The queueing system M₂^X/M/n with hysteretic control of the input flow intensity

We consider a multi-channel queueing system with unlimited queue and with exponentially distributed service time and the intervals between the arrival of customers batches, which uses a hysteretic control mechanism of the input flow intensity. The system receives two independent flows of customers, one of which is blocked in an overload mode. An algorithm for finding the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean waiting time in the queue, the probability of customers loss) is proposed. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.