Some Open Questions on the Borderline of Distributed Computing and Networking

Michael SchapiraSchool of Computer Science and Engineering

Hebrew University of Jerusalem

Some Open Questions on the Borderline of Distributed Computing and Networking

This Talk1. New questions in Internet protocol

design

2. Self-stabilizing Internet protocols

3. Incentive-compatible network protocols

• … illustrated via Internet routing examples

The Internet• Tremendous success– from research experiment

to global infrastructure

• Enables innovation in applications–Web, P2P, VoIP, social networks, virtual

worlds

• But, the Internet infrastructure fairly stagnant for decades…

Why Can’t We Innovate?• “Closed” equipment– software bundled with hardware– vendor-specific interfaces

• Slow protocol standardization

• Few people can innovate– equipment vendors write the code– long delays to introduce new features

Traditional Computer Networks

data plane:packet streaming

Handle packets in “real time”: forward, filter, buffer, mark, rate-limit, measure, …

slower time scale: track topology changes, compute routes, install forwarding rules, …

control plane:distributed algorithms

Traditional Computer Networks

Software Defined Networking (SDN):a New Paradigm

API to the data plane(e.g., OpenFlow)

Controller: logically-centralized control, smart, slow, implemented in software, …

Switch: dumb, fast, implementedin hardware

8

Network OS

Controller Application

events from switchestopology changes,traffic statistics,arriving packets,…

commands to switches(un)install rules,query statistics,…

Software Defined Networking (SDN):a New Paradigm

So…• Change is finally on the horizon

• But many challenges remain…– Realizing SDN (e.g., distribute the controller?)– What are the “right” protocols (for routing,

traffic engineering, etc.)?

• Distributed computing theory can play an important role here

Distributed Controller?

10

Network OS

Controller Application

Network OS

Controller Application

for scalability and reliability

partition and replicate state

Elect a leader?Distribute the computation?How to ensure consistency

(across controllers / switches)?Where to place the

controller(s)?

Rethinking (Routing) Protocols

• Routing is a control plane operation– slow (milliseconds – seconds)

• Packet forwarding is a data plane operation– fast (microseconds)

• Today’s (intradomain) routing– establishes connectivity– optimizes routes (= shortest paths)

• failure ⇒ re-convergence ⇒ dropped packets!

Pushing Connectivity (Only!)to the Data Plane

• … while retaining scalability– implemented in hardware– low overhead (end-to-end backup paths too costly…)– static forwarding tables (no changes in packet rates)– no change to packet header

• When packet to a node d arrives at node i,i’s outgoing link is a function only of

i dincoming link

set of “live” outgoing edges fid: Ei x P(Ei) -> Ei

Resilient Forwarding• A “forwarding pattern” {fid}i is t-resilient if

for any (at most) t-edge-failures the existence of a path between a node i and the destination d implies loop-free forwarding from i to d.

• Perfect resilience ≣ t →∞

i d

j

x

Theoretical Perspective• Thm [Feigenbaum-Godfrey-Panda-S-Shenker-Singla]: 1-

resilient forwarding pattern always exists

• Thm [Feigenbaum-Godfrey-Panda-S-Shenker-Singla]: Perfect resilience is not achievable

• Big gap! – does a 2-resilient forwarding pattern always

exist?– specific families of graphs?– relax restrictions (randomness, dynamic

forwarding tables, …)?

Practical Perspective

A perfectly-resilient mechanism for achieving connectivity in the data plane – [“Data Driven Connectivity”, Liu-Panda-

Singla-Godfrey-S-Shenker, NSDI 2013]

– utilizes existing mechanisms

– small (few bits) changes to forwarding tables at packet rate

• How to distribute the controller?

• Data-plane/control-plane perspective on other networking tasks (e.g., traffic engineering)

• Connectivity in the data plane

Directions for Future Research

(Self-)Stabilizing

Internet Routing

Border Gateway Protocol

Google

Verizon

Comcast

AT&T

The Border Gateway Protocol (BGP) establishes routes between the (over 42,000) networks that make up the Internet

BGP ≠ Shortest-Path Routing!

Google

Verizon

Comcast

AT&T

I want to avoid routes through

Comcast if possible I won’t carry

traffic between AT&T and Verizon

I want a cheap route I want

short routes

Illustration: BGP Dynamics

1 2

d2, I’m

available

1, my routeis 2d

1, I’m available

Prefer routes

through 2

Prefer routes

through 1

A stable state is reached

1 2

d

BGP might oscillateindefinitely between

1d, 2dand

12d, 21d

1, 2, I’m thedestination

1, my routeis 2d

2, my routeis 1d

Illustration: BGP OscillationPrefer routes

through 2

Prefer routes

through 1

Conjecture [Griffin-Wilfong, SIGCOMM 99]:2+ stable states → BGP can oscillate

Why are Oscillations Bad?

• Make the network unpredictable and hard

to debug.

• Might lead to the flooding on the network with BGP update messages.

• Deteriorate performance!– almost 50% of VoIP disruptions are due to BGP

route fluctuations

Internet Protocols, Markets, and Beyond

• Often, in computational and economic environments1. the prescribed behavior for each “node” (human,

machine) is simple and natural2. nodes’ interaction is not synchronized

• How can we reason about such environments?– Internet protocols (BGP routing, TCP congestion control)– large-scale markets– social networks– …

Dynamics:Game Theory vs. Distributed Computing

• Game theory: – establishes convergence to equilibrium for

“natural dynamics” (best-/better-response, fictitious play, no-regret, …)

– … but typically assumes synchronization.

• Distributed computing theory:– analyzes system behavior in asynchronous

environments– … but no general notions of natural behavior.

• n nodes 1,…,n

• Node i has action space Ai– A=A1•…•An

– A-i=A1•…•Ai-1•Ai+1•…•An

• Node i has reaction function fi:A-i→Ai– f=(f1,…,fn)– fi can capture node i’s “best-responses”

Simple Model

• Infinite sequence of discrete time steps t=1,…

• A schedule s:{1,…} →2[n] maps each time

step to the subset of nodes “activated” at that time step– a fair schedule activates each node infinitely often

• An initial action-profile and schedule naturally induce a dynamics.

Simple Model (Cont.)

• Defn: An action-profile a*=(a1,…,an) is a stable state if fi(a*)=ai for all i.– that is, a* is a fixed point of f– abusing notation…

• Defn: A system is convergent if for every choice of initial action-profile and fair schedule the induced dynamics converge to a stable state.

Simple Model (Cont.)

• Thm [Jaggard-S-Wright]: If there exist multiple stable states, then the system is not convergent.– valency argument!– no failures, just dumb nodes!

• So, a unique stable state is a necessary condition for guaranteed convergence.

• Can be generalized to bounded-recall, non-stationary reaction functions.

Towards a Characterization of Convergent Systems

Application: Internet Routing• BGP establishes routes between the smaller networks that

make up the Internet

• Question [Griffin-Shepherd-Wilfong, 2001]: Do multiple stable routing configurations imply the possibility of persistent route oscillations?

• Answer [Sami-S-Zohar, 2009]: Yes!

AT&T

Qwest

Comcast

Sprint

Other Applications

• Our “two people in a corridor” example…

• Models of congestion control on the Internet

• Load balancing

• Diffusion of technologies in social networks

• Asynchronous circuits

• …

Meanwhile, back in the corridor…

• Defn: An r-fair schedule activates each node at least once in every r consecutive time steps

• Defn: A system is r-convergent if for all choices of initial action-profile and r-fair schedule the induced dynamics converges to a stable state.– convergent r-convergent– not r-convergence not convergent

• Thm [Erdmann-S]: If there exist multiple stable states, then the system is not (n-1)-convergent.– tight!– much more delicate valency argument

Strengthening the Result:Convergence vs. Synchronism

• Thm [Jaggard-S-Wright]: Determining if a system with n nodes is convergent requires exponential communication (in n).

• Thm [Engelberg-Fabrikant-S-Wajc]: Determining if a succinctly described system is convergent is PSPACE-complete.

• Both results extend also to “stochastic convergence”.

Complexity of Convergent Systems

• Other protocols!

• Identify specific classes of (stochastically) convergent games and measure convergence rate (e.g., in terms of asynchronous rounds).

• Characterize guaranteed convergence, and design algorithms for determining such convergence for other game dynamics (e.g., fictitious play, no-regret

dynamics) other notions of equilibrium (e.g., mixed Nash,

correlated) other notions of asynchrony

Directions for Future Research

Incentive-CompatibleNetwork Protocols

queue

routerlink link

TCP Congestion Control is NOT Incentive Compatible

AIMD = Additive Increase Multiplicative Decrease

What About BGP?

• BGP was designed to guarantee connectivity between largely trusted and obedient parties.

• In today’s commercial Internet ASes are owned by self-interested, often competing, entities– might not follow the “prescribed behaviour”

• Simple examples show that BGP is, in fact, not incentive compatible– a node can obtain a better route by “lying”

How Can We Fix This?• Economic Mechanism Design: “the reverse-

engineering approach to game-theory”.

• Goal: Incentivize players to follow the prescribed behaviour– if others run the protocol so should I!– without money!

• Thm [Levin-S-Zohar]: Secure variants of BGP are incentive compatible.

• An exciting time to be in networking

• Internet protocols motivate new research directions

• Distributed computing theory has much to contribute

Conclusion

Thank You