An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok...
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Transcript of An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok...
![Page 1: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/1.jpg)
An Optimization-Driven Approach for Modeling AS-level Internet Connectivity
Presented by:Hyunseok Chang
Joint work with Sugih Jamin (UM) and Walter Willinger (AT&T)
![Page 2: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/2.jpg)
IPAM 2003
AS-level Internet graph
Autonomous System (AS)Peering relationship
Provider-customer typePeer-to-peer type
Autonomous System (AS) Point of Presence (PoP)
![Page 3: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/3.jpg)
IPAM 2003
Inferred Internet AS graph
Highly variable AS vertex degree distribution.
![Page 4: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/4.jpg)
IPAM 2003
Related research Generating Internet-like random graphs
Focusing on the quality of a generated graph, not on the generation process itself.
e.g., Inet generator. Modeling the Internet AS graph
A graph generation process reflects actual Internet growth history.
e.g., Barabasi-Albert model, Fabrikant-HOT model.
Our study focuses on the modeling aspect.
![Page 5: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/5.jpg)
IPAM 2003
Our research focus The related works have been very generic, based
only on topological properties (e.g., node degree). Our starting point: Fabrikant-HOT (Heuristically Op
timized Trade-off) model for Internet growth.
Attempt to explain how inter-AS peering relationships are established in an optimization-driven fashion.
![Page 6: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/6.jpg)
IPAM 2003
AS degree distributions
At first, we focus on PC subgraph single-homed.
![Page 7: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/7.jpg)
IPAM 2003
Fabrikant-HOT model Each new node solves the local optimization p
roblem to find a target node to connect to. Each new node i connects to an existing node
j that minimizes the weighted sum of two objectives: min (dij + hj) dij (last mile cost) = Euclidean distance from i to j hj (transmission delay cost) = average hop distanc
e from j to all other nodes
![Page 8: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/8.jpg)
IPAM 2003
Multi-PoP ISPs Fabrikant-HOT model assumes each node has
a single PoP, whereas ISPs maintain multiple PoPs.
In reality, dij and hj may not be independent.
AS# Name # of PoPs
2914 Verio 121
7018 AT&T 108
1221 Telstra 61
3356 Level3 52
1239 SprintLink 43
![Page 9: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/9.jpg)
IPAM 2003
Modified Fabrikant-HOT model Each node maintains multiple PoPs. The number of PoPs of an existing node increa
ses over time.
![Page 10: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/10.jpg)
IPAM 2003
Original Fabrikant-HOT model
ij jd h
For each new node i,
Find node j that minimizes Connect node i to node j.
( )l loc set j jild hmin
For each existing node u, increment |loc-set(u)| with prob. Krank(u)-.
|loc-set(i)| 1
Modified
![Page 11: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/11.jpg)
IPAM 2003
Modified Fabrikant-HOT model creates a hot spot!
(a) Fabrikant-HOT model (b) Modified Fabrikant-HOT model
![Page 12: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/12.jpg)
IPAM 2003
Our proposed models Univariate HOT model.
Criteria: (i) AS geography. Bivariate HOT model.
Criteria: (i) AS geography, (ii) AS business model. Various extensions.
![Page 13: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/13.jpg)
IPAM 2003
Our proposed models Univariate HOT model
Criteria: (i) AS geography. Bivariate HOT model
Criteria: (i) AS geography, (ii) AS business model. Various extensions.
![Page 14: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/14.jpg)
IPAM 2003
Univariate HOT model A single-objective optimization: minimize last-
mile connection cost. A newly arriving node i connects to an existing
node that has the closest PoP to i. An existing node u gradually increases the nu
mber of PoPs as later arriving nodes are attached to u.
![Page 15: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/15.jpg)
IPAM 2003
Modified Fabrikant-HOT model
For each new node i, |loc-set(i)| 1 Find node j that minimizes Connect node i to node j. For each existing node u, increment |loc-set(u)| with prob. Krank(u)-.
( )l loc set j jild hmin
Univariate HOT model
![Page 16: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/16.jpg)
IPAM 2003
Node size & degree distribution =0.1
Exponential-type distribution for the number of locations per node.
![Page 17: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/17.jpg)
IPAM 2003
Node size & degree distribution =1.0
Highly-variable distribution for the number of locations per node.
![Page 18: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/18.jpg)
IPAM 2003
AS size vs. AS degree Univariate model predicts that AS degree varia
bility would be comparable to AS size (i.e., # of PoPs) variability.
However, in the current Internet: Maximum AS degree ~ 103
Maximum # of PoPs per AS ~ 102
Q: Are there other criteria?
![Page 19: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/19.jpg)
IPAM 2003
Proposed HOT models Univariate HOT model.
Criteria: (i) AS geography. Bivariate HOT model.
Criteria: (i) AS geography, (ii) AS business model. Various extensions.
![Page 20: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/20.jpg)
IPAM 2003
Bivariate HOT model What if new AS i has multiple candidate provid
ers in close geographic proximity? e.g., global criteria set = {reliability, cost, cu
stomer service} and customer i’s local criteria set (i) = {reliability, cost}, ISP X: {99%, $100/Mbps, fair} ISP Y: {98%, $150/Mbps, good} ISP Z: {97%, $50/Mbps, bad}With respect to (i), ISP X and Z are Pareto optimal.
X >(i) Y
Y < >(i) Z
X < >(i) Z
![Page 21: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/21.jpg)
IPAM 2003
Bivariate HOT model Given a new node i, Initialize nbr-set(i) as containing all the nodes
which have a PoP in close proximity to i. Remove any node in nbr-set(i), which is not P
areto-optimal in terms of (i); an existing node u has quality vector Q(u)=(x1,…,xN).
Connect node i to one randomly selected node from nbr-set(i).
![Page 22: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/22.jpg)
IPAM 2003
Node size & degree distribution
Bivariate model matches the Internet well!
![Page 23: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/23.jpg)
IPAM 2003
Proposed HOT models Univariate HOT model.
Criteria: (i) AS geography. Bivariate HOT model.
Criteria: (i) AS geography, (ii) AS business model. Various extensions.
![Page 24: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/24.jpg)
IPAM 2003
Extension #1: multiple providers per AS Observation: # of providers for an AS increase
s over time (similar to # of PoPs).
In our original model: Every time a new node i is added to a graph,
each existing node u gets a chance to: i) increment |loc-set(u)| with prob. Krank(u)-, ii) increment |prov-set(u)|with prob. Rrank(u)- (R<<K).
In our extended model:
![Page 25: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/25.jpg)
IPAM 2003
Extension #2:peer-to-peer neighbors Observation: decision on providers is unilatera
l, but decision on peers is bilateral. For existing nodes u and v to become peering
partners, we expect: i) unbr-set(v) (or, vnbr-set(u)), ii) u (u) v and v (v) u (u), (v) : peering criteria set for u and v.
![Page 26: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/26.jpg)
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Extension #3: AS evolution Node death & change-of-provider
events. Role transition (e.g., provider peer). Evolving qualities.
![Page 27: An Optimization-Driven Approach for Modeling AS-level Internet Connectivity Presented by: Hyunseok Chang hschang@eecs.umich.edu Joint work with Sugih Jamin.](https://reader031.fdocuments.net/reader031/viewer/2022032206/56649efd5503460f94c110b8/html5/thumbnails/27.jpg)
IPAM 2003
Summary Our modeling approach:
Explores the possibility of studying the Internet AS evolution in an optimization-based framework.
Introduces domain-specific concepts in the modeling framework.
Challenges: Model validation Application(s)
Any kind of input is welcome!!