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Towards mathematical modeling of mass service processes. (English) Zbl 1308.93024

Summary: Generally, each case at the Court is preceded by preparatory work. If the number of judges, court halls or budget amount is not sufficient, resulting waiting list will require certain time to be considered. On the other hand, according to the law, each particular case should be considered within a certain period after its starting. Obviously, during the process of new court planning or existing court functioning, it is desirable to know in advance whether the time period for each case discussion is conformable to the terms defined by the law for the given number of judges, court halls or budget amount.
A lot of mathematical modelling tasks for mass service as well as for the Courts are reduced to the solution of homogeneous equation with two variables, the precise solution of which is often impossible.
The article considers the mathematical model of the Courts functioning as a three-phase system of mass service, where, the first phase (subsystem) reflects the specificity of the judge’s activities, the second phase - budget amount and the third – Court halls completeness. This mathematical model represents systems of differential and integral equations.
The paper considers the solution of a mathematical model (homogeneous equation with two variables) in the form of a row that enables identification between the real process and appropriate mathematical model, by the modern informatics technology and software achievements, thus providing the imitation of Courts normal functioning. Generally, a lot of mathematical modelling tasks are often reduced to the solution of homogeneous equation with two variables, the precise solution of which is often impossible. The article considers the solution of such equations in the form of a row that provides identification between the real process and appropriate mathematical model for each particular case and process by the modern informatics technology and software achievements.

MSC:

93A30 Mathematical modelling of systems (MSC2010)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
62P25 Applications of statistics to social sciences
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