TCP is competitive against a limited adversary

Abstract

While the well-known Transport Control Protocol (TCP) is a de facto standard for reliable communication on the Internet, and performs well in practice, the question "how good is the TCP/IP congestion control algorithm?" is not completely resolved. In this paper, we provide some answers to this question using the competitive analysis framework. First, we prove that for networks with a single bottleneck (or point of congestion), TCP is competitive to the optimal global algorithm in minimizing the user-perceived latency or flow time of the sessions. Specifically, we show that with O(1) times as much bandwidth and O(1) extra time per job, TCP is O(1)-competitive against an optimal global algorithm. We motivate the need for allowing TCP to have extra resources by observing that existing lower bounds for non-clairvoyant scheduling algorithms imply that no online, distributed, non-clairvoyant algorithm can be competitive with an optimal offline algorithm if both algorithms were given the same resources. Second, we show that TCP is fair by proving that it converges quickly to allocations where every session gets its fair share of network bandwidth.

On the Competitiveness of AIMD-TCP within a General Network

“…As said, the advantage of this approximation is that it smooths out the constant oscillations between a bottleneck reaching full capacity and then suddenly having all of allocations decrease by a factor of β. In [11], we prove that, at least for the single bottleneck case, the effect of these oscillations can be compensated by multiplicative changing the capacity by a constant.…”

“…Assume, for example that job J i just arrived and hence, b i,t 0 = 0. If we assume that the total frequency f i,t = k∈B i f k,t remains relatively constant for a few adjustment periods, then the single differential equation δb i,t /δt = α − (1 − β)b i,t f i,t can be solved in isolation from the others, giving b i,(t 0 +d) = [11]. This gives that for the single bottleneck case, this system quickly converges.…”

“…AIMD, however, is different from EQUI in that its allocations continually increase and decrease and it takes some (small) time for it to reconverge after jobs arrive or depart. [11] proves that if AIMD is given a constant number of adjustment periods per job to converge then it is also O(1)-speed O(1)-competitive.…”

“…Unlike [11], which takes into account the fact that AIMD constantly increases additively and decreases multiplicatively, for the multi-bottleneck case, we want to simplify AIMD in two ways. The first simplification is to smooth out the quick changes using approximating differential equations.…”

Competitive Two-Level Adaptive Scheduling Using Resource Augmentation

“…Moreover, we provide a framework for analyzing the mean response time of any algorithm that can be formulated as a two-level adaptive scheduler. The analysis given in this paper and in [18] offers a convenient technique for analyzing the mean response time of a wide spectrum of scheduling algorithms that utilize parallelism feedbacks from the jobs, while the analysis in the previous results [13,15,29,30,16] are applied more specifically to Equi and its variants.…”