Dyshliuk O. Models and methods for determination of indicators for the retrial queuing systems

The thesis is devoted to development and study of mathematical models of varieties of retrial queuing systems which adequately describe processes of air traffic control, processes of functioning of computer and telecommunication systems and networks and other means of information transfer. In particular, the theory of the queuing systems with flows of calls of a complex structure, as a variety of retrial queuing systems, has been developed. For such systems a number of indicators of their functioning have been obtained. For the queuing systems with retries and multiple-types calls flow, the formulas for calculation of probabilities of transitions in the embedded Markov chain have been derived. For integer-valued periodical model of a GI /G /1 queuing system with retries, with the FCFS discipline of service, the ergodicity conditions have been found. An algorithm for statistical modeling of GI /G /m /0/ /1/ G multi-channel queuing system with returns has been developed, with the purpose of evaluation of the indicators of the system operation effectiveness, in particular, for evaluation of stationary probability of demand losses. The values of the stationary probabilities of denial of service have been obtained. For the queuing systems with flows of calls of a complex structure the algorithms for determining of the measures of the intersections of two complex impulses have been developed. The estimations of probabilities of the intersections have been made. The conditions for equivalent replacement of a system with complex calls with a system with simple calls (individual pulses) have been found. Theorems on the stochastic limitedness and existence of the limit distribution have been proven. An algorithm for statistical modeling of queuing systems with complex calls and taking into account the time of preparation of the serving channel has been developed. For the systems with dual calls and for the shift measure on R+ ergodic theorems have been proven, the indicators of functioning have been obtained and statistical models are developed. Key words: retrial queues, multiple-type calls flow, call of a complex structure, dual call, ergodicity of queues, system simulation.