An Analysis of AIMD Algorithm with Decreasing Increases Yunhong Gu, Xinwei Hong, and Robert L. Grossman National Center for Data Mining

Outline TCP’s inefficiency in grid applications Improvements on AIMD AIMD with decreasing increases (DAIMD) The UDT algorithm Experimental result Conclusion and future work

TCP and AIMD AIMD (Additive Increase Multiplicative Decrease) Fair: max-min fairness Stable: globally asynchronously stable But, inefficient and not scalable –In grid networks (with high bandwidth-delay product)

Efficiency of TCP 1 Gb/s link, 200ms RTT, between Tokyo and Chicago 28 minutes On 10 Gb/s link, 200ms RTT, it will take 4 hours 43 minutes to recover from a single loss. TCP’s throughput model: It needs extremely low loss rate on high bandwidth-delay product networks.

Improvements of TCP Fixed parameter (e.g., 1 segment per RTT) is not scalable and hence inefficient –32 segments per RTT works fine for 1 Gb/s link, but how about its performance on 40Gb/s link or 1.5Mb/s link? Increasing the increase parameter as the congestion window increases –E.g., Scalable TCP and HighSpeed TCP –Cause fairness and convergence problem

AIMD with Decreasing Increases To reach high efficiency, the increase parameter of an AIMD-based algorithm should be correlated to the link capacity and the available bandwidth. –XCP uses available bandwidth and number of concurrent flows to calculate next increase parameter The increase parameter should be large at the beginning and decreases as the sending rate increases.

AIMD with Decreasing Increases

UDT - UDP based Transport Protocol Application level built above UDP End-to-end approach Rate based control The sending rate is tuned per constant interval (SYN).

UDT Algorithm UDT considers end-to-end link capacity L –It is hard to estimate the number of concurrent flows and real-time available bandwidth UDT tunes the increase parameter according to L-C, where C is the current sending rate.

UDT Algorithm (1) (2) (3) (4) (5)

UDT Algorithm C (Mbps)L - C (Mbps)Increment (pkts/SYN) [0, 9000)(1000, 10000]10 [9000, 9900)(100, 1000]1 [9900, 9990)(10, 100]0.1 [9990, 9999)(1, 10]0.01 [9999, )(0.1, 1] < L = 10 Gbps, S = 1500 bytes

UDT Algorithm

UDT: Efficiency and Fairness Characteristics Takes 7.5 seconds to reach 90% of the link capacity, independent of BDP Satisfies max-min fairness if all the flows have the same end-to-end link capacity –Otherwise, any flow will obtain at least half of its fair share Does not take more bandwidth than concurrent TCP flow as long as

Experiment - Setup

Experiment - Results

Conclusion Standard TCP is inefficient for grid applications in high bandwidth-delay product networks. We argued that the increase parameter should be correlated to such information as link capacity and available bandwidth. We analyzed a class of AIMD based control algorithm whose increase parameter is decreasing as the sending rate increases and proved that it is fair and stable. According to this analysis we designed a new control algorithm that uses estimated link capacity and the current sending rate as the hints to update increase parameter. This algorithm has been implemented in our UDT protocol and the experiments have demonstrated very good performance.

Future Work Bandwidth Estimation –Currently UDT uses packet pairs to estimate link capacity –We will consider more methods to deal with cross traffic and NIC interrupt coalescence

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