enabling information dissemination on dynamic peer-to-peer

Enabling Information Disseminationon Dynamic Peer-to-Peer Networks ∗

Evan A. Sultanik<[email protected]>

2005-04-22

Department of Mathematics Department of Computer Science

College of Arts and Sciences College of Engineering

Drexel University

Philadelphia, PA 19104-2875

∗Much of this work was made possible by Drs. William Regli and Moshe Kam, DoD contract DAAB07-01-9-L504.

Enabling Information Dissemination on Dynamic Peer-to-Peer Networks [1]

Introduction

Dynamic, peer-to-peer networksimpose numerous communication constraints:

• temporal dynamism;

• distributed computation;

• fault tolerance;

• QoS (or lack thereof).

As these architectures become more common, need to:

• obtain/predict global state information at the application and service layers

• achieve adaptable/survivable application performance on MANETs


Outline of the Talk

• Introduction to Service-Based Computing

• Introduction to the Problem Space

• Formal Model of Agent Transport

• Problem: Service Availability

– Service Discovery– Time-Critical Reasoning– Agent Population Management– Network Triage

• Problem: k-Center

– Service Placement– Distributed, Weighted, Asymmetric Variant– No Global State Needed


Service-Based Computing

Information is encapsulated by and distributed through a servicearchitecture. A service-oriented computing framework is generallycomprised of five basic elements:

• Service Description: Ontology

• Advertisement

• Discovery

• Invocation

• Composition


Open Problems

Domain: Web Services on Dynamic Peer-to-Peer Networks.

• Ontology How should the services/information be represented?Very little work done1.

• Discovery How can we find the services?Exceedingly hard on non-flat networks, not to mention dynamic networks.

• Composition How do we optimally deal with homogeneous services?In this domain, a service architecture must also optimize bandwidth.

1I. Howley, J. Kopena, and W. Regli, An OWL-S Registry for Semantic Web Services on MANETs. InternationalConference on Automated Planning and Scheduling, 2005 (Under Review).


Problem I:Service Availability


Problem: Service Availability

A group of agent-driven helicopters are deployed on a battlefield, as in thesynthetic aircraft domain2; one helicopter “disappears”:

• flies over a ridge• out of communication range• destroyed

How do the remaining agentsdecide if a node, or service on thatnode, has become unavailable?Is re-planning required?

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2M. Tambe, Implementing agent teams in dynamic multi-agent environments. Applied Artificial Intelligence,12(2–3):189–210, March 1998.


Problem: Service Discovery & Availability

In some domains mobile agents can be service providers3;this complicates service localization and availability calculation.

Example: Certificate authority for secure communication between helicopters:

• encapsulated by a mobile agent• capable of reasoning about the network• continuously migrate to portions of the network with low volatility.

– migrate to helicopters less likely to be removed from the network– proximity to geographic center of group– association with centroid of network topology graph

Conclusion: A method for pro-actively tracking the location of services indynamic networks is required.

3D. Artz, et al. Network meta-reasoning for information assurance in mobile agent systems. In Proceedings ofthe Eighteenth International Joint Conference on Artificial Intelligence, pages 1455–57, August 2003.


Our Research Objective:

Design an agent “society/collective”;

Goal is to minimize difference between hosts’ perceived global state and theactual global state.

Agent behavior should be simple;minimize bandwidth and computation.


Our Research

We...

Propose a fixed-memory randomized method for approximating the locationof a service in a dynamic network with a probabilistic certainty in a fixedamount of time.

Present a mathematical formulation of agent movement in the network and analgorithmic technique for approximating the parameters of the formulation.

Validate our model in simulation


Theoretical Approach

Deploy set of service monitoring agents: ARandomly walk a set of hosts of a peer-to-peer network: H

Agents act like bees:“pollinate” the network with their knowledge of services’ locations. Accurateon-line means of service discovery.

Network Layer

Agent Layer

Agent’s walks dictated by underlyingnetwork topology;

no guarantee that all agentsvisiting a host have encountered aservice.


Advantages Over Alternative Approaches

• minimal network bandwidth is used; important issue for resource-constrainedmobile devices and large-scale peer-to-peer networks;

– naıve, pro-active broadcast requires O(n2) messages

• services need not register themselves;

• number of agents is variable; can be optimized to balance speed and networkload; and

• properties of random walks relatively easy to mathematically model and makeinferences upon.


Random Walking Agents

Task Environment: Dynamic Peer-to-Peer NetworkStochastic, dynamic, and continuous. Delay between actual topology changesand the propagation of knowledge of these changes throughout the network.

Goal: agents’ sole purpose is to randomly walk the network gathering andpropagating information.

Percepts: set of services at current host, Sh, and the set of hosts neighboringthe current host, {x ∈ H|Eh,x > 0} (where E ⊆ H ×H is the set of edgesin the topology and the notation Ex,y denotes the weight of the edge fromnode x to node y).


Random Walking Agents

Actions: hop to a neighbor host from current host. At each host agents queryfor services, storing these data in memory (with timestamp).

Itineraries: dictated by the network; successor hosts for migration selectedrandomly from neighbors.


Predicting Agent Arrival at a Host

We want to approximate frequency of agent visits.Develop a function, F (N), for the probability that

an agent a ∈ A

with knowledge of a service s ∈ S

will visit a specific host h ∈ H

in a time interval t. h2

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Local State Description

N is a local state descriptionrepresented by a tuple containing the following elements:

t - length of the time interval;ν - probability an agent will be at host h;η - number of instances of the service s;

|H| - cardinality of the set of hosts;|A| - cardinality of the set of agents;

` - average time for agent to hop from one neighbor to another; andτ - maximum amount of time since an agent last saw service s.

Note: various parameters, such as ν, need not be calculated a priori; a methodfor dynamically calculating ν is presented in the paper.


Hypothesis

With up-to-date topology data,

we can infer the rest of the parameters to the function F ().

• Intuitively, the higher the eccentricity of a host, the more likely it should“see” random walking agents.

• Many routing algorithms already propagate topology data throughout thenetwork; this is a reasonable assumption.

• Broadcasting the remaining global state information with the topology is toobandwidth intensive.


Example

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Example

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Example

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Predicting Agent Arrival

• Model the probability of a random walking agent visiting a host, ν, usingMarkov Chains (i.e. the Stationary Distribution of the graph)

• Can be approximated using the iterative improvement PageRank algorithm4

• Predict agent arrival using this model:

F (N) = 1−

1− ν + ν

(1− η

|H|

)bτ`c

t

4S. Brin and L. Page. The anatomy of a large-scale hypertextual Web search engine. Computer Networks andISDN Systems, 30(1–7):107–117, 1998.


Simulation

• MATES: Macro Agent Transport Event-based Simulator5

• Exact connectivity method for mobile ad hoc network graph generation;connections determined by Euclidean distance.

• Hosts bounded by a 1200x1200 meter box• Movement using a variation of the random waypoint mobility model• Each host has a radio range of 300 meters

Communication

300m

300m

5E. Sultanik, M. Peysakhov, and W. Regli, Agent Transport Simulation for Dynamic Peer-to-Peer Networks.6th Annual Workshop on Multi-Agent-Based Simulation, 2005 (To Appear).


Every iteration of the simulation:

1. Hosts’ directions randomly chosen; either:• maintain in current heading (probability 0.6)• rotate 45◦ clockwise (probability 0.2)• rotate 45◦ counter-clockwise (probability 0.2)

2. hosts move forward one meter;3. agents not currently in transit migrate to a randomly-selected neighbor host.

Agent transit times calculated with an inverse exponential relationship to theEuclidean distance between hosts. (Average transit time, `, is 1 iteration);

4. every instance of s treated as a mobile agent; each service migrates to arandom neighbor host; and

5. every t iterations, each host uses F (N) to develop a probability of aknowledgeable agent visiting it in the subsequent t iterations. Actualfrequency of knowledgeable agent visits, |A|t , also recorded.


Experimental Results

Accuracy of the Stationary Distribution in Estimating Agent Arrival:

0

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Experimental Results

Accuracy of F (N) in Predicting Agent Visitation:

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Applying the Technique

Information updates provided by the agents used to create new capabilities formulti-agent, peer-to-peer systems. Examples include:

Learning Availability Thresholds, where if a service or host has not been“seen” by a discovery agent the remaining hosts and agents can (with highprobability) assume that it has become unavailable and re-plan accordingly.

Network Triage, where the disappearance of discovery agents or their lack ofcontact with vital network nodes can be used to infer that the network hasbeen damaged, compromised or segmented.


Applying the Technique

Time-Critical Reasoning, where hosts use information provided by discoveryagents to inform time-critical functions about how long they might reasonablyexpect to take to execute if they depend on remote services.

Optimizing # of Agents, where, given an expected value for ν, one cancompute the optimal number of agents needed to achieve a required frequencyof service discovery agent updates.


Limitations

• Elements of the state description, N , can be both variable and unknown insome domains.

• More efficient ways for the agents to traverse the network (i.e. self-avoidingwalks).

• Developing a belief of the global network topology, is a difficult problem onlarge dynamic peer-to-peer networks.


Problem II:k-Center


Problem: k-Center

Given a network and a set of homogeneous services, how can theservices be placed in order to minimize bandwidth usage whilemaximizing availability?

• Peer-to-Peer

• Decentralized

• Network Topology and Global State are not Known


Temporal Dynamism

Observation: the instantaneous optimum is not temporally-stable!

(a) (b) (c)

Three snapshots of a simulated MANET of 20 hosts with varying radio ranges. Snapshots (a), (b), and (c) occur chronologically, over a

10 second simulated span. Boxed vertices represent the instantaneous optimal 3-center cover. Filled vertices represent the 3-center cover

calculated using the proposed heuristic.


Definitions (I’m Sorry!)

Definition 1. (Vertex Eccentricity)The eccentricity of a vertex v is the maximum length of a shortest path fromv to any other vertex.Definition 2. (Graph Center)Given a graph G = 〈V,E〉, the center of G is the set of vertices C ⊆ V withminimum eccentricity.Definition 3. (Covering Radius)Given a graph, G = 〈V,E〉 and a set S ⊆ V , the covering radius of 〈G, S〉 isthe minimum length r such that ∀v ∈ V there exists a path of length less thanor equal to r from v to at least one s ∈ S.Definition 4. (Asymmetric Weighted k-Center)Given G = 〈V,E〉, a directed graph with non-negative edge weights, and positiveintegers k and r, does there exist a set S such that S ⊆ V , |S| = k, and thecovering radius of 〈G, S〉 equals r?


Definitions (I’m Really Sorry!)

Definition 5. (Stationary Distribution)Given the transition probabilities P (u, v) for a random walk on a graph (i.e.the probability that the walk will visit v immediately after u), the stationarydistribution, π(v), satisfies

π(v) = limi→∞

fP i(v),

where f : V → R is any initial distribution such that∑v

f(v) = 1.


Definitions (I’m Really, Really Sorry!)

Definition 6. (Agent Location)Given a set of agents, A, and a set of hosts, H, we define a function, η,mapping an agent to the host on which it is physically located in a given state:

η : A → H.

Inversely, the function η−1 maps a host to the set of agents located on thathost.


Problem StatementGiven:

• an agent, a ∈ A;• the host on which a is located: h = η(a);• the set of neighboring hosts,

N = {h′ : (h, h′) ∈ E} ⊆ H;

• the stationary distribution value of h: π(h);• the stationary distribution values of each h′ ∈ N ,

determine the optimal successor host h′ ∈ N to which to migrate in order tominimize communication cost throughout the network. “Communication cost”entails

• the cost of other agents’ communication with a;• the cost of other agents’ communication with services homogeneous to a;• and the cost of a’s migration.


Approximating the Stationary Distribution

• Current global adjacency matrix not available on every host;• However, it can be approximated by deploying a set of random-walking agents

on the network;• Agents chose successor hosts uniformly, ensuring a probability transition

matrix, R, such that (∀i, j : Ri,j = 1);• A host h records agent visitation frequency to determine its stationary

distribution value π(h);• We empirically showed that

C ={

v ∈ V : π(v) = maxu∈V

π(u)}

. (1)

However, we are not aware of any formal proof of this property6.

6E. Sultanik, W. Regli. Service Discovery on Dynamic Peer-to-Peer Networks Using Mobile Agents. Agentsand Peer-to-Peer Computing. Springer Verlag, 2004 (In Press).


Monotonicity

Important:Stationary distribution values are not guaranteed to increasemonotonically along the shortest path from a vertex to a center!

Implication:Naıve hill climbing search for the centers will encounter localmaxima.


Approach: Exploit Non-MonotonicityLocal Maxima Might be Good!

• deploy a set of random-walking agents on the network;

• each host records random-walking agent visitation frequency; and

• each service uses the visitation frequencies as a hill climbing heuristic,stopping at the first maximum found that is not currently inhabited byanother service.

• In the case that another homogeneous service is already located at the localmaximum, perform a self-avoiding random walk to find a new gradient.

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Results

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% o

f Opt

imal

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3 Services5 Services7 Services9 Services

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3 Services5 Services7 Services9 Services


Limitations

• Contention handling (when number of services is high).

• No formal proof of Equation 1.

• No tight bounds on optimality or convergence.


Current and Future Work

• Implementation on the Secure Wireless Agent Testbed (SWAT)7

– iPAQs– Tablet PCs– 802.11b Ad-Hoc Network

• Lockheed Martin’s EMAA8

7E. Sultanik, et al. Secure mobile agents on ad hoc wireless networks. In Proceedings of the FifteenthInnovative Applications of Artificial Intelligence Conference. American Association for Artificial Intelligence,August 2003.

8R. Lentini, et al. EMAA: an extendible mobile agent architecture. In Proceedings of the AAAI Workshop onSoftware Tools for Developing Agents, July 1998.


Conclusions

• Global state can only be partially observed

– Location/capabilities of services...– agents– hosts

• Proposed collective of service discovery agents; emergent property ofpropagating global network state.

• Principle contributions:

– mathematical formulation of agent traversal of a peer-to-peer network;– basis for multi-agent planning to sense/react to network-level events =⇒

improve plan execution and survivability; and– k-Center heuristic.

enabling information dissemination on dynamic peer-to-peer

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