Stationary characteristics of an M 2 X /M/n queue with hysteretic control of the input flow intensity

A multichannel queueing system with an unlimited queue length is considered. In the system, the service time and time intervals between arrivals of customer batches are characterized by exponential distributions and a hysteretic mechanism is applied to control the input flow intensity. The system receives two independent types of flows of customers one of which is blocked in the overload mode. An algorithm for determination of the stationary distribution of the number of customers and the stationary characteristics (the mean queue length, the mean time of waiting in the queue, the probability of a loss of customers) is proposed. The obtained results are verified with the help of a simulation model developed with the help of the GPSS World tools.