Scalar-vector recurrent algorithm for stationary probabilities in a heterogeneous system $\mathrm{M}/(\mathrm{M}_1, \mathrm{M}_2)/(\mathrm{N}_1,\mathrm{N}_2)/\infty/\mathrm{FIFO}$

This article proposes a generalized Erlang model with queue, the peculiarity of which is that two heterogeneous channels of finite volume and different service intensity are provided for data processing and transmission. When a message arrives, it first turns to a “faster” channel, if it has a sufficient number of channel resource units, then the message gets serviced. Otherwise, if there is not enough free service resource, the message is sent to the second “slow” channel. If it has a sufficient amount of free servise resource, then the message gets serviced. In the opposite case, the message gets into the queue. Messages in the queue have a lifetime, after which it makes no sense to transmit them. An original scalar-vector algorithm for calculating stationary probabilities of system states is proposed. The analysis of the characteristics of the quality of service is carried out. Namely, channel loading, average time spent in the system, the probability of instant service, the characteristics of service delays and the average number of service failures.