Transcript Queuing Simulation Model as Library Management Support in

Queuing Simulation Model as
Library Management Support
in Terms of Informatization
Gordana Dukić
Darko Dukić
Sanda Hasenay

Key words: library services,
library management,
queuing simulation model,
methods of descriptive and
inferential statistics,
software
Introduction
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One of the aims of library management is to
provide a quality service in meeting the users'
needs.
Very often it takes time to satisfy a customer
request, for different reasons such as: increasing
number of the customers to be served, lack of
publications, shortage of and inadequate staff,
poor technical resources or poor organization and
bad working conditions.
The consequence would be the library’s bad
reputation.
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The waiting problem can be solved much more
efficiently by means of adequate quantitative
models and computer support.
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With this aim in mind, in this paper a queuing
model is presented.
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The initial model has been improved in our
research by using simulations, as well as
methods of descriptive and inferential statistics.
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Therefore, the trained and educated staff, who
would know how to apply the proposed model
and other computer-aided quantitative models,
is extremely important, in order to have a good
quality service.
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Besides this, appropriate software should be
developed which would simplify and speed up
the intake of the customer request, as well as
help the customer to keep track of the queuing.
Model concept and the basic
elements of a queuing system
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The queuing models are a quantitative support to
the library management in solving the queuing
problem.
They represent an analytic tool, used to describe
and predict the queuing system functioning.
The potential solutions of queuing models are
obtained when the changes of the parameter
values are studied.
It is up to the manager to decide which of the
obtained solutions would be best to be
implemented.
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The queuing models are often studied in
management science and operation research,
so their formulations can be found in numerous
sources.
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If we want to understand the queuing system
functioning, it is necessary to know all the basic
elements of the model.
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Basic elements of the queuing system
Customer
arrivals
Calling
population
Waiting
line
Service
Processing
order
Exit
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It is often assumed in the analysis that the
distribution of interarrival time of the customers
follows the Poisson distribution with parameter l
and the process time follows the exponential
distribution with parameter m.
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If this is the case, we should apply Poisson
queuing models and if not, it is necessary to
choose some non-Poisson models or to perform
a simulation.
Model formulation
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The developed model has as its purpose to
solve the queuing problem in the borrowing of
library materials and was inspired by the existing
queuing model with a single server and with
multiple servers.
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Since the interarrival time of the customers and
the period they keep the book present a random
variable which values are simulated, our model
belongs to the group of the queuing simulation
models.
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It is assumed that the interarrival time of the
customers wishing to borrow the book is
normally distributed.
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It is assumed that the process time follows the
triangular distribution. The triangular distribution
is determined by three parameters, which can
be perceived as three time estimates - the
shortest (a), most probable (b) and the longest
(c) regarding the loaned book period.
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In order to reduce the probability of making
mistakes, the normal and the triangular
distribution parameters should be estimated as
correctly as possible.
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Therefore, an adequate database needs to be
modelled and constructed. If this kind of data is
not available, the library manager has to make a
prediction based on experience.
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Once we have defined the distributions, number
of the parallel servers, the processing order, the
calling population and the maximal library
customer number in the system, we can start
performing Monte Carlo simulations.
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In proposed model it is suggested performing
number sets of simulations for each example of
book. The library manager should determine the
set number, as well as the number of the
simulations within every set.
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The simulated waiting times for unavailable
books mutually vary, so it is possible to form
their distributions. For every distribution it is
necessary to determine the mean time.
The simulation sets whose mean waiting values
differ significantly are ignored in the further
analysis.
Those mean waiting values can be identified in
different ways such as the analysis of variance
(ANOVA) and post hoc comparisons, box-andwhisker diagrams.
The confidence interval for the mean waiting
time for the book is formed on the basis of the
means which are not extremes:
sWq
sWq 

  1   
P Wq  t  / 2
 E Wq  Wq  t  / 2


n
n


Where:
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Wq = Mean of the average waiting time for the
book, which is not extreme
t / 2 = Critical value of the t-distribution
sWq = Estimate of the standard deviation
n = Number of simulation sets, i.e. the number of
means
An example of the queuing system
analysis in the library
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The library manager decided to analyze the
queue for a certain book, which was asked for by
the student personally, or via web page, e-mail or
texting.
On the basis of observation data, the manager
concluded that the interarrival time of the students
is normally distributed with the parameters m = 2
days and s2 = 0.5 days, whereas the loan time
follows a triangular distribution with the
parameters a = 1 day, b = 14 days and c = 19 days.
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The library manager has estimated that
maximum 200 students can queue for the book
and that the book is borrowed according to the
FIFO principle (first in, first out).
The books are defined as the servers in the
preformed model.
The Queuing System Simulation application,
which is one of the modules within the WinQSB
software package, was used to perform
simulations.
Each stimulation was performed for the period of
150 days, meaning approximately one academic
semester, including exam period.
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The first simulation results in the situation when the
library has four examples of the needed book.
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It can be also concluded that all book examples
were loaned for 93.31% of the time and the
longest period was 18.1957 days.
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Two books in the observed period were loaned
to the students 11 times and the other two
examples 13 times.
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23 students could not get the book.
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The simulation procedure, under the condition
that the library has four examples of the book,
was repeated 150 times within 30 sets.
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For each simulation set the distribution of the
expected waiting time is determined, and their
mean values are calculated.
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Using a box-and-whisker plot diagram, created
with the help of the Statistica package, we
identified one extreme value and it was excluded
from further analysis .
24
23
Number of days
22
21
20
19
Median
25%-75%
Non-Outlier Range
Outliers
Extremes
18
17
Mean waiting time
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In the end, the confidence interval for the mean
waiting time for the book was determined on the
basis of the mean values, except the extreme
one:


P 19.021  E[Wq ]  20.016  0.95
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To see how the purchase of the new book
examples would affect the queuing, the library
manager repeated the described procedure.
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Table presents the mean values and standard
deviations of the mean waiting time, determined
for the increased book examples.
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The table shows also the bounds of the 95%
confidence interval for the mean waiting time.
NUMBER
OF BOOK
MEAN
E Wq 
STANDARD
DEVIATION
95% CONFIDENCE INTERVAL
FOR THE MEAN
Wq
LOWER BOUND UPPER BOUND
s 
4
19.519
1.332
19.021
20.016
5
6
7
8.821
0.596
0.156
1.198
0.172
0.133
8.374
0.532
0.107
9.269
0.660
0.206
8
0.055
0.115
0.012
0.098
The satisfying results are obtained only if the library
has six book examples. However, the increased
number of the book examples would not significantly
decrease the waiting time but the number of the
unused books would increase.
Conceptual model of customer informing
about library materials via online request
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In order to fully use the advantages of the
suggested queuing model for the library
materials, it is necessary to develop and
implement in the library information system the
adequate software.
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The usage of this software would speed up the
request entry and help customers to monitor
permanently the queuing for the book.
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Some information for the customer about library
materials available on the on-line service:
Number of available
examples of publication
and libraries to be
borrowed at
Alternative
materials
Number of persons
in front of the
customer
Possibility of
inter-library
Allowed time to
keep the
borrowed
material
Customer
Information that
publication
became available
Estimated
waiting time
Number of
requested materials
being loaned so far
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Using the information provided by this system,
the management could predict the potential
problems and create the adequate library
development policy.
Conclusion
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Library management is subject to permanent
change and development and libraries have to
adjust their work to these challenges.
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Despite sophisticated technologies, the most
frequent problem that the library management
deals with is queuing due to the lack of some
library materials.
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In order to solve this problem, we have presented
in our paper the queuing simulation model.
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The model is rather specific, since it implements
the appropriate statistics methods, which provide
the customers with additional information before
they make a decision.
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The model points out the importance of the
quantitative approach to the organization and
managing of the library.
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Our paper also shows the necessity to develop
the model which would provide the customers
with more information about the library materials
via online request.
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Through the example, we tried to make the
model more accessible to a wider circle of users,
and especially to the library managers.
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The efficient solving of the problems in the
library work could be achieved only if the library
managers have the right skills and knowledge
about the quantitative methods and models.
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We believe that the needed librarian training has
been neglected and that in the near future we
should try harder to change this situation.
Thank you!