Modeling efficiency of the State Financial Monitoring Service in the context of counteraction to money laundering and terrorism financing

This article considers the peculiarities of scientific and methodical approach construction to the evaluation of the State Financial Monitoring Service effectiveness as a component of the national system for Prevention and Counteraction to Legalization (Laundering) of the Proceeds of Crime or Terrorism Financing. The mechanism of functioning of the State Financial Monitoring Service of Ukraine is treated as a queueing system. Namely, denials of service requests, which provides for a possibility to form a queue with unlimited waiting and no limit on the queue length. Practical approbation was obtained with respect to the characteristics of the input and output service flows, indicators for assessing the stability and efficiency of the state regulation system and supervision under investigation.


Literature review
There is a significant amount of theoretical and methodological developments devoted to the specifics of assessing economic and financial risks in the modern scientific literature.This problem is investigated and developed by such scientists as M.I.Bondar, T.A. Vasil'eva, I.Yu.Ivchenko, A.V. Smaglo, V.V. Vitlinsky, S.A. Dmitrov, A.V. Kuzmenko (A.V. Merenkova), T.A. Medvid', I.Yu.Ivchenko, S.М.Ilyashenko.However, the unsolved problem remains not directly the assessment of economic and financial risks, but the reactions of government regulatory bodies to identified risks.It becomes necessary to form the methodological basis for assessing the effectiveness of the State Financial Monitoring Service of Ukraine in terms of the efficiency and effectiveness of its activities.The aim of the study is the development of a scientific and methodical approach to the effectiveness of the State Financial Monitoring Service as a subsystem of the National System for the Prevention and Counteraction to Legalization (Laundering) of the Proceeds of Crime or Terrorist Financing based on application of a queueing system.

Main results of investigation
The methodological bases of the assessment of the effectiveness of the State Financial Monitoring Service in question provide an assessment of processing level of the stream of applications receipt from primary monitoring subjects.The subjects of primary financial monitoring are banks, insurance companies, private pension funds, credit unions, pawnshops, joint investment institutions.That is, the proposed methodology should evaluate the information that is sent to the State Financial Monitoring Service associated with the relevant illegal financial transactions and their participants, as well as consider the irregularity and randomness of applications receipt, that is, the possibility of a queue for processing information and service channels' stoppage.
Based on the analysis of the above aspects, it can be concluded that the system of the State Financial Monitoring Service of Ukraine should be considered a queueing system (QS) with denial of service requests that allows for the formation of a queue with unlimited waiting and no limit on the queue length.
Thus, when presenting the system of the State Financial Monitoring Service of Ukraine, as a queueing system, it is necessary to determine the basic parameters of its functioning.Thus, the characteristics of the input stream of the queueing system are information on financial transactions and their participants and information on a number of databases necessary for the performance of financial intelligence functions; the characteristics of the service stream of queueing system requests are information about the measures taken based on the analysis of the above information and data; characteristics of the output stream of the queueing system are information on the implementation of measures taken, that is, information that will characterize the results of the previous actions of the State Financial Monitoring Service.In addition, the indicators of the effectiveness of its activities, that is, the indicators for assessing the sustainability and efficiency of the functioning of the system of the State Financial Monitoring Service of Ukraine, are of great importance in describing the functioning of the queueing system and they are presented in Table 1.Having entered before a set of assumptions, let's consider the essence and technique of calculation of each indicator of a quantitative characteristic in queueing system of the offered model.
Let requests in a form of information on financial transactions and their participants enter the QS with a request for processing by chance, that is, it can be assumed that the probability of receipt of an application for any negligible time interval     t t, is proportional to  with some inseparable coefficient .At the same time, the probability of absence at least of one service request for a given period of time can be defined as So, considering this fact, in the theory of probability it is considered to be: 1.
Time intervals  between two consecutive receipts of orders are subject to exponential distribution The probability that for any time interval the flow of receipt of processing applications will be equal to k is determined as follows: where  is the intensity of the input stream of information about financial transactions and their participants.
Thus, taking into account for the given QS the implementation of the above points, it can be concluded that the input stream is Poisson.
Continuing the coverage of the assumptions of the proposed model, we note the following aspects: 1) The random waiting time for an application in the processing queue can be considered to be distributed exponentially: where v is the intensity of the of the queue movement, that is, the average number of applications received for processing per unit time; q t is an average waiting time in queue.

2)
The output stream of applications that have been processed, associated with the service flow requests in the SQ channel and subject to exponential distribution law with density: where  is the service intensity, that is, the average number of applications processed per unit time; 0 t is average service time for one application for identified financial irregularities.
So, let's move directly to the essence and methods of calculating each of the indicators of the quantitative characteristics in the queueing system.
Intensity of input stream defines the number of units of information on financial transactions and their participants identified per unit time (year, half year, quarter, month, day, hour) and is calculated as the sum of the products of the number of receipts of applications (requests) for the frequency of receipts, observed in the study, divided (weighted) by the total number of receipts of applications i.e.: , where  is intensity of input stream; ki is a number of receipt of applications (requests); fi is a frequency of receipt of applications (requests).
Calculating the intensity of the QS input stream involves the implementation of a preliminary determination of the input information block in the context of its individual components presented in Table 2, which contains both a list of characteristics of the input stream (graph A) and money term (graphs 1, 3, 5), and quantification (graphs 2, 4, 6) of individual components.The derived indicator of the intensity of the input stream in the queueing system of the State Financial Monitoring Service of Ukraine, the average time of receipt of one application is defined as a value back to the intensity of the input stream, namely: where .rec t is an average time of receipt of one application;  is an intensity of incoming flow.
Service intensity is the indicator that reflects the average number of applications processed per unit time and is calculated as the ratio of the sum of the number of processed applications (requests) multiplied by the frequency of their receipts to the total number of receipts of applications, is determined by formula: where µ is a service application rate; ti is a number of applications processed (requests); fi is a frequency of receipt of applications (requests).
The value, inversely proportional to the intensity of servicing the application in the queueing system of the State Financial Monitoring Service of Ukraine, is the indicator such as an average service time of one application, which is calculated as follows: where .exec t is an average service time of one application; µ is a service intensity of one application.
According to the results of the research, it was revealed that with the value of  < , that is, when the intensity of the input stream is less than the intensity of the service of the application, there are no delays in resolving the issues, because the explanation of the situation occurs before the next application is received.
The queue length represents the variable calculated as the difference between the intensity of the input stream and the intensity of service application, that is: where m is a queue length;  is the intensity of the input stream; µ is the intensity of service application.
One of the key indicators of the queueing system, which binds such values as the intensity of the input stream and the intensity of service applications, is the density of the flow of applications, characterizing the flow density of applications, that is, the average number of claims, corresponding to the average time of application service.This value shows the degree of consistency between the input stream of applications and the intensity of the service of these applications, and is determined by formula: where  is an application flow density;  is the intensity of input stream;  is the intensity of application service.
Analyzing the application flow density, it can be concluded that the process of application service is stable, provided that the intensity of the load is less than the number of service channels.If the density of the stream is equal to or greater than the number of service channels, the average length of the queue will grow in the system under investigation, and, accordingly, the average waiting time for receipt of applications of information processing, and therefore the queueing system will be unstable.
In parallel with the described indicators, which form the array of input information of the queueing system, the value of the control variable during the calculation of the next block of indicators of the activity analysis of the system under consideration is the number of service channels.This amount is proposed to be determined on the basis of existing number of functioning units of the State Financial Monitoring Service of Ukraine, as well as those information processing channels characterizing law enforcement restrictions and courts.
The derived index from the of the flow density of applications and the number of service channels is the load level of the queueing system, defined as follows: where X is the loading level of QS;  is a flow density of applications; n is a number of service channels.
The system in question can be characterized as a system in a stationary, stable state with a loading level of less than one.Under this condition, the service queue is not created, the probability of receipt of a certain number of requests within the specified time interval depends on its duration.
The next but no less important indicator of the functioning of the system of the State Financial Monitoring Service of Ukraine as a queueing system is the probability of the absence of requests in the system that can be determined using the following relationship: At the same time, we assume that when n QS runs in the standby mode for servicing and restrictions on the length of the queue, that is, there can be no more m requests in the queue; the input stream of applications of processing is subject to the Poisson distribution law with intensity  while the time for service requirements is distributed according to the exponential law with intensity µ.
Failure probability is the characteristic of QS, which indicates the probability of denial of service request (application) in the case when the system receives processing applications, that is, the amount of the number of applications that can be processed in the light of the queue, and the number of applications that are not processed and receive a refusal.This indicator is calculated by the following mathematics: Relative channel capacity is an indicator that characterizes the probability of servicing an application received and calculated using the formula: . . .fail Р is a failure probability.
The indicator of absolute channel capacity reflects the number of processed applications (requests) per unit time, is determined by the product of the intensity of the input stream and relative channel capacity, that is: where А is an absolute channel capacity;  is an intensity of input stream; . fail Р is a failure probability.
The probability of queue formation is calculated by formula: . * * 1 The use of this formula is reasonable in the event that the fact of the queue formation is possible, that is, when the receipt of the next application occurs at the time of having at least n applications in processing system.Quantitatively, this fact can be described by the receipt of n, n + 1, n + 2,…n + m -1 of service applications.
In addition, considering that applications are received in QS independently of each other, the probability of simultaneous occupancy of all service channels is equal to the sum of probabilities Рn, Pn+1, Pn+2,…Pn+m-1.In parallel with these aspects, it should be noted that in the case of m = 0, we obtain a QS with failures, and in the case m  , we get the QS with the expectation without the limit on the length of the queue.
The verage number of occupied channels is defined as the ratio of absolute channel capacity to service intensity of the application, because А is the intensity of application service stream and each channel can serve µ number of applications.The average number of occupied channels is also calculated by multiplying the density of the application stream by the relative channel capacity.The indicator studied is determined by formula: where aver.

N
is the average number of occupied channels; A is an absolute channel capacity; µ is the intensity of application service;  is the application flow density; . exam Р is a relative channel capacity.
Coefficient of channel occupancy characterizes the degree of channels use and is calculated by producing the loading level of QS and the relative channel capacity, or as the ratio of the average number of applications to the number of service channels, i.e.: .exam Р is a relative channel capacity; n is the number of service channels.
In calculating the coefficient of the channel stoppage, three approaches are singled out: N is an average number of occupied channels; n is the number of service channels; X is the level of QS load; . exam Р is a relative channel capacity.
Average number of requests in the queue: Average waiting time in queue occurs when service request arrives at the time of occupancy of all requests processing channels and the simultaneous absence of queue, i.e., the waiting time will average 1/n; if there is one request in the queue, the average waiting time will be 2/n, etc. Considering the described principle of forming the transformation chain, we get the formula for calculating the average wait time in the queue: An average time for service requests is the value, defined as the ratio of relative channel capacity to application service intensity, is calculated by formula: .exam Р is a relative channel capacity; µ is the application service intensity.
Average time of application stay in the system is indicator calculated by summing the average waiting time in the queue and the average time for servicing the requests, i.e.: Considering all the contradictory aspects of the queueing system operation, a general criterion can be an indicator characterizing its economic efficiency.This indicator considers the costs of reversibility and the cost of applications, which will take on a minimum value with a minimum of total costs for system maintenance.When carrying out the cost estimation, it is necessary to consider not only the costs associated with failures, but also the costs associated with the channel stoppage, the cost of queueing system operation.Consequently, system maintenance costs are calculated by formula: where ts cos С  system maintenance costs; Presenting the work system of the State Financial Monitoring Service of Ukraine as a queing system, it is necessary to determine the basic parameters of its functioning.Thus, the characteristics of the input stream of the queueing system are information on financial transactions and their participants, as well as information on a number of databases necessary to perform the functions of financial intelligence (Table 7); characteristics of the service flow of requests of the queueing system are the information on the measures taken based on the analysis of the above information and data (Table 8); characteristics of the output stream of the queueing system are information on the implementation of the measures taken based on the analysis of the above information and data (Table 9).In addition, the indicators of the effectiveness of its activities, that is, the indicators for assessing the sustainability and efficiency of the functioning of the system of the State Financial Monitoring Service of Ukraine, are important in describing the processes of the functioning of the queueing system, and they are presented in Table 8 on average for considered period from 2011 to 2015.
The intensity of the input stream determines the number of units of information about financial transactions and their participants, as well as information on a number of databases identified per unit of time (year, half year, quarter, month, day, hour) and is calculated as the sum of products of the number of applications (requests) on the frequency of receipts, observed in the study, is divided (weighted) by the total number of receipts of applications.Guided by this approach, we obtain the calculated data presented in Table 7.In formulating practical recommendations for the application of queueing theory in determining the efficiency of the State Financial Monitoring Service of Ukraine, let's turn to the calculation of the next indicator -the service intensity based on Table 9. Service intensity is the indicator that reflects the average number of requests processed per unit of time and is calculated as the ratio of the sum of the number of processed applications (requests) multiplied by the frequency of their receipts to the total number of receipts of applications.Thus, the average number of applications processed per unit time is 870593,40 per year, 435296,70 per half year, 217648,35 per quarter, 72549,45 per month, 2418,32 per day and 100,76 per hour (Table 10).The next stage in the formation of practical recommendations for the application of queueing theory in determining the efficiency of the State Financial Monitoring Service of Ukraine is to calculate the intensity of the output stream, based on the data in Table 11.
Analyzing the number of units of information on financial transactions and their participants and information from a number of databases identified per unit time according to the intensity of the output stream of the system of the State Financial Monitoring Service of Ukraine, we note that the number of units of information in the output stream (  In parallel with the described parameters, which form an array of input information of the queueing system, the number of service channels is the value which acts as a control variable when calculating the next block of indicators in the analysis of the system activity under consideration, it is proposed to determine this value in the range of 30 to 44.
The derived indicator of the density of application stream and the number of service channels is the loading level of the queueing system, which is determined by the ratio of the stream of requests to the number of service channels.In turn, the the application density stream characterizes the intensity of the load, that is, the average of the requests, corresponding to the average time of service.This value shows the degree of consistency between the input stream of applications and the service intensity of these applications.average, over the period from 2011 to 2015, the level of loading in the system of the State Financial Monitoring Service of Ukraine decreased from 0.42 particles per unit with the number of service channels in the amount of 30 units to 1.00 particles per unit with the number of service channels in the amount of 44 units.
Another, but not less important, indicator of the system functioning of the State Financial Monitoring Service of Ukraine, as queueing system is the probability of absence of requests in the system for the period from 2011 to 2015 which acquired almost zero values although this showing varied from 0.56 units at the number of service channels in the amount of 30 units to 0.88 with the number of service channels in the volume of 44 units.
The probability of failure is the characteristic of the QS, it indicates the probability of denial of request (application) service in the event that the system receives n + m processing requests, that is, the sum of the number of applications that can be processed in the queue and the number of applications that are not processed and will be refused.This indicator for the period from 2011 to 2015 also took almost zero values, as well as the probability of absence of requests in the system, except for 2011 and 2012, when this indicator takes the value of 0.63 and 0.71 of the particle unit.
Turning to the analysis of the indicator -the relative channel capacity, namely, the indicator characterizing the probability of service of received application, is equal to unity of the showing for the period from 2011 to 2015.The estimated value of this indicator is 64% to 72%, that is, the number of actually processed applications (requests) per unit of time is from 64 to 72 applications.

Table 2 .
Information on financial transactions and their participants and information on a number of databases coming to the State Financial Monitoring Service of Ukraine (characteristics of the input flow of the queueing system) financial transactions subject to financial monitoring, including: ➢ with signs of mandatory financial monitoring ➢ with signs of internal financial monitoring ➢ with signs of mandatory and internal financial monitoring ➢ tracking (monitoring) of financial transactions Number of financial transactions provided by banks Number of financial transactions provided by non-banking institutions Table 3. Indicators characterizing the processing of incoming information flow Number of received financial transactions subject to financial monitoring, including: ➢ the quantity of transactions, not registered due to providing information with errors Number of messages selected to form the record Number of request files sent to banking institutions Number of financial transactions for which the request files were sent The number of decisions and orders of the State Financial Monitoring Service of Ukraine to stop financial operations Number of regulated requests in the Unified State Information System Table 4.The intensity of the input stream of the system of State Financial Monitoring Service of Ukraine as the service system Indicator Numerical characteristics А 1 Number of information units per year Number of information units per half a year Number of information units per quarter Number of information units per month Number of information units per day Number of information units per hour time for service requests; time of application stay in the system; time for service requests.


Costs associated with channels stoppage in system service; n  number of service channels; the probability of failure;   the intensity of the input stream;.syst С  expenses related to the application stay in the queueing system; QS aver Т . average time of application stay in the system.System efficiency is the ratio between the intensity of the output and input streamsin QS.Table 5. Information on the implementation of measures taken based on the results of control measures (characteristic of the output stream of the queueing system) records Number of summarized materials submitted to law enforcement agencies Number of additional summarized materials submitted to law enforcement agencies Number of summarized materials, on which criminal proceedings have been initiated Number of criminal proceedings initiated under summarized materials Number of summarized materials used in criminal trials Number of criminal proceedings in which summarized materials were used The number of criminal cases with conviction, initiated by summarized materials The number of responses to foreign Financial Intelligence Unit (FIU)Table 6.The intensity of the output stream of the system of the State Financial Monitoring Service of Ukraine, as a queueing system Indicator Numerical characteristic А 1 Number of units of information per year Number of units of information per half year Number of units of information per quarter Number of units of information per month Number of units of information per day Number of units of information per hour

Table 1 .
Indicators for assessing the sustainability and efficiency of the system functioning of the State Financial Monitoring Service of Ukraine

Table 7 .
Information on financial transactions and their participants passed to the State Financial Monitoring Service of Ukraine (characteristic of the input stream in the queueing system)

Table 8 .
The intensity of the input stream in the system of the State Financial Monitoring Service of Ukraine, as a queueing system for 2011

Table 9 .
Information on control measures taken (the characteristic of the service flow of requests in the queueing system)

Table 10 .
The intensity of the system service of the State Financial Monitoring Service of Ukraine, as a queueing system for 2011

Table 11 (
cont.).Characteristics of the input stream of the queueing system

Table 12 .
The intensity of the output stream in the system of the State Financial Monitoring Service of Ukraine, as a queueing system for 2011