1. Performance Evaluation of TCP over Multiple Paths in Fixed Robust Routing Wenjie Chen, Yukinobu Fukushima, Takashi Matsumura, Yuichi Nishida, and Tokumi Yokohira The Graduate School of Natural Science and Technology, Okayama University, Japan 1 CQR 2011

2. Background Penetration of bandwidth-consuming applications (e.g., P2P file sharing and video streaming) Traffic patterns in ISP networks become variable Need for ISP networks to accommodate those variable traffic patterns Routing for variable traffic patterns  Dynamic routing  Increases operational complexity  Can lead to route instability  Fixed robust routing [1, 3]  Low operational complexity  No route instability (static routing) CQR 2011 2 [1] M. Kodialam, T. V. Lakshman, and S. Sengupta, “Maximum throughput routing of traffic in the hose model,” in Proceedings of IEEE INFOCOM2006, pp. 1–11, Apr. 2006. [3] V. Tabatabaee, A. Kashyap, B. Bhattacharjee, R. J. La, and M. A. Shayman, “Robust routing with unknown traffic matrices,” in Proceedings of IEEE INFOCOM 2007, pp. 2436–2440, May 2007.

3. Fixed Robust Routing Tries to achieve the best worst-case performance (e.g., maximum link load), given variable traffic patterns  Traffic patterns are assumed to vary within the region specified by some traffic variation models (e.g., hose model) Performs multipath routing  Traffic of every source-destination pair is routed on multiple paths Multipath routing causes out-of-order packet arrivals TCP performance may be degraded CQR 2011 3

4. Research Objective Investigation of TCP performance over general fixed robust routing Proposal of fixed robust routing algorithm that tries to improve TCP performance in addition to decreasing maximum link load CQR 2011 4

5. Formulation of Fixed Robust Routing Problem [3] CQR 2011 5 Input Output : Candidate paths of every ( i, j ) pair : Set of traffic matrices that follow hose and pipe traffic model : Maximum link load : Fraction of traffic of the corresponding ( i, j ) pair routed on path p Linear semi-infinite programming problem (convertible to polynomial size linear programming problem [3]) : Set of all links in the network : capacity of link l Path 1 Path 2 Path 3 [3] V. Tabatabaee, A. Kashyap, B. Bhattacharjee, R. J. La, and M. A. Shayman, “Robust routing with unknown traffic matrices,” in Proceedings of IEEE INFOCOM 2007, pp. 2436–2440, May 2007. subject to Node i Node j : Set of paths routed on link l

6. Performance Degradation of TCP over Fixed Robust Routing CQR 2011 6 Time Reception of three duplicated Acks Time Source Destination 1 2 3 4 1 2 3 4 Packets on shorter path overtake preceding packets on longer path Out-of-order packet arrivals at destination host Source host receives three duplicated Acks and decreases its congestion window size TCP throughput is degraded Shorter Path Longer Path 4 3 2 1 Source Destination

7. Evaluation of TCP Performance over Fixed Robust Routing: Simulation model Two kinds of path between R 1 and R 2  L (Long path): 2.0 + d [ms]  S (Short path): 2.0 [ms] Combination of paths: SLLL, SSLL, SSSL One TCP connection for every end-host pair ( S i, D i ) S i ’s data transmission rate: 20 [Mbps] CQR 2011 7 S1S1 S2S2 S3S3 S4S4 S5S5 R1R1 R2R2 D1D1 D2D2 D3D3 D4D4 D5D5 Bandwidth: 50 [Mbps] Propagation delay: 0.2 [ms] Bandwidth: 100 [Mbps] Propagation delay: 2.0 + d [ms] for L 2.0 [ms] for S

8. Evaluation of TCP Performance over Fixed Robust Routing: Result Larger delay difference more candidates for overtaking packet Higher ratio of shorter path higher probability of three out-of-order packet arrivals CQR 2011 8 d (delay difference between path L and path S) [ms] 0.4 0.81.2 1.6 2.02.42.8 0 0 20 40 60 80 100 Total throughput [Mbps] SLLL SSLL SSSL Lower TCP throughput

9. Proposal of Fixed Robust Routing Taking Account of TCP Performance (1/2): Basic Strategy CQR 2011 9 Input Output : Maximum link load subject to Linear semi-infinite programming problem Our proposed fixed robust routing selects such candidate paths ( ) that avoid TCP performance degradation as much as possible : Set of all links in the network : capacity of link l : Set of paths routed on link l : Set of traffic matrices that follow hose and pipe traffic model : Candidate paths of every ( i, j ) pair : Fraction of traffic of the corresponding ( i, j ) pair routed on path p

10. Proposal of Fixed Robust Routing Taking Account of TCP Performance (2/2): Algorithm 10 Step. 1 Selection of candidate paths of every source-destination pair Step. 1.1 We select K shortest hop paths Step. 1.2 From the K paths, we select M paths with the minimum delay difference between the shortest and the longest delay paths Step. 2. We solve the formulated problem and obtain maximum link load ( t ) and fraction ( x p ) of traffic routed on every path. When solving the problem, we bound fraction of traffic routed on the shortest delay path by α Path 1, 15ms Path 2, 8ms Path 3, 3ms Path 4, 14ms Path 5, 10ms Node i Node j MDD-LF (Minimum Delay Difference with Limited Fraction)

11. Simulation Model One TCP connection for every node-pair ( R i, R j ) Source host’s data transmission rate: 10 [Mbps] Parameter settings in MDD-LF  K = 5  M = 2  α = 0.25 Comparison: k-shortest  A straightforward fixed robust routing algorithm that selects M (= 2) shortest hop paths as candidate paths for every node-pair CQR 2011 11 R4 [2%] 4.7ms 2.8ms 7.0ms 3.5ms 2.8ms 3.5ms 8.4ms 4.9ms 5.6ms 11.2ms 2.8ms 9.1ms 0.7ms 1.4ms Link bandwidth: 1 [Gbps]

12. Evaluation Results Compared to k-shortest, MDD-LF: 27% higher throughput Candidate path selection policy of MDD-LF is effective for improving TCP throughput CQR 2011 12 0 2 4 6 8 10 Average Throughput [Mbps] k-shortest MDD-LF k-shortest MDD-LF 0 0.2 0.4 0.6 0.8 1 Maximum link load Compared to k-shortest, MDD-LF: 2.3 times higher load MDD-LF tends to select longer hop paths than k-shortest

13. Conclusions and Future Work Conclusions  Investigation of TCP throughput over fixed robust routing  Larger delay difference  Higher ratio of shorter path  Proposal of fixed robust routing algorithm that tries to improve TCP throughput  MDD-LF: 27% higher throughput but 2.3 times higher load Future work  Performance evaluation of our proposed algorithm in detail  Modification of our proposed algorithm  Selection of link-disjoint paths as candidate paths CQR 2011 13 Lower TCP throughput

14. Number of Candidates for Overtaking packets CQR 2011 14 d (delay difference between path L and path S) [ms] 0.4 0.81.2 1.6 2.02.42.8 0 0 20 40 60 80 100 Total throughput [Mbps] SLLL SSLL SSSL # of candidates for overtaking packets 0 123456 Time Source Destination 1 2 3 4 1 2 3 4 d = 1.0 0.4 Average packet transmission interval

15. Evaluation of TCP Performance over Fixed Robust Routing: Result Larger delay difference more candidates for overtaking packet Higher ratio of shorter path higher probability of three out-of-order packet arrivals  SLLL: 0.012  SSLL: 0.063  SSSL: 0.11 CQR 2011 15 d (delay difference between path L and path S) [ms] 0.4 0.81.2 1.6 2.02.42.8 0 0 20 40 60 80 100 Total throughput [Mbps] SLLL SSLL SSSL Lower TCP throughput

16. Traffic Variation Models Assumed in Fixed Robust Routing Hose traffic model Pipe traffic model CQR 2011 16 T = t 11 t 12 t1nt1n ・・・ t 21 t 22 ・・・ t2nt2n t 21 t 22 ・・・ t2nt2n ・・・・・・ ・・・ ・・・ : Upper bound on traffic volume that enters the network at node i (e.g., bandwidth of external ingress link of node i ) : Upper bound on traffic volume that leaves the network at node j (e.g., bandwidth of external egress link of node j ) T = t 11 t 12 t1nt1n ・・・ t 21 t 22 ・・・ t2nt2n t 21 t 22 ・・・ t2nt2n ・・・・・・・・・ ・・・ : Upper bound on traffic volume from node i to node j (The value is determined based on traffic histories or service level agreement)

17. Evaluation Results Compared to k-shortest, MDD: 22% higher throughput MDD-LF: 27% higher throughput candidate path selection policy of MDD and MDD-LD are effective for improving TCP throughput CQR 2011 17 0 2 4 6 8 10 Average Throughput [Mbps] k-shortest MDD MDD-LF k-shortestMDD MDD-LF 0 0.2 0.4 0.6 0.8 1 Maximum link load Compared to k-shortest, MDD: 1.7 times higher load MDD-LF: 2.3 times higher load MDD and MDD-LF tend to select longer hop paths than k-shortest

18. Evaluation of TCP Performance over Fixed Robust Routing: Result Larger delay difference more candidates for overtaking packet Higher ratio of shorter path higher probability of three out-of-order packet arrivals  SLLL: 0.012  SSLL: 0.063  SSSL: 0.11 CQR 2011 18 d (delay difference between path L and path S) 0.4 0.81.2 1.6 2.02.42.8 0 0 20 40 60 80 100 Total throughput [Mbps] SLLL SSLL SSSL Lower TCP throughput Average packet transmission interval

19. Proposal of Fixed Robust Routing Taking Account of TCP Performance (2/2): Algorithm 19 Step. 1 Selection of candidate paths of every source-destination pair Step. 1.1 We select K shortest hop paths Step. 1.2 From the K paths, we select M paths with the minimum delay difference between the shortest and the longest delay paths Step. 2. We solve the formulated problem and obtain maximum link load ( t ) and fraction ( x p ) of traffic routed on every path. In MDD-LF, we bound fraction of traffic routed on the shortest delay path by α Path 1, 15ms Path 2, 8ms Path 3, 3ms Path 4, 14ms Path 5, 10ms MDD (Minimum Delay Difference)MDD-LF (MDD with Limited Fraction)and Node i Node j

20. Simulation Model One TCP connection for every node-pair ( R i, R j ) Each source host’s data transmission rate: 10 [Mbps] Parameter settings in MDD and MDD-LF  K = 5  M = 2  α = 0.25 Comparison: k-shortest  A straightforward fixed robust routing that selects M (= 2) shortest hop paths as candidate paths for every node- pair CQR 2011 20 R4 [2%] 4.7ms 2.8ms 7.0ms 3.5ms 2.8ms 3.5ms 8.4ms 4.9ms 5.6ms 11.2ms 2.8ms 9.1ms 0.7ms 1.4ms Link bandwidth: 1 [Gbps]

21. Conclusions and Future Work Conclusions  Investigation of TCP throughput over fixed robust routing  Larger delay difference  Higher ratio of shorter path  Proposal of fixed robust routing algorithms that try to improve TCP throughput  MDD: 22% higher throughput but 1.7times higher load  MDD-LF: 27% higher throughput but 2.3 times higher load Future work  Performance evaluation of our proposed algorithms in detail  Modification of our proposed algorithms  Selection of link-disjoint paths as candidate paths CQR 2011 21 Lower TCP throughput