Предложено обосновывать количественные решения при проектировании и эксплуатации систем безопасности автономных объектов на основе методов теории массового обслуживания. Рассмотрены задачи анализа и синтеза систем массового обслуживания при решении задач обеспечения безопасности объектов (например, систем противопожарной или противоаварийной защиты автономного удаленного объекта), особенностью которых является наличие различных типов заявок, требующих разного времени обслуживания (например, пожарно-спасательными подразделениями или ремонтно-восстановительными бригадами). Получены аналитические выражения для вероятностей состояний систем обслуживания. Сформулирована задача анализа как нахождение вероятности отказа системы в приеме заявки какого-либо типа по причине занятости всех каналов обслуживания, когда известны интенсивности поступления заявок и скорости их обслуживания. Сформулирована задача синтеза как нахождение необходимого числа каналов обслуживания при заданных ограничениях на вероятности отказа в приеме заявок. Приведены примеры расчета данных характеристик для одно-, двух- и трехканальной систем массового обслуживания с двумя и тремя типами заявок.
It was proposed to substantiate quantitative solutions in the design and operation of safety systems of autonomous objects on the basis of methods of the theory of queuing systems. The article deals with the problems of analysis and synthesis of the queuing systems when solving the problems of ensuring the safety of objects (for example, fire-fighting or emergency protection systems of an autonomous remote object), which feature is the availability of different types of applications that require different maintenance time (for example, fire and rescue units or repair and recovery teams). While solving problems of analysis the probability p of finding the system in key states determines. S0 - there were no problematic situations, all the service channels are free; Su - at least one service channel is available, capable of responding to the problem (service request); Sref - all n service channels are busy, there is no possibility to react to the problem that has arisen (the application receives a denial of service). While solving the synthesis problem, the necessary quantitative characteristics of the system, such as the number of service channels n , the number of queues and the speed of service {λ}, are selected from the given permissible values of probabilities p0, pu and pref and known frequencies {μ}. Step by step systems are considered with applications of two types - one-channel and two-channel applications and a system with applications of three types - one-channel, two-channel and three-channel applications. Graphs and equations describing the states of the system and analytical solutions for finding the probabilities of the ground states are given for each of the considered types of systems. Universal expressions are obtained for finding the probabilities of key states for an n -channel queuing system without a queue under standard assumptions for m type applications. The justification of the obtained expressions is given. Examples of characteristics calculation for one-channel, two-channel and three-channel queuing systems with two and three types of applications are given. In particular, the probability of finding a system in a state when no applications are received ( p0) is calculated, when the requests arrive and one service channel ( pu ) is left and when all the service channels are occupied ( pref ). Examples of solving problems of analysis and synthesis are given for each of the considered types of systems. The article clearly demonstrates the possibility of applying the above methods to the problems of creating integrated security systems for remote autonomous objects, in particular, located in the Far North and in the Arctic zone. This work is a logical continuation of the article Tarantsev A. A., Kholostov A. L., Ishchenko A. D., Potapenko V. V. Problems of analysis and synthesis of application service systems of several types. Pozharovzryvobezopasnost / Fire and Explosion Safety , 2017, vol. 26, no. 3, pp. 31-38.
The authors declare that there are no conflicts of interest present.