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Alternate Path Availability (APA) Shortest path: T ms total propagation delay Y Gbps SP capacity Y Gbps Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Links on Alternate Path Availability (APA) shortest path 1 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Links with viable alternative paths Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 1 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 2 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 3 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 3 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Path too long or not enough capacity Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 4 Shortest path: 5 T ms total propagation delay Y Gbps SP capacity Y Gbps Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Alternate Path Availability (APA) 4 5 = 0.8 Shortest path: T ms total propagation delay Y Gbps SP capacity Y Gbps For this PoP pair 80% of the links on the SP have an alternate path with acceptable low latency Exclude each link on the shortest path; can we route Y Gbps over one or more alternative paths with delay < 1.4 T?

Low-latency path diversity (LLPD) 1. Compute APA for all PoP pairs

Low-latency path diversity (LLPD) 1. Compute APA for all PoP pairs Fraction of PoP pairs with 2. Compute LLPD = “good” path availability

Low-latency path diversity (LLPD) 1. Compute APA for all PoP pairs Fraction of PoP pairs with 2. Compute LLPD = “good” path availability number of PoP pairs with APA ≥ 0.7 = total number of PoP pairs

Low-latency path diversity (LLPD) Empirically derived; 1. Compute APA for all PoP pairs metric not sensitive to picking different values Fraction of PoP pairs with 2. Compute LLPD = “good” path availability number of PoP pairs with APA ≥ 0.7 = total number of PoP pairs

fraction of pairs congested 90th percentile GTS Median 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD 100+ real-world ISP topologies, ranked by low-latency path diversity (LLPD)

fraction of pairs congested 90th percentile GTS Median 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD Generate TMs for each topology; plot fraction of (Src,Dst) PoP pairs in each TM that crosses at least one congested link

Shortest path routing congests links fraction of pairs congested 90th percentile GTS Median 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD Two points per topology: median TM and 90 th percentile TM; line shows spread of distribution

Shortest path routing congests links fraction of pairs congested 90th percentile GTS Median 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD Networks with high LLPD offer lots of alternative paths à shortest path routing experiences congestion

Shortest path routing congests links fraction of pairs congested 90th percentile GTS Median 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD Networks with high LLPD offer lots of alternative No surprises here. What paths à shortest path routing experiences congestion about B4?

B4 congests networks with high potential for low latency fraction of pairs congested Better at using • 90th percentile GTS Median alternative paths 0.5 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

B4 congests networks with high potential for low latency fraction of pairs congested Better at using • GTS alternative paths 0.5 0.0 1.0 GTS latency stretch 1.2 total prop delay of all flows 90th percentile 1.4 Median total prop delay if all flows 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 routed on SP LLPD

B4 congests networks with high potential for low latency fraction of pairs congested GTS Better 0.5 Congestion 0.0 1.0 GTS latency stretch Better 1.2 Propagation delay 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

B4 congests networks with high potential for low latency fraction of pairs congested Better at using • GTS alternative paths 0.5 Some flows routed • on non-shortest paths 0.0 1.0 GTS latency stretch 1.2 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

B4 congests networks with high potential for low latency fraction of pairs congested Better at using • GTS alternative paths 0.5 Some flows routed • on non-shortest paths 0.0 1.0 Still incurs • GTS latency stretch congestion, and 1.2 precisely on 90th percentile 1.4 Median high-LLPD networks! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

B4 congests networks with high potential for low latency fraction of pairs congested Better at using • GTS alternative paths 0.5 Some flows routed • on non-shortest paths 0.0 1.0 Still incurs • GTS latency stretch congestion, and 1.2 Need a different routing scheme. How precisely on 90th percentile 1.4 Median about one that prioritizes avoiding high-LLPD networks! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 congestion above all else? LLPD

Minimizing utilization avoids congestion

Minimizing utilization avoids congestion Spread traffic out to leave • spare capacity in case traffic levels increase 33% A well-known technique • called MinMax Does not care about • propagation delay

Minimizing utilization avoids congestion Spread traffic out to leave • spare capacity in case traffic levels increase 33% A well-known technique • called MinMax Does not care about • propagation delay How does MinMax do?

MinMax inflates propagation delay fraction of pairs congested Minimizes utilization, • designed to avoid 0.5 congestion 0.0 1.0 latency stretch GTS 1.2 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

MinMax inflates propagation delay fraction of pairs congested Minimizes utilization, • designed to avoid 0.5 congestion Routes some flows on • 0.0 1.0 paths with high latency stretch GTS propagation delay 1.2 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

MinMax inflates propagation delay fraction of pairs congested Minimizes utilization, • One extreme of the design designed to avoid 0.5 space. The other one? congestion Routes some flows on • 0.0 1.0 paths with high latency stretch GTS propagation delay 1.2 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

Latency-optimal placement fraction of pairs congested Minimizes prop delay • and avoids congestion 0.5 Maximizes utilization • of links on low-delay 0.0 GTS 1.0 paths latency stretch 1.2 90th percentile 1.4 Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD

Latency-optimal placement fraction of pairs congested Minimizes prop delay • and avoids congestion 0.5 Maximizes utilization • of links on low-delay 0.0 GTS 1.0 paths latency stretch 1.2 Assume it is possible to 90th percentile 1.4 compute this at scale, Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 more about that later… LLPD

Two extremes of congestion-free routing fraction of pairs congested fraction of pairs congested 0.5 0.5 0.0 0.0 GTS 1.0 1.0 latency stretch latency stretch GTS 1.2 1.2 90th percentile 90th percentile 1.4 1.4 Median Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD LLPD Minimize utilization Minimize propagation delay (MinMax) and avoid congestion

Two extremes of congestion-free routing fraction of pairs congested fraction of pairs congested 0.5 0.5 0.0 0.0 GTS 1.0 1.0 latency stretch latency stretch GTS 1.2 1.2 90th percentile 90th percentile 1.4 1.4 Median Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD LLPD Minimize utilization Minimize propagation delay (MinMax) and avoid congestion

Two extremes of congestion-free routing fraction of pairs congested fraction of pairs congested GTS 0.5 0.5 GTS 0.0 0.0 GTS 1.0 1.0 latency stretch latency stretch GTS 1.2 1.2 90th percentile 90th percentile 1.4 1.4 Median Median 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD LLPD Minimize utilization Minimize propagation delay (MinMax) and avoid congestion

Two extremes of congestion-free routing fraction of pairs congested fraction of pairs congested GTS 0.5 0.5 GTS 0.0 0.0 GTS 1.0 1.0 latency stretch latency stretch GTS 1.2 1.2 90th percentile 90th percentile 1.4 1.4 Median Median GTS sees 5x difference in propagation delay! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD LLPD Minimize utilization Minimize propagation delay (MinMax) and avoid congestion

Two extremes of congestion-free routing fraction of pairs congested fraction of pairs congested GTS 0.5 0.5 GTS 0.0 0.0 GTS 1.0 1.0 latency stretch latency stretch GTS 1.2 1.2 90th percentile 90th percentile 1.4 1.4 Median Median GTS sees 5x difference in propagation delay! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 LLPD LLPD Minimize utilization Minimize propagation delay Let’s focus on a single traffic matrix (MinMax) and avoid congestion

Two extremes of congestion-free routing 1.0 CDF 0.5 Latency-optimal (mean 0.32) MinMax (mean 0.30) 0.0 0.0 0.2 0.4 0.6 0.8 1.0 link utilization Significant delta in prop delay, but mean utilization the same

Two extremes of congestion-free routing 1.0 CDF 0.5 Latency-optimal (mean 0.32) MinMax (mean 0.30) 0.0 0.0 0.2 0.4 0.6 0.8 1.0 link utilization Links on short prop-delay paths “in demand” in latency-optimal placement

Two extremes of congestion-free routing 1.00 0.95 CDF 0.90 Latency-optimal (mean 0.32) 0.85 MinMax (mean 0.30) 0.80 0.6 0.7 0.8 0.9 1.0 link utilization

Two extremes of congestion-free routing 1.00 0.95 CDF 0.90 Latency-optimal (mean 0.32) 0.85 MinMax (mean 0.30) 0.80 0.6 0.7 0.8 0.9 1.0 link utilization All possible congestion-free routing solutions lie in this range

Two extremes of congestion-free routing 1.00 0.95 CDF 0.90 Latency-optimal (mean 0.32) 0.85 MinMax (mean 0.30) 0.80 0.6 0.7 0.8 0.9 1.0 link utilization 100% utilization? On an ISP?

A minute from a core link 4 3 Gbps 2 1 0 Source: CAIDA 0 10 20 30 40 50 60 +3.2e3 time (s)

A minute from a core link 4 3 Gbps 2 Mean rate. Could run traffic through a path with this 1 capacity, but long queuing delay. 0 0 10 20 30 40 50 60 +3.2e3 time (s)

A minute from a core link 4 3 Gbps 2 Need to allocate headroom to allow 1 for variability 0 0 10 20 30 40 50 60 +3.2e3 time (s)

The headroom dial 1.00 0.95 CDF 0.90 Latency-optimal (mean 0.32) 0.85 MinMax (mean 0.30) 0.80 0.6 0.7 0.8 0.9 1.0 link utilization Not feasible because of variability

The headroom dial 1.00 0.95 CDF 0.90 Latency-optimal (mean 0.32) 0.85 MinMax (mean 0.30) 0.80 0.6 0.7 0.8 0.9 1.0 link utilization MinMax is one extreme of the headroom dial