The author will present the analytical matrix methods for analyzing queuing systems in transient modes and with sudden and smooth changes in the input and service rates. Such models adequately describe communication and information processing systems during installation, malfunctions, virus attacks, and spoofing. The mathematical models are based on the probability translation matrix introduced by the author. This matrix relates the probabilities of system states at time t to the same probabilities at the initial time. The difference between the probability translation matrix and the fundamental matrix of solutions to Kolmogorov's equations is that its dimension is one greater than the dimension of the fundamental matrix. The proposed method is applicable to both Poisson input flows and MAP-flows. The analytical expressions for the key characteristics of the considered queuing systems under consideration, as well as for the transient response time, were also obtained. Furthermore, the author presented the analytical study of multiphase queuing systems with a shared buffer, which corresponds, for example, to the operation of controllers, computers, and cloud systems. For the first time, the mathematical model of an n-phase system with a shared buffer of the dimension N is constructed. For this purpose, the author introduced new sign functions. The solution to the constructed system is performed using the probability transformation matrix method, and the key characteristics of such systems are also identified. So call nonlinear queuing systems are considered, where the service intensity depends on the probability of lost orders, etc. The example of such the system is a queue at a store, where as the queue lengthens and customers leave, the salespeople speed up their work. The human body's fight against viruses, where the number of antibodies in the human body increases as viral activity increases, is also an example of such systems. In telecommunication systems, the example is so-called adaptive systems, in which the service intensity depends on the intensity of the incoming flow. For such systems with a Poisson input flow, a system of Kolmogorov equations is constructed and the solution was obtained using numerical methods.