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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 36
Modeling of Citizen Claims
Processing by Means of Queuing
System
Oleksandr Markovets and Andriy Peleschychyn
Social Communications and Information Activity Department, L'viv Polytechnic National University, Ukraine, L'viv, 12 Bandera Str.
ABSTRACT
This article considers the work of the system “Electronic Reception” as the queuing system. An overview the structure of the system “Electronic Reception” as a chart is given. The initial descriptions for the queuing system are formed. Also scheme simulation model of “Electronic Reception” is represented and found probabilities of states of the system using the application of queuing theory. Context diagram of process of queuing system “Electronic Reception” is designed. Data flow diagrams of the first level of the queuing system “Electronic Reception” and data flow diagram of the subsystem “Analysis of claim” which detailed the context diagram of process of queuing system “Electronic Reception” is designed. A simulation model of single-channel service system “Electronic Reception” is realized. The initial output characteristics of a service system “Electronic Reception” and the parameters of the simulation model are formed. The state probabilities of the service system are found. For a description of the mathematical model queuing system “Electronic Reception” use data that were obtained in one of the experiments.
Keywords
Queuing system; Simulation model; States marginal probability; Consolidation; Electronic Reception; System.
1. INTRODUCTION
Under the modern conditions of information technologies development, increases the role of the Internet in people's lives has emerged the concept of "information society". Therefore there is a necessity to implement electronic governance for communication between authorities and citizens in various spheres of life.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 37 The advantages of implementing electronic receptions in the field of electronic governance are:
• ensure transparency of information by public authorities (citizen can track their claims at all stages of consideration);
• citizens save time (you can get consultation through the Internet and personal computer at home);
• access to resources at any time; • saving privacy of citizens.
Despite listed above advantages, still remain some disadvantages: • the processing time is unknown;
• because of large number of claims, some can be lost and not considered;
• the time it takes to review an claim, may exceed the time limits specified in the notice of consideration of claims and therefore claims may remain unanswered.
In this case, in order to assess the performance of electronic receiving and, if necessary, to make it more efficient, it is necessary to analyze it as a queuing system.
It is necessary to solve a number of problems that may arise in the queuing system. The main reason of these problems is irregular income of claims. It is not possible to predict how and when complaints will be received by the queuing system "Electronic Reception", and so there can be cases when the system may not cope with incoming applications. There is a negative state of system when system is almost always in a state of inaction. In such case, the cost of its implementation is not justified [2].
It is important to organize the system to increase its throughput and minimize losses of claims. On this depends on the number of channels that are working on stream of claims, their productivity and discipline service. Therefore it is important to analyze the work of the "Electronic Reception" in artificially created conditions to obtain empirical results for the proper relationship of government with citizens and quick respond.
2. THE ACTUALITY OF THE RESEARCH
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 38 electronic appeal from the receipt time is impossible to determine by mathematical means. Despite this requirement using simulation modeling is obvious and undeniable. To construct the imitation model it is necessary to reproduce as accurately as possible all the processes that occur in the system. This requires analyzing in detail all system components and the relationships between these components.
Established simulation model of system of electronic processing of appeals applied and successfully used in the field of e-governance, particularly in city councils that in improved service delivery to the city citizens are interested. Also, this model is used in the educational organizations in order to establish feedback to applicants, students, teachers, and, in general, institutions, organizations and companies to establish regular contact with its customers and to receive quickly respond to the proposals, complaints or shortcomings in the work.
3. MODELING OF FUNCTIONING PROCESS OF QUEUING
SYSTEM "ELECTRONIC RECEPTION"
The article is supposed to explore applying queuing systems in claims processing with the aim to consolidate information. Thus, there will be description of processes that occur in the "Electronic Reception", formulation of baseline characteristics of the structure of the queuing system and found marginal probabilities of states based on the results of simulation [3]. To represent the system of electronic reception and further define primary characteristics of the queuing system, it is necessary to build data flow diagram, which will show the major stages of the processing of citizens’ claims in the system.
Queuing system "Electronic
reception" new claims
processed claims Departments of the City
Council Users
claims
reply
Figure 1. Context diagram
Contextual diagram shows two external entities, which queuing system "Electronic reception" interacts with. The first external entity represents citizens who are users and source of claims in the system. The second external essence denotes structural units (departments of the City Council). They are receiving citizens’ claims coming from email reception, and after processing requests, send a reply back to the email reception.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 39 reply
new claims
processed claims incoming flow of applications
1.1. Analysis of claim
1.4. Sending a reply 1.3. Processing
claims in certain department
Information about claims
and users data storage
data about users and status of claims
1.2. Deleting spam spam
change the status
of claims
confirm the deletion
Figure 2. Data flow diagram of the first level of the queuing system "Electronic Reception»
Figure 2 shows the major subsystems that a claim passes, namely: • analysis of a claim;
• deleting spam;
• processing claim in certain departments; • sending a reply.
After analyzing the subsystems that resulted from the decomposition of contextual diagrams we can conclude second level decomposition of the subsystems "Analysis of claims" and "Reply to the user." is possible.
The first subsystem "Analysis of claims", which is shown in Figure. 3, is divided into the following processes:
• analysis of user data and text of claim;
• definition of the claim category and appropriate department; • sending a claim to the department;
• composing of a response.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 40 1.1.4.
Formulation and responses
1.1.2. Definition of the category
claims and department 1.1.1 Analysis of
user data and text claims
1.1.3. Sending an claim to the
department new claims incoming flow
of applications
spam
data about users and status of claims
data storage
confirm the deletion
Figure 3. Data flow diagram of the subsystem "Analysis of claim"
After sending an claim through the City Council portal to the electronic reception, text and user data should be analyzed and identified the nature of the claim: a request, complaint, question, etc. Because electronic reception performs multiple functions, the claims it receives have different types that may give priority to one type of claim over the other claims. Claims that require immediate consideration are processed first. If the electronic reception gets large number of claims, it forms a queue, which can be limited in time during which claim is waiting to be considered. The time allotted for consideration of one claim from the moment of its filing, is defined by the statement of City Council about consideration of electronic applications.
At this stage, it is determined whether a claim is not spam. This can be deduced from the text of the claim and user`s personal data. If claim is identified as a spam, it is not considered and it leaves the system. Another important feature that indicates user while filling online electronic forms is a claim category. This feature determines the department to which a claim will be sent for further processing. Also from the contents of claim depends on which service stage it goes: if the claim does not require detailed review and electronic reception employee can consult a user himself, it proceeds to the stage of formation response.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 41 considering claim and date of its completion is added to the status of a claim.
1.4.1. Preparation posts
1.4.3. Send a reply to email
1.4.2.Fixing discuss treatment completion status
in the database processed claims
change the status
of claims
reply
Figure 4. Data flow diagram of the subsystem "Sending reply»
Subsystem "Send reply" is used to form the response to claim and fix status of claim. This subsystem includes three processes: preparing the message, fixation status, completion of claim in the database and send reply to the user’s e-mail. Input data of subsystem: response to claim, processed claim. Output: responding to claim.
At this stage, processed claims are reviewed in the appropriate department, the status of the claim is labeled in the database as "processed" and a reply for the user is prepared.
4. FORMATION OF THE INITIAL OUTPUT CHARACTERISTICS
OF A SERVICE SYSTEM "ELECTRONIC RECEPTION" AND THE PARAMETERS OF THE SIMULATION MODEL
Baseline data of the service system is determined by the structure and processes taking place in the “Electronic Reception”. In order to comprehensively evaluate the functionality of the service system, are created the critical conditions, using the assumption of the simplest flows. Thus, the system “Electronic Reception” is the service system of type M/M/1, which means that the input is the simplest and the requests service of time is exponentially distributed. As a result, the output stream is also the simplest.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 42 in the citizens` claims of three types: application of the relative priority (claim1), application of conventional type (claim2) and processed claim that only requires an answer (claim3). An arrival time of application is determined by the exponential distribution law. The service time is given to implement the system with priority, but it is believed to be exponentially distributed [4].
Only one claim is served by a channel at a time period. If the channel is not loaded when a message comes, claim will be processed. If there are no claims, the system is idle.
The discipline of service is following: if the system is already analyzing an ordinary claim or a processed claim, the claim with priority does not displace the claim of these types of services, and becomes the next.
If the system has no claim with priority, claims are served according to the FIFO discipline. If the system has several claims with priority, they are ordered for processing adhering to the rules of the discipline FIFO discipline.
Basing on the described above initial output characteristics perform, the simulation model is constructed and common parameters to the system as a whole and blocks separately are formed. As a result of simulation and analysis of the results is proved that the number of service channels, necessary for the simplest flows manages flows and other types processing.
FIFO path combiner
(setting priorities) Exponentially
distribution
Exponentially distribution
Exponentially distribution
answer
answer
Claim 1
Claim 1
Claim 2
Claim 2
Claim 3
Claim 3
uniform distribution
Figure 5. A simulation model of single-channel service system "Electronic receiver»
5. FINDING STATE PROBABILITIES OF THE SERVICE SYSTEM
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 43 mathematical model QS "Electronic receiver" type M/M/1 and M/M/2, and thus find the probability states in which the system may be.
For a description of the mathematical model QS "Electronic receiver" type M/M/1 use data that were obtained in one of the experiments.
It is necessary to describe all possible states of single-channel service system "Electronic Reception":
• S0– service channel is free;
• S1– service channel is busy, but there are no queues; • S2– service channel is busy, there is a claim in the queue;
• Sm– service channel is busy, all m claims are queuing, the condition λ<μ should be true.
Calculate the value of μ:. 0,897666
114 , 1
1
1
ser
t
. From the formula
we find λ:
0,39150,8976660,351436. Since theintensity of the input stream λ is smaller than the intensity of the channel and the load factor μ ρ <1, the marginal probability of the system exists and the queue is not growing constantly. As a result of the service system "Electronic Reception" will go down in a steady (stationary) mode. The relative bandwidth of the system is QPser1, and the absolute bandwidth is.
To find the probability of system states we use already defined formulas that describe the processes of "death and reproduction."
The probability that the message will be processed Ppro is 1, and in turn, the
probability of denial of service Pden is 0.
The maximum probability that channel of maintenance is free, determined by the ratio p0 1 10,39150,6085, it means that 60.85% of the system is in a free state.
The probability that the servicing channel is busy:
3915 , 0 6085 , 0 1
1 0
busy
p , it means 39.15% system busy.
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 44 Maximum probability that provided employment service facility, in turn is one appeal, is p2 2(1)0,391520,60850,0932660,0933, that
the probability of this event is 9.33%.
Maximum probability that provided employment service facility, in turn is two appeals, isp3 3(1)0,391530,60850,0365140,0365, that the probability of this event is 3.65%.
The probability that the queue waiting to be of service to two appeals is
368 , 0 368008 , 0 ) 3
(k p1 p2 p3
P .
Thus, considering the counted above probability of the system states, could be made the following statement: the single-channel service system will be in the free state, which increases the probability of received claims to be sent for considering.
For multi-channel service system of type M/M/2 characterized by the following conditions:
• S0– all channels are available, k = 0; • S1– one channel is busy, other free, k = 1;; • Sn– busy all 2 channels, no queues, k = 2;
• Sn1– both channels are busy, one requirement in line k = 3; • Snr– all n channels are busy, r requirements in line, k = n + r Calculate the value of μ and λ:
97276265 , 0 028 , 1 1
1
ser t ; 53715954 , 0 97276265 , 0 5522 ,
0
Relative and absolute bandwidth equal, respectively, Q = Рser = 1 and 53715954
, 0
Q
A .
The probability that the message will be processed is 1, and the probability of failure is 0.
Maximum probability that service channels are at rest is
567 , 0 4478 , 1 2 5522 , 0 2 5522 , 0 1 5522 , 0 1 ) 2 ( ! 2 ! 2 ! 1 1 1 3 2 1 3 2
0
p
The probability that one, two or three appeals are processed is:
3131 , 0 3130974 , 0 ! 1 0
1 p
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ISSN: 1694-2108 | Vol. 15, No. 1. JANUARY 2015 45
0865 , 0 08644619 , 0 ! 2 0 2
2 p
p or 8,65%;
0159 , 0 01591186 , 0 ! 3 0 3
3 p
p or 1,59%.
The probability that in the queue are one or two appeals is defined as follows: 0239 , 0 02386779 , 0 567 , 0 2 2 5522 , 0 ! 2 2 3 0 1 3 1
2
p
p ;
0066 , 0 006589897 , 0 567 , 0 2 4 5522 , 0 ! 2 2 4 0 2 4 2
2
p
p
The probability that the queue will be formed is:
0329 , 0 0329711198 , 0 ) 2 ( ! 2 0 3
q
p P .
The average number of available channels is
4478 , 1 5522 , 0 2
a n
n , and the employment rate channel is
2761 , 0 2 5522 , 0 e
e
n n n
k .
Thus, multi-channel service system is the equal time period in free and busy state, which may indicate that the system is functioning normally.
6. CONCLUSIONS
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7. REFERENCES
[1] Serenok, A., 2011. Introduction of technologies of e-government in activity of organs of local self-government, Journal of Kharkiv Regional Institute of Public Administration of the National Academy of Public Administration, No. 1.
[2] Markovets, O., Peleshchyshyn, A., Zhezhnych, P., 2011. Designing a system processing appeals to local authorities, Computer Science and Information Technology: Proceedings of the National University "Lviv Polytechnic", No.694, pp. 153-160.
[3] Markovets, O., 2011. A mathematical model for the applicant of e-government, Information Systems and Networks: Proceedings of the National University "Lviv Polytechnic", No. 699, pp.154-163.
[4] Anikovskiy, V., Erofeeva, L., Novgorod, N., 2010. Elements of queuing theory. Basic concepts. Tasks. Guide to solving problems, Novosibirsk State Technical University.
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