CHAPTER 14 Waiting Lines and Queuing Theory Models

14.1 A goal of many waiting line problems is to
help a firm find the ideal level of services that minimize the cost of waiting
and the cost of providing the service.

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14.2 One difficulty in waiting line analysis is
that it is sometimes difficult to place a value on customer waiting time.

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14.3 The goal of most waiting line problems is to
identify the service level that minimizes service cost.

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14.4 Two characteristics of arrivals are the line
length and queue discipline.

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14.5 Limited calling populations are assumed for
most queuing models.

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14.6 An “infinite calling population”
occurs when the likelihood of a new arrival depends upon the number of past
arrivals.

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14.7 On a practical note – if we were to study
the waiting lines in a hair salon that had only five chairs for patrons
waiting, we should use an infinite queue waiting line model.

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14.8 If we are studying the arrival of
automobiles at a highway toll station, we can assume an infinite calling
population.

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14.9 When looking at the arrivals at the ticket
counter of a movie theater, we can assume an unlimited queue.

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14.10 Arrivals are random when they are dependent
on one another and can be predicted.

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14.11
On a
practical note – if we are using waiting line analysis to study customers
calling a telephone number for service, balking is probably not an issue.

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14.12
On a
practical note– if we are using waiting line analysis to study cars passing
through a single tollbooth, reneging is probably not an issue.

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14.13
On a
practical note – we should probably view the checkout counters in a grocery
store as a set of single channel systems.

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14.14
A bank with
a single queue to move customers to several tellers is an example of a
single-channel system.

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14.15
Service
times often follow a Poisson distribution.

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14.16
An M/M/2
model has Poisson arrivals exponential service times and two channels.

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14.17 In a single-channel, single-phase system,
reducing the service time only reduces the total amount of time spent in the
system, not the time spent in the queue.

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14.18 The wait time for a single-channel system is
more than twice that for a two-channel system using two servers working at the
same rate as the single server.

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14.19 The study of waiting lines is called queuing
theory.

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14.20 The three basic components of a queuing
process are arrivals, service facilities, and the actual waiting line.

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14.21 In the multichannel model (M/M/m), we must
assume that the average service time for all channels is the same.

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14.22 Queuing theory had its beginning in the
research work of Albert Einstein.

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14.23 The arrivals or inputs to the system are
sometimes referred to as the calling population.

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14.24 Frequently in queuing problems, the number
of arrivals per unit of time can be estimated by a probability distribution
known as the Poisson distribution.

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14.25 An automatic car wash is an example of a
constant service time model.

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14.26 Balking customers are those who enter the
queue but then become impatient and leave without completing the transaction.

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14.27 In a constant service time model, both the
average queue length and average waiting time are halved.

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14.28 A hospital ward with only 30 beds could be
modeled using a finite population model.

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14.29 A finite population model differs from an
infinite population model because there is a random relationship between the
length of the queue and the arrival rate.

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14.30 A transient state is the normal operating
condition of the queuing system.

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14.31 A queue system is in a transient state
before the steady state is reached.

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14.32 Little’s Flow Equations are applicable for
single-channel systems only.

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14.33 Little’s Flow Equations are advantageous
because if one characteristic of the operating system is known, the other
characteristics can be easily found.

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14.34 Using a simulation model allows one to ignore
the common assumptions required to use analytical models.

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14.35 If we are using a simulation queuing model,
we still have to abide by the assumption of a Poisson arrival rate, and
negative exponential service rate.

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MULTIPLE
CHOICE

14.36 Queuing theory had its beginning in the
research work of ________________________.

(a) Albert
Einstein
(b) A.K. Erlang
(c) J.K.
Rowling
(d) P.K.
Poisson
(e) A.K. Cox

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14.37 Assume that we are using a waiting line
model to analyze the number of service technicians required to maintain
machines in a factory. Our goal should
be to ________________________

(a) maximize
productivity of the technicians.
(b) minimize
the number of machines needing repair.
(c) minimize
the downtime for individual machines.
(d) minimize
the percent of idle time of the technicians.
(e) minimize
the total cost (cost of maintenance plus cost of downtime).

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14.38 In queuing analysis, total expected cost is
the sum of expected _______ plus expected ________.

(a) service
costs, arrival costs
(b) facility
costs, calling costs
(c) calling
cost, inventory costs
(d) calling
costs, waiting costs
(e) service
costs, waiting costs

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14.39 In queuing theory, the calling population is
another name for ________________.

(a) the queue
size
(b) the servers
(c) the
arrivals
(d) the service
rate
(e) the market
researchers

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14.40 Which of the following is not true about
arrivals?

(a)
Random arrivals are independent of each other.
(b)
Random arrivals cannot be predicted exactly.
(c)
The Poisson distribution is often used to represent the
arrival pattern.
(d)
Service times often follow the negative exponential
distribution.
(e)
The exponential distribution is often used to
represent the arrival pattern.