Qualitative properties of the Erlang blocking model with heterogeneous user requirements (Q914270)

The author considers an Erlang blocking model with heterogeneous user requirements. Arrival rates are state-dependent Poisson processes. Both the analytical and numerical aspects for the equilibrium behavior of Erlang-like traffic models have received past attention. Motivated by growing interest in circuit-switched networks that support different characteristics, the effects of increasing the model parameters on the performance measures of interest is analyzed. The main focus of this work is on the monotonicity properties and on concavity properties of the performance measures such as loss probabilities, throughput and channel occupancy, both in transient and in steady state cases. A coupling technique is employed to derive time- dependent monotonicity results. Also, it is proved that the expected number of channels in use at any time is a concave increasing function of the arrival rate.