Ergodicity, Stability, and Insensitivity for One Class of Circuit Switching Networks

We consider communication networks defined by a graph of arbitrary structure. The information between the calling and the called nodes is transmitted by a uniquely determined path in circuit switched mode with loss of blocked calls. We prove the theorems of ergodicity and stability of the stationary mode under broad assumptions on the probabilistic structure of the stream of arriving calls. For $M/GI$ networks we further prove insensitivity of the stationary distribution of the number of transmitted messages to the form of the transmission time distribution function with a fixed mean. We additionally investigate the asymptotic behavior of the number of transmitted calls for large stellar $M/GI$ networks.