted to investigate
service provided by your...

Coffee Talk is a local café on the waterfront. There is counter
service only with one clerk working the counter. On an average
Friday (6 hour operation), 6 customers arrive at the counter every
20 minutes; on average, it takes 3 minutes to serve a customer.
Find the following measures of performance of the café:
a) The average utilization of the counter clerk
b) The average number of customers waiting in line
c) The average time a customer spends in...

Problem 15-9 (Algorithmic)
Marty's Barber Shop has one barber. Customers have an arrival
rate of 2.3 customers per hour, and haircuts are given with a
service rate of 4 per hour. Use the Poisson arrivals and
exponential service times model to answer the following
questions:
What is the probability that no units are in the system? If
required, round your answer to four decimal places.
P0 =
What is the probability that one customer is receiving a
haircut and no...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 12 minutes ago

asked 16 minutes ago

asked 37 minutes ago

asked 38 minutes ago

asked 47 minutes ago

asked 49 minutes ago

asked 58 minutes ago

asked 58 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago