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SIMULATION OF QUEUING SYSTEM WITH MULTIPLICATION OF REQUESTS IN QUEUES
Nikolay A. Kuznetsov, Krasnodar higher military school named after army General S. M. Shtemenko, Krasnodar, Russia, cuznetsow.colia2014@yandex.ru
Alexander A. Mozol, North Caucasus branch of the Moscow technical University of communication and Informatics, Rostov-on-Don, Russia, amozol@bk.ru
Abstract
The article proposes a method for constructing a stochastic simulation model for assessing the characteristics of the Queuing system (QMS) with the multiplication of applications in queues and developed a mathematical model in semimartingal terms, which includes a methodology for the application of models for assessing the extent of information threats and a method of protection against them. The QMS constructed in the article consists of a certain number of service units, the so-called service devices, and implements the process of receipt of applications, the mechanism and discipline of their service. The application process consists of a description of the mechanism for the appearance of requirements in the QMS. The mechanism of service in the QMS will be determined by the following factors: the number of service devices, the presence of a queue for each device, the distribution of the probabilities of the time of service requirements. The service discipline is determined by the rule that the service device uses to select the next requirement
(if any) from the queue when the current requirement is serviced. The advance of time in the model by means of a constant step is performed with the help of the mechanism «from event to event». Requests that arrive when all devices are busy form one or more queues to service devices. A distinctive feature of this view is that queues are processes with maintenance and with the reproduction of applications. The results presented in the article describe a new approach to the design of QMS and the construction of a system for assessing their characteristics. An illustrative example is presented.
Keywords: stochastic simulation model, queuing system, compensator, indicator function, estimation system.
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