On Packet Marking Function of Active Queue Management Mechanism: Should It Be Linear, Concave, or Convex?

Recently, several gateway-based congestion control mechanisms have been proposed to support the endto-end congestion control mechanism of TCP (Transmission Control Protocol). In this paper, we focus on RED (Random Early Detection), which is a promising gateway-based congestion control mechanism. RED randomly drops an arriving packet with a probability proportional to its average queue length (i.e., the number of packets in the buffer). However, it is still unclear whether the packet marking function of RED is optimal or not. In this paper, we investigate what type of packet marking function, which determines the packet marking probability from the average queue length, is suitable from the viewpoint of both steady state and transient state performances. Presenting several numerical examples, we investigate the advantages and disadvantages of three packet marking functions: linear, concave, and convex. We show that, although the average queue length in the steady state becomes larger, use of a concave function improves the transient behavior of RED and also realizes robustness against network status changes such as variation in the number of active TCP connections. Moreover, by applying our analytic approach to Adaptive RED, we discuss its steady state performance and transient state performance. Our analytic results show that Adaptive RED is effective for improving steady state performance compared with the original RED, but it has little performance gain in terms of transient state performance and robustness.