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Queuing Simulation Model as Library Management Support in Terms of Informatization Gordana Dukić Darko Dukić Sanda Hasenay

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Key words: library services, library management, queuing simulation model, methods of descriptive and inferential statistics, software

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Introduction 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 librarys bad reputation.

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The waiting problem can be solved much more efficiently by means of adequate quantitative models and computer support. With this aim in mind, in this paper a queuing model is presented. 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. 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.

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Model concept and the basic elements of a queuing system 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. 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

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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 and the process time follows the exponential distribution with parameter. 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.

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Model formulation 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. 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. 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. 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. 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-and- whisker diagrams.

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The confidence interval for the mean waiting time for the book is formed on the basis of the means which are not extremes: Where: = Mean of the average waiting time for the book, which is not extreme = Critical value of the t-distribution = Estimate of the standard deviation n = Number of simulation sets, i.e. the number of means

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An example of the queuing system analysis in the library 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 s 2 = 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. Two books in the observed period were loaned to the students 11 times and the other two examples 13 times. 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. For each simulation set the distribution of the expected waiting time is determined, and their mean values are calculated. 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.

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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:

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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. Table presents the mean values and standard deviations of the mean waiting time, determined for the increased book examples. The table shows also the bounds of the 95% confidence interval for the mean waiting time.

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NUMBER OF BOOK MEAN STANDARD DEVIATION 95% CONFIDENCE INTERVAL FOR THE MEAN LOWER BOUNDUPPER BOUND 419.5191.33219.02120.016 58.8211.1988.3749.269 60.5960.1720.5320.660 70.1560.1330.1070.206 80.0550.1150.0120.098 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.

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Conceptual model of customer informing about library materials via online request 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. 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: Customer Estimated waiting time Number of requested materials being loaned so far Alternative materials Possibility of inter-library Number of available examples of publication and libraries to be borrowed at Allowed time to keep the borrowed material Number of persons in front of the customer Information that publication became available

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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.

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Conclusion Library management is subject to permanent change and development and libraries have to adjust their work to these challenges. Despite sophisticated technologies, the most frequent problem that the library management deals with is queuing due to the lack of some library materials. 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. The model points out the importance of the quantitative approach to the organization and managing of the library. 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. 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. We believe that the needed librarian training has been neglected and that in the near future we should try harder to change this situation.

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Thank you!

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