Shmygevs'kyj M. Multi-channel Jackson's networks with controlled source of calls.

The thesis is devoted trend of queuing theory connected with investigation of queuing system and networks with controlled parameters. Service process of calls in multi-channel Jackson's netqorks of the Markov and semi-Markov type with controlled source of calls is investigated for the first time. Service parameteres in transient regime are found by the Laplace transformation method. Conditions of existence in stationary regime are determined and the extended Jackson's law is proved for stationary distribution. Service process properties in stationary regime are analyzed in terms of multivariate binominal moments. Functional limit theorems of the diffusion approximation type are proved for multi-channel system in heavy traffic regime. Effective algorithms, evident and approximate formule for the service process parameters in transient and stationary regimes are constructed on the basis of the performed research.