Optimization of multi-channel queuing systems with a single retail attempt: Economic approach

This paper deals with retrial queues of the |MQ/M/c/|-type in which the rate of input flow depends on the number of sources of repeated calls and each call has only one retrial attempt. That is, if a call fails to enter the server facility at the retrial attempt, then it leaves the system without service. The existence conditions of stationary regime and the vector-matrix of the stationary probabilities of the service process are represented. This representation uses an approximation of the initial model by means of the truncated one and the directs passage to the limit. For these systems a threshold strategy for the rate of input flow is used. The multi-criterion optimization problem for finding optimal strategy of control is considered. The quality functionals of the optimization problem are represented through the stationary probabilities.