On a critical regime for linear finite-buffer networks

Linear networks consisting of finite-buffer nodes in tandem are considered. In particular, throughput properties of such networks are investigated, as their size increases. Using an approximation, we establish an asymptotic critical loading regime in which the ratio of the throughput to the input arrival rate is strictly within (0, 1). Such a regime is desirable from the point of view of both the throughput and network cost. Our results indicate that the qualitative behavior of the achievable throughput under the critical regime depends on whether the buffer size is greater than 1.