ИСТИНА

In this report three models of queueing systems with priorities are investigated. The first model is a queueing system with an autoregressive Poisson input flow, a generalized distribution of service times, one server and infinite buffer size. The second one is a priority queueing system with generalized distributions of an input flow and service times, one server, infinite buffer size and multiple vacations. The third system has finite amount of Poisson input flows, a generalized distribution of service times, one server and infinite buffer size. This system operates under mixed priority discipline, either non-preemptive priority or preemptive priority might be chosen for each pair of flows. A non- stationary distribution of the vector of lengths is found for all the mentioned systems. Also, the first and the third systems are analyzed under the heavy traffic condition.