ИСТИНА

We consider a multi-server queueing system with a regenerative input flow X(t). Let Y(t) be the number of customers that can be served during the time interval [0, t) under assumption that there are always customers for service. Supposing Y(t) to be a strongly regenerative process we define a sequence of common regeneration points for the both processes X(t) and Y(t). The intensities of these processes can be expressed in terms of the means of their increments during the common regeneration period. Hence, the traffic rate for the system can be also obtained in these terms. If the sequence of common regeneration points can be defined in such a way that increments of Y(t) on the regeneration period stochastically dominate the real number of customers served on this period then a theorem about conditions of the instability of the system is proved. To obtain the stability condition we additionally assume that there are two possibilities for the process Q(t) which is the number of customers in the system at time t. Namely, Q(t) tends in probability to infinity or Q(t) is stochastically bounded process as t tends to infinity. We show that the first possibility cannot take place if the traffic rate is less than one. Therefore the process Q(t) is stochastically bounded in this case. We also give some examples: multi-channel queueing system with heterogeneous servers and interruptions of the service, queueing models with priority and others.