Bicriteria optimization of a queue with a controlled input stream

Motivated by a certain situation in communication networks, we will investigate the M/M/1/infinity queuing system, where one can change the input stream. Performance criteria coincide with the long-run average throughput of the system and the queue length. We will present a rigorous mathematical study of the constrained version of the multicriteria optimization problem for jump Markov processes. Subsequently, it will be shown that the stationary control strategies of the threshold type form a sufficient class in the initial bicriteria problem considered.