Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca...

Hierarchical P2P Overlays for DVE:An Additively Weighted Voronoi Based Approach

Michele AlbanoLuca GenovaliLaura Ricci

HIERARCHICAL P2P OVERLAYS FOR DVE: AN ADDITIVELY

WEIGHTED VORONOI APPROACH

Michele Albano, Luca Genovali, Laura Ricci

International Conference on Ultra Modern Telecommunications, ICUMT

Saint Petersburg, October 12-14th, 2009

Università degli Studi di Pisa Dipartimento di Informatica



DISTRIBUTED VIRTUAL ENVIRONMENTS

Real-Time Distributed Virtual Environments :

• provide to geographically distributed end-users the illusion of being immersed in a unique shared virtual world

• real time interactions among users and/or among users and computer controlled entities

• Examples:

– distributed multiplayer games, military simulations

Multiplayer Games:

• a set of entities (avatars, monsters, tanks,…) populate a virtual world

• each entity communicates to the other ones its state (position, colour,energy,...), or the updates of the passive objects of the DVE

real time requirements: the action performed by an entity must be visible to other entities within a bounded interval of time

• examples:World of Warcraft,Second Life,.....



DISTRIBUTED VIRTUAL ENVIRONMENTS

Architectural Choices

Client – Server

• Consistency

• Persistency

• Security

• Cost

• Scalability

• Fault-tolerance

Peer to Peer

• Scalability

• Fault-tolerance

• Cost

• Complexity

• Consistency

• Persistency

Architectural Challenges: consistency of the virtual world synchronization state replication real time requirements



IMPROVING DVE SCALABILITY

• Interest Management: DVE communication requirements reduction

• Area of Interest (AOI) of an entity E: portion of the virtual world

including entities that may interact with E

– example: a player interacts with entities (players, monsters)

located in its surroundings, e.g. in the same room.

• The definition of the AOI of E depends upon the semantics of the

application, e.g. the sight capability of E

• E is interested in receiving information from entities in its AOI only

• Existing Approaches:

– Multicast groups

– Publish-subscribe systems



NEIGHBOURS DYNAMIC DISCOVERY

When the blue node moves: All its neighbours exit its AOI, the blue nodes is isolated Definition of mechanisms to maintain overlay connectivity

When the blue node moves • Some nodes enters its AOI (red green), others exit its AOI (greenred)• Definition of mechanisms to dinamically discover new nodes entering AOI



VORONOI TESSELLATIONS

Voronoi Tessellation: A partition of the plane into cells

Consider a set of sites (black points in the figure) a cell for each site s including the set of points closer to s than to any other site all edges of the Voronoi tessellation belongs to the bisectors between the sites

Voronoi neighbours sites whose cell have an overlapping border

Delaunay Triangulation graph connecting Voronoi neighbours



VORONOI-BASED DVE

The position of each peer in the DVE is exploited to define a Voronoi tessellation of the virtual world

P2P overlay = includes Delaunay links which guarantee overlay connectivity

A peer P dinamically computes a Voronoi tessellation including the peers in

its AOI connects to all its Voronoi neighbours through Delaunay links periodically notifies its position (heartbeat). Two alternative

solutions

• P sends the notification only to its Voronoi neighbours. A routing mechanism to reach all the peers in the AOI is required

• P sends the notification to all the peers in its AOI

• 'Pass the word mechanism'. Peers become acquainted of each other through peers located their AOI



WEIGHTED VORONOI TESSELLATIONS

Weighted Voronoi Tesssellation: exploit metrics different from the standard eucliden one

The cell associated with a site si includes the points closer to si than to

any othet site, according to the new metric

Each site is associated with a weight wi

Distance of a point x from the site si

Additively Weighted Voronoi: d(si,x) = ll si-x ll – wi

Multiplicative Weighted Voronoi: d(si,x) = ll si-x ll / wi

Weighted Voronoi Tessellations: sites with larger weights 'attract' a larger number of points, i.e. are associated with larger Voronoi regions



ADDITIVELY WEIGHTED VORONOI

• Weight is represented by a circle. Weightless peers (weight=0) may exist

• Bisectors are hyperbolic

• A simple model: every site begins to grow in a different point in time, proportional to its weight

• In the figure

– Sites B(weightless), rs. D (heavy) are

hidden, they own no Voronoi region, because

they have been absorbed by A, rs. C

– Weightless sites F, rs. E, are visible, i.e.

they own a Voronoi region, because they

are far enough from heavy sites

• weightless sites may be visible, heavy sites (weight 0) may be hidden

• visible peers are associated with a Voronoi region

AB

CD

E

F

A



MULTIPLICATIVE WEIGHTED VORONOI

• Each site grows at a different rate

• Bisectors are usually circular arcs

• Regions can be surrounded

• The regions associated to the sites may

not cover the whole plane



MODELLING HIERARCHICAL P2P OVERLAYS

• P2P overlays often include heterogeneous peers, characterized by different computational resources

• Hierarchical P2P networks exploit the heterogeneity of peers to define a hierarchy of peers

• This solution is often exploited in file-sharing P2P overlays (Gnutella 0.6, Kazaa,..)

• No DVE hierarchical P2P overlay has been proposed till now

• Our proposal: to exploit AWV tessellation to define a hierarchical P2P overlay

– A site for each peer P

– The weight of P proportional to its bandwidth (further computational resources may be considered)



MODELLING HIERARCHICAL P2P DVE

• Load among peers may be balanced by a proper chooice of their weights

• Balancing the load of passive objects management

– each peer is assigned to the peer whose Voronoi region includes the coordinates of the object

– peer with larger weights owns larger Voronoi regions and manage more objects

• Balancing the notification traffic

– Superpeer = Visible Peer which has absorbed some hidden peer

– A superpeer may act as a proxy on the P2P overlay for its hidden peers

• hidden peers exploits P to forward/receive their notifications, for instance heartbeat notifications



MODELLING HIERARCHICAL P2P

OVERLAYSAWV based DVE: an example

• Red points = visible peers, Black points = hidden peers

• Circles radius is proportional to the peer weight

• A, B = Superpeers

– A rs. B propogate the notifications of D rs. E

to their visible Voronoi neighbours

• When a weightless peer is far away from

an heavy peer

– It is not absorbed by a superpeer and owns a voronoi region

– It manages objects, belongs to the overlay network and send/receive events notifications

– further load balance mechanisms are required in this case



ROUTING OVER AWV OVERLAYS

Several strategies for routing heartbeats in Voronoi based overlays have been recently proposed

These approaches must be revised to take into account hidden peers

Each hidden peer H sends its notification to its superpeer SP

SP dispatches this notifications to its further hidden peers in the AOI of H its visible neighbours which

belongs to the AOI of H or have an hidden peer whose AOI

intersects the AOI of H



ROUTING OVER AWV OVERLAYS

• A propagates the heartbeat of D to further hidden peer belonging to the AOI of D

• A propagates the heartbeat of D to B because E, hidden by B, belongs to the AOI of D



AWT EVALUATION

• Evaluation through a set of preliminary simulations

• Peersim: A scalable event driven P2P simulator

• CGAL (Computational Geometry Algorithms Library) An Open Source Project providing easy access to efficient and reliable geometric algorithms in the form of a C++ library

– A package implementing Apollonius graphs

• Additive Weighted Voronoi Diagram = Voronoi diagram of a set of disks under the Euclidean metric

• No support for Multiplicative Weighted Voronoi

• SWIG (Simplified Wrapper and Interface Generator) exploited to link CGAL and Peersim



TUNING THE WEIGHT

Different simulation runs, each one characterized by a different weight

800 weightless peers, 100 heavy peers

Left hand side: mean number of visible peers against cycle number

Right hand side : mean number of hidden peers against cycle number



DECREASING THE WEIGHT

800 weightless peers, 100 heavy peers all with the same weight

p is decreased during the simulation when p 80

• only all the weightless peers are hidden, i.e. each

weightless peer has a superpeer

• Each Superpeer manages 8 hidden peers, on the average



OBJECT MANAGEMENT

800 weightless peers, 100 heavy peers all with the same weight 4000 passive objects p is decreased during the simulation when p 80 only the heavy peers owns the objects, because the 800 weightless peers are hidden by the 100 heavy peers



NUMBER OF LINKS OF VISIBLE PEERS

800 weightless peers, 100 heavy ones the weight p is modified during the simulation, from p=100 to p=0 the figure shows the mean number of links

from heavy peers to visible peers (upper line) from weightless peers to visible peers(middle line)



CONCLUSIONS

• An additive weighted Voronoi approach to model hierarchical P2P networks

• Object Management is balanced among the peers according to their computational power

• Peers with low bandwidth can rely on a close heavy peer as a proxy for notification forwarding

• Future works:

– definition of a proper routing algorithm for AWV tessellations

– investigation of

• multiplicative weighted Voronoi Diagrams

• more sophisticated mobility models

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