Fairness Evaluation

We use ns-2 simulation [NS06] and examine the fairness of eight different schemes to determine whether they meet the TCP-equivalence and TCP equal-share criteria. The source codes of TEAR, TFRCP, SIMD, and AIAD are not included in the package of ns-2 simulation, but instead are published individually on the Web sites of their authors. Also, this study like [FHP00, JGM03, BB01] uses SACK [MMF96] as the TCP version and assumes no delayed acknowledgments. For the simulation, we use packets that were 1,000 bytes long and a maximum window size of 200 packets.

2.4.1 TCP-equivalence: Artificial-losses testing scenario with identical network conditions

A link with artificial packet losses was used to test for TCP-equivalence. The link discards the passing packets with a specific mathematical model. Such a link guarantees that any two passing flows experience identical loss conditions, thus satisfying the premise in TCP-equivalence, making this link suitable for the test of TCP-equivalence. Sufficient bandwidth was allocated for this link to prevent the packets from being dropped due to overflow.

The selected schemes were tested to determine whether they are robust enough to have the same throughput as TCP under varied artificial links, which have different means or Coefficient-of-Variations (CVs) of inter-loss time. The two statistics were varied because both affect the TCP throughput [AAB05]. A general exponential random variable allows its coefficient-of-variation to be changed while fixing its mean, or vice versa, so it is employed to drop packets at the link. The time between two packet losses thus forms a general exponential distribution, which is also used in [VB05] to investigate the conservativeness of TFRC. Only the testing result under links with different coefficient-of-variations is shown herein. The result with different means has already been obtained [JGM03, BB01].

The artificial link plotted as the link R1-R2 in Fig. 2.1(a), drops one packet every T seconds. T denotes a general exponential distributed random variable where E[T] is fixed at 5 and CV[T] uniformly increases from 0 to 1. The results in Fig. 2.1 were averaged from five runs of 5200 seconds each, where the data within the first 200 seconds were discarded, and the mean coefficient-of-variation of the simulation results between the five runs was 0.025. Because this coefficient-of-variation is small,

it is ignored in plot to improve the clarity of the figure.

Observation 1: Non-periodic losses should be considered in adopting WB/RB fairness policies.

Figures 2.1(b)(c) reveal that none of the WB/RB schemes meet TCP-equivalence under non-periodic packet loss (CV[T]>0). When CV[T]=1, GAIMD and TFRC only have 80% throughput of TCP while TEAR, IIAD, SQRT, and AIAD/H have 60% on average, because all schemes, except SIMD, were proposed based only on the periodic-loss assumption, i.e. the packet losses occur periodically. The unfairness under CV[T]=1 should be handled by these schemes because the inter-loss time in the Internet may approximate an i.i.d. exponential distribution equivalent to the link with CV[T]=1, according to the observation in [ZDP01].

Notably, the TFRCP and SIMD flows exhibit a different trend from other flows in Fig. 2.1(b)(c). The difference of TFRCP is due to the convex TCP throughput equation and the fixed rate-adjusting period [VB05], while that of SIMD occurs because its specific relationship between parameters is based on the packet loss model with CV T  [JGM03]. Figures 2.1(b) also plots the curve of SIMD variant, [ ] 1 SIMD/Period, with this design based on CV[T]=0. Unfortunately, SIMD/Period violates the TCP-compatibility criterion under non-periodic conditions.

Fig. 2.1. The throughputs of TCP-friendly schemes normalized with the throughput of TCP, under the loss link whose inter-loss time has a general exponential distribution. For clarity, results are separately shown in (b) and (c).

S R1 R2 D

100Mbps 20ms

100Mbps 20ms 100Mbps

30 ms Discarding packets

by math model

(a) The artificial-loss topology used in Chapter 2.4.A and 2.5.A

(b) (c)

2.4.2 TCP equal-share: Low-multiplexing testing scenario with the same bottleneck A dumbbell topology provides the premise of TCP equal-share, i.e. “competing for the same bottleneck,” and thus is used to verify the TCP equal-share of a scheme in the steady state. As shown in Fig. 2.2(a), n TCP-friendly flows compete with n TCP flows for a single bottlenecked link. All flows have backlogged data for the whole testing period. This study particularly investigates a low-multiplexing scenario [F00], where n is small and Drop-Tail is deployed to manage the bottleneck link, because previous results [YL00, FHP00, ROY00, BBF01, LT03] imply that a TCP-equivalent flow may violate TCP equal-share under such a scenario. Drop-Tail is a queuing management algorithm which discards new arrival packets when its managed queue is full.

To indicate the cause of the violation, the scenario used in [YL00, FHP00, ROY00, BBF01, LT03] was slightly modified at two points. First, instead of using a fixed capacity, e.g. 15 or 60 Mbps, the link had 2n Mbps. Such a link can provide on average 1Mbps of bandwidth for each flow, avoiding the influence of the TCP timeout-handling mechanism, as expected from previous studies [YL00, FHP00, ROY00, BBF01, LT03]. Second, although multiple rounds were tested for the same n,

SQRT Fig. 2.2. n TCP-friendly and n TCP flows compete for the bottleneck link. The propagation delays among each set of n flows are distributed uniformly with CV[RTT]=0~0.42.

IIAD

the RTT-heterogeneity of n TCP flows and of n studied flows were enlarged equally over different rounds. The RTT-heterogeneity of n flows represents the coefficient-of-variation of the RTTs of these flows, denoted as CV[RTT]. The mean end-to-end propagation delay was set to 50ms for all rounds. The queue size was 1.5 times the bandwidth-delay product.

Observation 2: RB fairness policy wins and RTT-heterogeneity matters for TCP equal-share.

Figure 2.2(b) indicates that the tested schemes do not always ensure TCP equal-share under the scenario, because they are based on the premise of TCP-equivalence, i.e. “any two flows experiencing identical network conditions,” but not that of TCP equal-share. Thus, these schemes cannot have the same throughput as TCP when the premise of TCP-equivalence is false, i.e. they do encounter different numbers of packet losses.

To show that the premise of TCP-equivalence is false under the scenario, Fig.

2.2(c) plots the normalized packet loss rate experienced by the TCP-friendly flows with the shortest RTT, compared with that of TCP flows. The loss rates of shortest-RTT flows are shown because their differences are the most significant among all flows. Three RB schemes, namely TFRCP, TFRC and TEAR, clearly suffer a higher loss rate than TCP at CV[RTT]=0, but an equal rate at CV[RTT]>0.25, which explains their bandwidth sharing with TCP in Fig. 2.2(b). Similarly, the other five schemes suffer a lower loss rate than TCP, so they occupy much more bandwidth than TCP.

Figure 2.2(b) also reveals that the RTT-heterogeneity of the competing flows significantly affects the fairness between TCP and TCP-friendly flows. GAIMD and SIMD occupy more bandwidth on average than TCP flows (1.5~4 times), particularly when CV[RTT]=0 (>10 times), where the number of competing flows is small (n=8, total is 16). The seriously unfair situation at CV[RTT]=0 also exists even when the total number of competitory flows is 64.

The unfair situation in the five WB schemes results from their exercising the packet acknowledgement mechanism. These schemes, like TCP, delay the transmission of the next data packet if the transmitter does not receive an ACK packet because the queue of a router in the transmission path has overflowed. By the delay, they encounter fewer packet losses and thus have higher throughput than the three RB

schemes. Moreover, because the overflow is alleviated by TCP significantly reducing its CWND, these five schemes, which slowly reduce their CWNDs, may monopolize the link until the queue is overflowing again. Thus, they have higher average throughput than TCP.

Although neither the WB and RB fairness policies can ensure TCP equal-share, the RB flows would experience similar packet loss rate to TCP flows, and can meet TCP equal-share in most cases, i.e. under CV[RTT]>0.05. By contrast, the WB flows may severely starve TCP flows. Therefore, the RB fairness policy should have a better chance than WB of meeting the TCP equal-share. Notably, these TCP-friendly schemes were also tested under a topology with multiple bottlenecks, but the results reveal that their TCP equal-share is unrelated to the number of bottlenecks, when this number increases from 1 to 10.

2.5 Evaluation on Aggressiveness and