The given article deals with the development of analytical model of request service process by multichannel technical system with unreliable, repaired and reconfigured service facilities. It is assumed that the system is functioning in service mode of random length random request flows. The system considers the existence of time redundancy for afterservice of calls, the service of which is interrupted with refusal, non-depreciating the performed part of the task. Special probability functions are introduced which on the basis of probability reasoning allow to make the systems of integral equations describing the dynamics of request service process.