UNDERSTANDING TCP CUBIC PERFORMANCE IN THE CLOUD: A MEAN-FIELD APPROACH

IEEE Cloudnet 2013

Sonia Belhareth*, Lucile Sassatelli◊, Denis Collange*, Dino Lopez-Pacheco ◊, Guillaume Urvoy-Keller ◊

*Orange Labs, Sophia Antipolis, France◊ Laboratoire I3S, Université Nice Sophia Antipolis – CNRS, France

2

Motivation• Preliminary: TCP is (obviously) the dominant transport

protocol in cloud and data center scenarios

• We focus on the following scenario: N long-lived TCP connections sharing a bottleneck link

• Two flavors of TCP:• TCP Cubic (default CC of Linux)• TCP NewReno as a legacy reference

3

Contributions• Mean field approach -> fluid model of interactions of TCP

connections

• Validation against ns-2 simulations

• Extensive comparison between Cubic and New Reno in cloud scenarios

4

• For large BDP (bandwidth delay product) network – long fat pipe

where: • t is the time since the last loss• C is a constant• wmax is the largest congestion window prior to last loss

•

TCP Cubic

5

TCP Cubic• Advantages of Cubic :

• Window growth independent from RTT but only time t since last loss

• Fast increase until last max congestion window followed by smooth probing for additional bandwidth

• Linux kernel since 2.6.19

6

TCP Cubic• Cubic can also operate in low BDP networks:

where R(t) is the estimated RTT at time t

• In practice: w(t)=max(wc(t),wtcp(t)) and the state of Cubic connection is < w(t),wmax>

• Key remark: for a given scenario (latency, capacity and buffer size), Cubic is either in Cubic or TCP mode• [See paper for details]

7

Target scenarios : FTTH, intra-DC and inter-DC

• Scenario A: FTTH client DC• Scenario B: intra DC• Scenario C: inter DC

Bandwidth RTT BDP Buffer size

FTTH client 100 Mbps 20 ms 166 pkts 50 pkts

intra DC 1 Gbps 1 ms 83 pkts 50 pkts

inter DC 1 Gbps 50 ms 4150 pkts 500 pkts

8

Network model

• The state of a connection is • The state of the queue is• The current RTT is • The current loss probability is

N TCP Cubic connections

Capacity : NL pkts/s

Buffer size: NB

9

Performance analysis• State of the system:

• is a mean-field interaction system with N objects

• The occupancy measure is the fraction of connections in each state at time t:

• Theorem 3.1 of [K70] ensures that converges uniformly almost surely to the solution of coupled ODE:

[K70] T. G. Kurtz, Solutions of Ordinary Differential Equations as Limits of Pure Jump Markov Processes, Journal of Applied Probability, vol. 7, no. 1, pp. 49–58, 1970. [BL08] M. Benaïm and J.-Y. Le Boudec, A class of mean field interaction models for computer and communication systems, Performance Evaluation, vol. 65, no. 11-12, pp. 823–838, 2008.

10

Performance analysisThe cx detects a loss

The cx gets the ACK

Input rate

11

Performance analysis• Former model derived from the model for NewReno

proposed in

F. Baccelli, D. R. McDonald, and J. Reynier, “A mean-field model for multiple TCP connections through a buffer implementing red,” Perform. Eval., vol. 49, no. 1-4, Sep. 2002.• Our extensions :

• Extension to Cubic whose window growth rate depends on time• Need to account for loss time (loss process is assumed Poisson as

in Baccelli et al.)

12

Numerical validation

• Comparison against ns-2 simulations• Note that we do not model the slow start

•Very good accuracy for FTTH DC and intra DC scenarios

13

Numerical validation

• Less accuracy for inter-DC• Only scenario in pure Cubic mode

• The synchronization also studied by Hassayoun et al. through simulations.• Persists even with RED, traffic on reverse path or multiplexing

level.

14

Performance Analysis• Question 1: is TCP Cubic as fair as NewReno?

• At least for TCP mode of Cubic in first two scenarios

• Question 2 : how efficient is TCP Cubic with small buffer sizes?• [Lei07] observed through experimentation detrimental effects of

small buffers for Cubic• Hence the question : is it due to (early) implementation of Cubic or

is it intrinsic to Cubic itself?

15

Fairness

• CoV (std/mean) of congestion window• CoV close to 0 : very good fairness• The larger the CoV, the smaller the fairness• (CoV related to Jain Fairness index)

• Take-away: Cubic is more fair than TCP (in TCP mode)

16

Impact of buffer size

• Better utilization by Cubic• Both Cubic and New Reno are greedy not good for newly arriving cx• Cubic is more greedy than New Reno• TCP New Reno is clearly less efficient than Cubic for buffer sizes smaller

than 60% of the BDP• Our model suggests that Cubic is able to survive with buffer sizes as

small as 20% of the BDP

17

Conclusions and future work• Model for TCP mode of Cubic (and NewReno)

• Valid for a large set of cloud related scenarios• (for 1 Gb/s link, need 16 ms or RTT for triggering Cubic mode)

• Allow to investigate some fundamental features related to fairness and impact of buffer sizes

• Future work:• Introduction of heterogeneity - mix of short and long-lived

connections, different RTT, other versions (Compound)• Need to investigate synchronization effects of Cubic mode