# Quiz 9: Queuing Models

Business

Q 1Q 1

One method for reducing the randomness of customer arrivals at a retail business is to allow for customer appointments.

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True False

True

Q 2Q 2

Random arrival processes must be modeled using continuous
probability distributions, not discrete ones.

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True False

False

Q 3Q 3

Airline passenger arrivals at U.S.Customs counters, at a
port-of-entry airport, would not likely be modeled as Poisson due to arriving in groups.

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True False

True

Q 4Q 4

The size of the population of potential customers may have an impact on the validity of the Poisson arrival pattern assumption.

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True False

Q 5Q 5

"Jockeying" occurs when a customer in the waiting line gets upset with the time the process is taking and leaves the system.

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True False

Q 6Q 6

The priority rule chosen for determining the next customer to be served affects both waiting time variance and average customer
waiting time.

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True False

Q 7Q 7

A Poisson distribution with mean λ is equivalent to an
exponential distribution with mean 1/λ.

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True False

Q 8Q 8

μ, in the service segment of a queuing process, is the average number of customers actually served per unit of time.

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True False

Q 9Q 9

The steady state service measure formulas for the M/G/k/k queue are the same as those for the M/M/k/k queue.

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True False

Q 10Q 10

Although service times may be relatively constant at sequential work stations in an assembly line, the line still may be treated as a tandem queue.

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True False

Q 11Q 11

The optimal situation (in terms of minimizing the average number of customers in the queue) in an M/M/1 queuing system is when the arrival rate λ exactly equals the service rate μ.

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True False

Q 12Q 12

The probability distribution for the arrival process can be estimated if we know either the time between customer arrivals or the number of customers in a given time interval.

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True False

Q 13Q 13

If the service times are not memoryless, then the Erlangian distribution might be a better basis than the exponential distribution for modeling service.

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True False

Q 14Q 14

The average waiting time in the system is less than the sum of the average waiting time in the queue plus the average service time because some customers do not have to wait in the queue.

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True False

Q 15Q 15

For an M/M/k queue to reach steady state, the service rate for each server μ must be greater than the arrival rate λ.

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True False

Q 16Q 16

Necessary assumptions underlying a Poisson arrival process do not include:
A)orderliness.
B)homogeneity.
C)independence.
D)stationarity.

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Multiple Choice

Q 17Q 17

Which of the following would best be characterized as a Poisson arrival process?
A)Football game attendees,
B)Tax returns received by a regional IRS office.
C)Incoming phone calls to a business switchboard.
D)Ladies visiting a hair salon.

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Multiple Choice

Q 18Q 18

In order to achieve steady state performance in a queuing system, the sum of the effective service rates of all servers must:
A)exceed the effective arrival rate of all customers.
B)equal the effective arrival rate of all customers.
C)be less than the effective arrival rate of all customers.
D)be exponentially distributed.

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Multiple Choice

Q 19Q 19

"Balking" is:
A)refusing service.
B)leaving the queue.
C)refusing to enter the queue.
D)refusing to leave after service.

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Multiple Choice

Q 20Q 20

Where would one most likely face a tandem queue?
A)A local post office.
B)A supermarket.
C)A cafeteria.
D)A bank.

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Multiple Choice

Q 21Q 21

If a service facility changes from a first-come, first-served basis to a random basis in selecting the next customer to be served, one should expect average customer waiting time to:
A)decrease slightly.
B)remain constant.
C)increase slightly.
D)increase dramatically.

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Multiple Choice

Q 22Q 22

In the exponential distribution of service times, the mean customer service time equals the:
A)variance of customer service times.
B)standard deviation of customer service times.
C)median customer service time.
D)most likely customer service time.

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Multiple Choice

Q 23Q 23

In a situation where the distribution of service times is assumed exponential, suppose the probability that service time is under five minutes is 0.40.If a given customer has already had five minutes of service, the probability that he/she will have service totally completed in less than ten minutes, is:
A)0.40.
B)greater than 0.40.
C)less than 0.40.
D)indeterminate.

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Multiple Choice

Q 24Q 24

A Markovian queuing process has a(n) __________ arrival pattern, and a(n)__________ service pattern.
A)Poisson; Poisson.
B)Poisson; exponential.
C)exponential; Poisson.
D)exponential; exponential.

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Multiple Choice

Q 25Q 25

The exponential distribution is:
A)generally discrete.
B)never symmetrical.
C)usually symmetrical.
D)not related to the Poisson distribution.

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Multiple Choice

Q 26Q 26

Suppose that an office has one secretary who can put up to two callers on hold while speaking to a third caller.(If two callers are on hold, additional callers will get a busy signal and will not
Call back.) If the arrival rate of calls follows a Poisson
Distribution with a mean rate of 20 per hour and the average length
Of a telephone conversation is 2 minutes, the average number of
Callers who will be on hold is approximately:
A)2.0.
B)1.3333
C)1.0154.
D).4308.

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Multiple Choice

Q 27Q 27

Suppose a penny arcade worker is in charge of keeping ten machines in operation.The failure rate of each machine follows an exponential distribution with a mean time of ten hours and the time required to repair each machine follows an exponential distribution with a mean time of thirty minutes.Over the long run, approximately what percentage of machines, on average, will be operating?
A)76.5%
B)92.4%
C)53.8%
D)46.2%

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Multiple Choice

Q 28Q 28

Ray's Barber Shop has 3 barber's chairs, and 8 seats for waiting customers.The greatest number of people ever waiting for a haircut, in Ray's experience, is 6.For analytical purposes, then, Ray's queue length is:
A)infinite.
B)6.
C)8.
D)11.

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Multiple Choice

Q 29Q 29

You go to your local hospital for your complete annual physical exam.From a queuing standpoint, you are facing:
A)single server; single queue.
B)multiple servers; single queue.
C)multiple servers; multiple queues.
D)tandem queues.

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Multiple Choice

Q 30Q 30

In queuing analysis, the exponential distribution is a special case of which other distribution?
A)Erlangian.
B)Poisson.
C)normal.
D)Markovian.

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Multiple Choice

Q 31Q 31

Which of the following is a basic component of a queuing system?
A)Poisson distribution.
B)Waiting in a queue.
C)Priority rules.
D)Exponential distribution.

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Multiple Choice

Q 32Q 32

Homogeneity means:
A)all customers arrive according to the same pattern and receive the same service.
B)past service time does not affect future service time.
C)processes reach steady state.
D)all servers are available as long as the queue functions.

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Multiple Choice

Q 33Q 33

You are studying service times at Derman's Department Store, which is open 7 days a week from 10:00 AM to 9:00 PM.Why might you ignore data from 10:00 to 10:30 AM?
A)Insufficient sample size.
B)Start up bias.
C)The doors do not open at exactly 10:00 AM.
D)The data do not fit the hypothesis.

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Multiple Choice

Q 34Q 34

Which of the following is not a common steady state performance measure?
A)The probability that a customer does not have to wait in the queue.
B)The average number of customers who do not have to wait in the queue.
C)The probability all servers are idle.
D)The average time a customer spends between entering and leaving the system.

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Multiple Choice

Q 35Q 35

The Pollaczek-Khintchine formula comes from the study of:
A)M/G/1 queues.
B)simulation.
C)M/M/1 queues.
D)Markov chains.

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Multiple Choice

Q 36Q 36

If λ is the non-constant average arrival rate, and μ (or kμ with multiple servers) is the average service rate, why does a queuing system not approach maximum efficiency when these two values are approximately the same?

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Essay

Q 37Q 37

In an M/M/1 queuing system, λ = 6, and the system is idle 40%
of the time.What is the average service rate, μ?

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Essay

Q 38Q 38

A local dry cleaning establishment is open from 7
a.m.to 7 p.m., weekdays.The average arrival rate of customers is 15 per hour, both from 7 to 10
a.m., and from 4 to 7 p.m.In between, it is 9 per hour.In all time periods, the Poisson assumption for the
arrival process seems to be valid.Can this be treated as a queuing
system, with λ = 12 ([15 + 9]/2)?
(No.The rush hours (morning plus evening) and the in-between hours
need to be treated as two, separate queuing systems.Each represents a stable process, and treating the two as one will yield results that are applicable to neither.) (medium)

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Q 40Q 40

Using Little's formula, if we know the mean arrival rate, mean service rate, and the average time a customer spends in the queue (W

_{q}), what else can we calculate?Free

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Q 42Q 42

If the standard deviation of service time in an M/G/1 queue is zero, what type of system does it become? What if σ = 1/μ?

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Q 45Q 45

For many queue types, Pw, the probability a customer must wait for service, = ρ, the server utilization rate.For what types of queues is this not true?

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Q 46Q 46

Harry and Larry have opened up an automated carwash near the edge of town.There is a single service lane, and cars line up in a

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Q 47Q 47

Ajax, Inc.specializes in the maintenance and repair of all types of electronic products.Tools and test equipment needed by its many skilled technicians on various diverse jobs must be drawn from and returned to a centrally-located tool room.Technicians arrive at

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Q 48Q 48

The new community of Lemon Heights is planning to set up a paramedic station.It is estimated that calls will come into this station according to a Poisson distribution, and the station receives an average of twenty calls a day.The time an ambulance is out responding to a call follows an exponential distribution with a mean time of one hour and thirty minutes.If no ambulance is available, an ambulance from a nearby town will be dispatched, but this will significantly increase the response time.Due to the potentially tragic consequences associated with not having an ambulance readily available when a call comes in, the city council has mandated that the probability of this happening should be no more than .005.Determine how many ambulances the paramedic station should purchase.

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Q 49Q 49

The Red Rock School District has six buses in its fleet.Maintenance of the fleet is handled by Joe Clem, a mechanic who works for the district.The time between bus failures follows an exponential distribution with a mean of twenty days.During the time a bus is out of commission, the district must lease another bus at a cost of $80 per day.

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Q 50Q 50

The computer help desk at Averill University receives an average of 40 calls per hour and calls come in according to a Poisson distribution.The average time a technician takes to diagnose a problem is three minutes and twenty seconds, and the service time follows an exponential distribution.For 60% of the callers the diagnosis is satisfactory, but for 40% of the callers, the technician must transfer the call to a specialist.The time a

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Q 52Q 52

For the post-Christmas gift returns, Paver's store added a second clerk on December 26.Paver's expects 10 customers an hour, and the mean service time is 10 minutes.Assuming an M/M/2 queue and a single waiting line, compute the average time a customer spends in the queue.What if there were two lines with jockeying allowed?

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Q 53Q 53

Given these parameters: λ = 25 per hour, μ = 30 per hour, and W

_{q}= .3 hours, calculate the average number of customers in the system, average number of customers in the queue, and the average time a customer spends in the system.Free

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Q 54Q 54

For an M/G/1 queue, λ = 12 per hour, μ = 24 per hour, and the standard deviation of the service time σ = .05.Calculate the average number of customers in the system, average time a customer spends in the system, and the probability that there are exactly two customers in the system.

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