Mathematical Model of the Production Processes, Taking into Account Their Specific Features
Statement of the problem. Stationary Queuing systems are standard mathematical model to describe many engineering, biological and other systems. However, in areas such as automation process control, management of environmental monitoring, planning combat actions, real systems are characterized by running in unsteady mode. The parameters of the real systems depend on the States of the system. Non-stationary queueing systems as mathematical models of these real systems are more than adequate. These queueing systems are formalized on the basis of systems of differential equations. The purpose of the work. We have developed and investigated a mathematical model of the production process on the basis of non-stationary queueing systems. Production processes are considered In work with consequent time and cellular spatial structure typical of small serial type production. The methods used. Methods of the device queueing theory, methods of the decision of the systems of the differential first-order equations, theory Markovskih processes. Result. A mathematical model of the production process was studied taking into account the parameters varying in time. The non-stationary characteristics of the production process have been identified depending on changes of intensities of the income and service of requests in time. Use got models allows most packed to present the process of the operating the production processes with consequent time and cellular spatial structure typical of small serial type production.