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

2. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci 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,.....

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

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

5. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci 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 (green  red) ‏ Definition of mechanisms to dinamically discover new nodes entering AOI

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

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

8. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci WEIGHTED VORONOI TESSELLATIONS Weighted Voronoi Tesssellation: exploit metrics different from the standard eucliden one The cell associated with a site s i includes the points closer to s i than to any othet site, according to the new metric Each site is associated with a weight w i Distance of a point x from the site s i Additively Weighted Voronoi: d(s i,x) = ll s i -x ll – w i Multiplicative Weighted Voronoi: d(s i,x) = ll s i -x ll / w i Weighted Voronoi Tessellations: sites with larger weights 'attract' a larger number of points, i.e. are associated with larger Voronoi regions

9. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci 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 A B C D E F A

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

11. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci 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) ‏

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

13. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci MODELLING HIERARCHICAL P2P OVERLAYS AWV 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

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

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

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

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

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

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

20. Hierarchical P2P Overlays for DVE: An Additively Weighted Voronoi Based Approach Michele Albano Luca Genovali Laura Ricci 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)

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