Vitaliy Rapp and Kalman Graffi. Continuous Gossip-based Aggregation through Dynamic Information Aging. In IEEE ICCCN ’13: Proceedings of the International Conference on Computer Communications and Networks, 2013. Abstract—Existing solutions for gossip-based aggregation in peer-to-peer networks use epochs to calculate a global estimation from an initial static set of local values. Once the estimation converges system-wide, a new epoch is started with fresh initial values. Long epochs result in precise estimations based on old measurements and short epochs result in imprecise aggregated estimations. In contrast to this approach, we present in this paper a continuous, epoch-less approach which considers fresh local values in every round of the gossip-based aggregation. By using an approach for dynamic information aging, inaccurate values and values from left peers fade from the aggregation memory. Evaluation shows that the presented approach for continuous information aggregation in peer-to-peer systems monitors the system performance precisely, adapts to changes and is lightweight to operate.

1. Continuous Gossip-based Aggregation
Through Dynamic Information Aging
Vitaliy Rapp, Kalman Graffi
Technology of Social Networks Group,
University of Düsseldorf, Germany
Email: graffi@cs.uni-duesseldorf.de

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
1008 1622 2011
PeerID = PubKey
3485
Peer-to-Peer
Service Delivery
IP Network
(Underlay)
Overlay
Connection
H(„my data“ )
= 3107
2207
2906
709
611
?
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 2

3. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 3

4. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 4

5. Agenda
Gossip based Aggregation
Continuous Gossip-based Aggregation
Evaluation
Conclusions
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 5

6. ► 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)
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 6

7. Gossip-Protocol: PushSum
Assumptions
– Input: local states 푥푖 (푡) of peers 푝푖 at time 푡
– Initialization defines aggregation function
round(0){
– 1. 푠0,푖 = 푥푖 (for average calculation)
– 2. 푤0,푖 = 1 (for average calculation)
– 3. 푠푒푛푑 푠푖 , 푤푖 푡표 푠푒푙푓 }
Round (r>0){
∗, 푥푡
– 1. Let {(푠푡
∗)} be all pairs sent to 푖 during round r-1
∗ ; 푤푟,푖 = 푡 푤푡
– 2. 푠푟,푖 = 푡 푠푡
∗
– 3. Choose a target node 푗 ≠ 푖 uniformly at random
– 4. Send the pair (
1
2
푠푟,푖 ,
1
2
푤푟,푖 ) to j and self
– 5.
푠푟,푖
푤푟,푖
is the estimate of aggregate in round r }
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 7

8. Initialization of PushSum
Result of gossiping:
– Input: 푠푖 , 푤푖
– Output: F t =
푎푣푒푟푎푔푒(푠푖)
푎푣푒푟푎푔푒(푤푖)
Calculating the average:
– For all nodes: 푠푖 = 푥푖 ; wi = 1
푎푣푒푟푎푔푒(푥푖)
– Output:F t =
1
Node count:
– One single node: 푠푖 = 1; 푤푖 = 1
– All other nodes: 푠푖 = 1; 푤푖 = 0
– Output: F t =
1
1/푛
with 1/n being the average share of 1 among n peers
Calculating the sum:
– One single node: 푠푖 = 푥푖 ; 푤푖 = 1
– All other nodes: 푠푖 = 푥푖 ; 푤푖 = 0
푎푣푒푟푎푔푒(푥푖)
– Output: F t =
1/푛
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 8

9. Example Average Calculation
Example: 12 nodes
– Initial state
– After 1 round
• With communication links
– After 5 rounds
– After 10 rounds
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 9

10. 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
Inpre-cise
Convergence time
• n = number of nodes
• 휀 = 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)
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 11

11. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 12

12. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 13

13. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 14

14. Agenda
Gossip based Aggregation
Continuous Gossip-based Aggregation
Evaluation
Conclusions
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 15

15. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 16

16. Aging - Example
1
 = 4
4.6
4.2
7
5
3
 = 4
 = 4
 = 4
 = 4, α = 0.2
3.4
3.8
4.2
3.8
3.8
4.2
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 17

17. Aging - Example
1
 = 4
7
5
3
 = 3.513
 =  = 3.66
3..161465
 = 3.5115
3.51
3.32
 = 3.9
4
 = 3.6
== 33..3.75
3.8
66435
3.5115
3.516
4
3.513
 = 34, αα = 0.2
3.4
3.51
3.904
3.636
3.9
3.75
4
4.2
3.6
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 18

18. 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
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19. Agenda
Gossip based Aggregation
Continuous Gossip-based Aggregation
Evaluation
Conclusions
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 20

20. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 21

21. ► 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
User
Simulation Engine
Application
Service
Overlay
Transport
Network
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 22

22. Network Size Estimation
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 23

23. 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
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 24

24. Operation Cost Estimation
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25. Agenda
Gossip based Aggregation
Continuous Gossip-based Aggregation
Evaluation
Conclusions
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 26

26. 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)
Kalman Graffi Heinrich Heine Universität Düsseldorf 10/09/14 27

27. Thank You for Your Attention
Jun.-Prof. Dr.-Ing. Kalman Graffi
Technology of Social Networks Group
Institute of Computer Science
Heinrich-Heine-Universität Düsseldorf
eMail: graffi@cs.uni-duesseldorf.de
Web: www.p2pframework.com
Web: www.peerfact.org
?
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