Fairness

3.5.1.1 Simulation topologies

WARC and other selected schemes are evaluated in three cases. The former two use an artificial packet loss link, as plotted in Fig. 3.9, to drop packets based on mathematical model. Such a link is usually for testing the fairness between TCP and the TCP-friendly scheme because it ensures the identical loss conditions experienced by any two passing flows, which is a basic assumption for these schemes to perform fairness. The mathematical model used here follows a general exponential distribution,

Fig. 3.8. The probability of the false-positive invocation of the HR procedure

2.2 2.4 2.6 2.8 3 3.2 3.4 k

which has two degrees of freedom and thus allows its coefficient-of-variation to be changed while fixing its mean, or vice versa. By the general exponential distribution, we can test the fairness behavior in term of different means and different CVs, individually. Sufficient bandwidth is allocated for this link to prevent the packets being dropped because of overflow.

The third case makes all flows compete for a single bottleneck, which may be managed by the Drop-Tail or RED algorithms. The test is used to verify whether a TCP-friendly scheme is safe to deploy in the Internet. Fig. 3.10 shows the dumbbell topology used in this test. The v TCP-friendly flows compete with v TCP flows for a single bottlenecked link. All flows have backlogged data for the whole testing period.

Such a scenario tests whether v TCP-friendly flows can share the same bandwidth with v TCP flows under different levels of congestion. The capacity of the congested link is configured to 15Mbps or 60Mbps, and that of other links to 100Mbps. The value v is changed from 1 to 64. The queue size is 1.5 and 2.0 of bandwidth-delay product when R1 is managed by Drop-Tail and RED, respectively. The propagation delay of the links from the sources to R1 or from R2 to the destinations is uniformly distributed between 10 to 30 ms.

3.5.1.2 Case I - Under artificial-loss links with different means

Fig. 3.11 displays the normalized throughput of each TCP-friendly scheme, compared with TCP, over the links with different means of the number of inter-loss packets. The link discards packets every time when receiving P packets, where P is a

Fig. 3.10. The dumbbell topology used to test the fair sharing between TCP and TCP-friendly R2 by general exp. distribution

Fig. 3.9. The artificial loss-link topology is used to provide the same loss condition for any two flows running through the link R1-R2.

100Mbps 2ms

100Mbps 2ms

general exponential distributed random variable with a small coefficient-of-variation (CV[P]=0.01). The results are averaged from three 2200-seconds runs and the data in the beginning 200 seconds is ignored. Error bounds of the results are not presented because the three runs almost have the same results.

Fig. 3.11 shows WARC like SQRT has better fairness than other schemes under various loss ratios. Particularly under the cases where the ratio>0.03, WARC provides 0.8~1.1 of TCP’s throughput while GAIMD, SIMD⁵ and IIAD provide lower throughput than TCP’s (0.4~0.6). The curve “WARC w/o TO” in the right part of Fig.

3.11 represents the result of WARC without the fluid-based timeout mechanism. By comparing this curve with that of WARC, it is demonstrated that the timeout mechanism proposed in Chapter 3.2.2.3 does prevent WARC from using more bandwidth than TCP under the heavy-loss conditions. Moreover, although GAIMD, SIMD and IIAD use the TCP timeout mechanism to control their rate under heavy-losses, their lower throughput reveals that directly using the TCP timeout mechanism does not ensure fairness, which results from that they trigger the timeout mechanism more frequently than TCP, according to our further observation.

3.5.1.3 Case II - Under artificial-loss links with different CVs

The following reveals the fairness behaviors of schemes under the link with different coefficient-of-variations of inter-loss time. The used link drops packets per T

5 The congestion control parameters of SIMD used in Case I is specially calculated for CV[P]=0 to match the loss model used here. Under this case, the original parameters [JGM03], optimized for CV[P]~1, will cause SIMD to get lower bandwidth than

Fig. 3.11. The throughputs of TCP-friendly schemes normalized with that of TCP under different loss probabilities. Results are separately plotted in two parts for clarity.

seconds where T follows a general exponential distribution with E[T]=5 and CV[T]

uniformly increases from 0 to 1. In this testing case, the link drops packets based on the escaping time from the last loss, instead of the number of received packets as that in Case I, since dropping-by-time would be more realistic to emulate the loss conditions in the highly multiplexing network like the Internet [BCC98]. Actually, we also observed the fairness behaviors of schemes under the link with different coefficient-of-variations of inter-loss packets. However, the result is skipped because it is similar to that in Fig. 3.12.

Fig. 3.12 shows that WARC uses the same throughput as TCP under all CV[T]’s because it is supposed to perform fairness under stationary losses, as proved in Chapter 3.3. Contrarily, most schemes only have the fairness as CV[T]=0, i.e. as the loss occurs periodically, because the assumption of periodic losses is given in these schemes. Actually, this assumption does not consist with the loss pattern in the Internet. The inter-loss time in Internet may approximate an i.i.d. exponential distribution [ZDP01], which is the link with CV[T]=1. Under CV[T]=1, WARC provides the fairness, but GAIMD and TFRC only have about 80% throughput of TCP while TEAR, IIAD, SQRT, and AIAD/H have 60% on the average.

The TFRCP and SIMD flows exhibit different trends from others. The distinctness of TFRCP is due to the convex TCP throughput equation [VB05] while that of SIMD results from that SIMD computes the congestion control parameters under the loss model with CV[P]~1 [JGM03]. We also plot the curve SIMD/Period for the SIMD with the parameters computed under CV[P]=0, which does not use the same

Fig. 3.12. The throughputs of the TCP-friendly schemes normalized with that of TCP under the artificial-loss links with different CV[T]. Results are separately plotted in two parts for clarity.

throughput as TCP.

3.5.1.4 Case III - Under Drop-Tail or RED

Fig. 3.13 and 3.14 show the results that TCP individually competes with five TCP-friendly schemes under the four configurations of the congested link: (Drop-Tail, 15Mbps), (Drop-Tail, 60Mbps), (RED, 15Mbps), and (RED, 60Mbps). For each configuration, five schemes are separately shown in two figures for clearness. As shown in Fig. 3.13(a)(c) and Fig. 3.14(a)(c), WARC almost has the similar behavior as TFRC to equally share the bottleneck bandwidth with TCP under the four configurations. As shown in Fig. 3.13(c), WARC, as well as TFRC and TEAR, has slightly lower throughput than TCP, because the rate-based control mechanism taken in the three schemes may experience a bit higher loss ratio than the window-based control mechanism taken in GAIMD and SIMD. These additional losses results from that the former does not really control the data packet transmission by the received acknowledgement packet and thus cannot respond to the overflow of the Drop-Tail queue within a RTT.

Fig. 3.13. The competing results between TCP and five TCP-friendly schemes under the links managed by Drop-Tail are shown. TCP(X) plots the average normalized throughput of TCP flows which compete with the flows controlled by the scheme X.

(a) (b)

(c) (d)

15Mbps link

60Mbps link 60Mbps link

15Mbps link

WARC TEAR TFRC

GAIMD SIMD

WARC, TEAR,TFRC

Fig. 3.13(a)(b) and Fig. 3.14(a)(b) display that TEAR and SIMD may have unequal sharing to TCP when the number of flows v exceeds 16. Our further study finds that under such conditions, TCP may encounter many losses, so controlling its rate with the timeout mechanism. In such a situation, as mentioned in Chapter 5.1.2, TEAR may use more bandwidth while SIMD and GAIMD may use less one than TCP.

3.5.2 Smoothness

Herein the smoothness degree of a WARC flow is revealed and compared with that of the flows carried by TCP and other TCP-friendly schemes. The smoothness degree is observed over different time scales, because a scheme would be more favorable to control the rate of a streaming flow if it can provide a smooth rate even under a small time-scale. We define the smoothness metric as follows. The rate of a flow, R, is sampled per 0.1 second. The CVk[R] is the coefficient-of-variation of R (CV[R]) calculated over k samplings and represents the smoothness of a flow at the time scale k.

The topology shown in Fig. 3.10 is applied for the testing. Ten TCP flows compete with ten WARC flows for a 40 Mbps-link. RED is employed as the queue management policy in this link and the queue size is set as twice bandwidth-delay product. The competition continues 2200 seconds and the data in the former 200

Fig. 3.14. The competing results between TCP and five schemes under the links managed by RED are shown.

(a) (b)

(c) (d) 15Mbps link

60Mbps link 15Mbps link

60Mbps link

WARC, TEAR TFRC

GAIMD SIMD

seconds is eliminated from the statistics of results. We also run such a competition for other TCP-friendly schemes.

For each TCP-friendly scheme, Fig. 3.15 plots its CVk[R] normalized with that of TCP over different time scale k’s. WARC, as well as TFRC and TEAR, has better smoothness than other schemes because of its RTE control. It is also demonstrates that the smoothness in WARC does not be destroyed by its fast aggressive and responsive capabilities. Moreover, the results in this figure shows these TCP-friendly schemes do provide smoother rate than TCP in the long term, observed from the normalized CV512[R]~0.5. Lastly, because these schemes avoid largely changing their rates between two losses, they have better smoothness at the time scale 16 (1.6 second) which approximates the average inter-loss time in the testing.