IEEE ICCCN 2013 - Continuous Gossip-based Aggregation through Dynamic Information Aging

Continuous Gossip-based AggregationThrough Dynamic Information Aging

Vitaliy Rapp, Kalman GraffiTechnology of Social Networks Group,

University of Düsseldorf, Germany

Email: [email protected]

Kalman Graffi Heinrich Heine Universität Düsseldorf 13. April 2023 2

P2P Systems

Peer-to-Peer Network– Decentralized self-organizing

overlay network with shared resource usage

– Consist of several independent peers, cooperating with each other

Advantages:– Scalability through distribution of

responsibility– No single point of failure

Types of P2P Networks– Structured

• Use of distributed index structure (DHT)

• Peers have assigned unique IDs, and can be addressed directly

– Unstructured• Peers can communicate only with their

direct neighbors• Peers do not have special

responsibilities

IP Network(Underlay)

Overlay Connection

Peer-to-Peer Service Delivery

H(„my data“)= 3107

2207

29063485

201116221008709

611

H(„my data“)= 3107

2207

29063485

201116221008709

611

PeerID = PubKey

Direct communication


Future Peer-to-Peer Applications: Social Networks

A P2P Framework for Social Networks (LifeSocial)– Framework: combining a wide set of useful modules

• Storage, messaging, security, caching, app-hosting, multicast, pub/sub …

• Distributed data structures, monitoring – Social network on top of platform

• Build through “plugins” (apps)• Configurable GUI supports app growth

See p2pframework.com


Main Challenges for Future P2P Applications

Security:– Secure overlays, user management, key infrastructure– Secure (encrypted, authenticated, integer) communication– Access control, role-based, identity-based

Controlled quality / performance– First step monitoring: statistical aggregation over all nodes– Hop count, node count, reply times, traffic overhead, used overlay

functions, …– Statistics:

• Min, max, average,standard deviation

– Requirements• Precise• Timely• Low-cost


Agenda

Gossip based Aggregation

Continuous Gossip-based Aggregation

Evaluation

Conclusions


► Gossiping Protocols

Idea:– Communicate only with neighbors (gossip)

• Assumes no specific overlay topology– Exchange and aggregate information

• E.g. calculate averages, minimum, maximum

Characteristics– Gossip protocols are round-based (epochs)– For every round

• Each node selects a subset of nodes to interact with (pairwise)• The selection function is often probabilistic;• Nodes interact via “small” messages• Local state changes due to new information

– In general: “quick” convergence

D. Kempe, A. Dobra,J. Gehrke, “Gossip-Based Computation of Aggregate Information,” IEEE Symposium on Foundations of Computer Science (FOCS’03)


Assumptions– Input: local states of peers at time – Initialization defines aggregation function

round(0){– 1. (for average calculation)– 2. (for average calculation)– 3.

Round (r>0){– 1. Let be all pairs sent to during round r-1– 2. ; – 3. Choose a target node uniformly at random– 4. Send the pair to j and self– 5. is the estimate of aggregate in round r }

Gossip-Protocol: PushSum


Initialization of PushSum

Result of gossiping:– Input: – Output:

Calculating the average:– For all nodes: – Output:

Node count:– One single node: – All other nodes: – Output: with being the average share of 1 among n peers

Calculating the sum:– One single node: – All other nodes: – Output:


Example Average Calculation

Example: 12 nodes– Initial state– After 1 round

• With communication links– After 5 rounds– After 10 rounds


Inpre-cise

Performance and Complexity of Push-Sum

Performance: precision– Simulations with 1M nodes

• Gossip every 5 second– For most time:

• False values• Although convergence exist

– Problem• Peer count starts always at 0

Convergence time• n = number of nodes• = accepted relative error

– Push-Sum converges quickly– Problem:

• Huge message overhead per node

•

W. Terpstra, C. Leng, A. Buchmann: Brief Announcement: Practical Summation via Gossip, ACM Symposium on Principles of Distributed Computing (PODC 2007)


Churn – Reference: Node Count

Comparative Evaluation– Node count: 1000, churn– Tree-based monitoring: update

interval 15 sec, branching factor 8 – PushSum:30 messages per epoch– Centralized for comparison, update

interval 60 sec– Same overhead allowed for all

monitoring approaches

Simulation setup– Churn with joining and

instantly leaving nodes– Both decentralized

solutions• Use ca. 200 bytes/s per

node• For better comparability


Reference Signals: Steps, Sawtooth and Sine

PushSum– Imprecise monitoring – Epochs are visible– Although same traffic overhead

Centralized and tree-based– Precise– Tree become imprecise with

too much churn


Epoch based Approach

Idea:– Restart the calculation after N rounds to consider new measurements

Implementation:– Bound N round to one so called epoch– At the start of each epoch all peers resets their estimates– All peers witch join the network do not participate at the current epoch

• All joining peers receives the current round of running epoch

Advantages:– Robust, easy to implement, works with any algorithm

Disadvantages:– Requires synchronization for epoch starts– How to estimate a good epoch length

• Long: good convergence on old data• Short: bad convergence of fresh data

– Restarts the algorithm even when it’s not necessary


Agenda



Evaluation

Conclusions


Aging Approach

Idea:– Consider new measurements in each round with a ratio of α

Approach:– Let calculated values converge to holding values– Convergence rate is the same at every peer– Proposed function: (v, c) (1 - α)·c + α·v

• c – current estimation / statistic• v – fresh measurement• α – aging factor (e.g. 0.01)

Advantages:– Dynamic adaptation, no need to restart– No synchronization required at joining or due to epoch starts

Disadvantages:– Calculated aggregate values do not converge in the actual sense– Sum calculation need adjustment


Aging - Example

1

5

7

3

= 4

= 4

= 4

= 4

= 4, α = 0.2

= 3.4

= 4.6

= 3.8

= 4.2

= 3.8

= 3.8

= 4.2

= 4.2

= 4

= 4

= 4

= 4


Aging - Example

1

5

7

3

= 4

= 4

= 4

= 4

= 4, α = 0.2 = 3, α = 0.2

= 3.4

= 4.2

= 3.8 = 3.6

= 3.6

= 3.9

= 3.9

= 3.75

= 3.75

= 3.32

= 3.6

= 4

= 3.66

= 3.66 = 3.63

= 3.63 = 3.645

= 3.645 = 3.116

= 3.904

= 3.516

= 3.51

= 3.51

= 3.513

= 3.513

= 3.5115

= 3.5115


Sum Calculation with Aging

Idea:– Apply “aging” – Restart only when the peer holding 1 leaves the system

Basic implementation:– Every Peer is holding following values:

• MAX • VERSION • AVG

– MAX is used to identify the loss of the initial value• When MAX value fells under defined threshold calculation is restarted• With a small probability every peer can initialize the restart• Peer initializing restart set its AVG value to 1

– Version is used to identify duplications


Agenda



Evaluation

Conclusions


Evaluation through Simulations

Main questions– Monitoring precision (relative error) – Costs (traffic and messages)

Setup– 5000 nodes, just join, no lookups– Two scenarios - Churn: no and KAD-based

• 0 - 60 minute: joining phase• 65 – 240 minute: churn (if activated)

– Aging factor: α = 0.01– Gossip round: 10 seconds, unsynchronized

Layer setup– User / application: no overlay usage, just maintenance– Overlay: Chord (as graph)– Network model:

• Global Network Positioning delay model• OECD bandwidth model


► PeerfactSim.KOM (see www.peerfact.org)

Type– Event-based simulator in Java– Focus on simulation

of p2p systems on various layers • User, application• Services: monitoring, replication …• Overlays• Network models

Layered Architecture– Easy exchange of components– Testing of new applications / mechanisms

Main idea– Layers have several implementations– Enables testing of individual layer

mechanisms• on its own and • in combination with other layers

Application

Overlay

UserS

imula

tion

En

gine

Network

Service

Transport

Application

Overlay

UserS

imula

tion

En

gine

Network

Service

Transport


Network Size Estimation


Online Time Estimation

Node estimation– Calculation of sum is worst case scenario

• Average of once 1 and (n-1) times a 0– Relative error

• No churn < 0.01, with churn < 0.1 in average 0.05

Average calculations easier: e.g. online time estimation


Operation Cost Estimation


Agenda



Evaluation

Conclusions


Conclusions

Gossiping – Monitoring is needed for future p2p applications– Gossiping can be used in any topology

• Very robust and versatile– Problems with epoch-based gossiping

• New measurements are considered only at restart of epochs• Results of previous epochs are not reused• Hard to identify ideal epoch length

– Tradeoff between convergence and freshness

Continuous Gossip-based Aggregation – Continuously measures current network status– Integrates fresh measurement in every round with fixed ratio– High precision ( 0.01 average, 0.05 sum under churn)– Low costs (1,5 kb/s in average at a round length of 10s)


Thank You for Your Attention

Jun.-Prof. Dr.-Ing. Kalman Graffi Technology of Social Networks GroupInstitute of Computer ScienceHeinrich-Heine-Universität Düsseldorf

eMail: [email protected] Web: www.p2pframework.comWeb: www.peerfact.org

?

http://www.p2pframework.com/

http://www.peerfact.org/

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IEEE ICCCN 2013 - Continuous Gossip-based Aggregation through Dynamic Information Aging

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