Using Geometrical Routing for Overlay Networking in MMOGs

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1 Using Geometrical Routing for Overlay Networking in MMOGs Behnoosh Hariri 1,2, Shervin Shirmohammadi 1, Mohammad Reza Pakravan 2 and Mohammad Hossein Alavi 2 1 Distributed and Collaborative Virtual Environment Research (DISCOVER) Lab School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada 2 Advanced Communications Research Institute (ACRI) Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran At a first glance, transmitting update information to a geographic region in the virtual space seems to be an attractive primitive in Massively Multiplayer Online Gaming (MMOG) applications where players are constantly moving and need to send updates to their neighbours who are in the same region of the virtual space. The system would become more scalable if entities did not need to keep track of each other or send messages directly to one another. Rather, an entity could just send a message to a specific region in the virtual space (its area of effect), as opposed to sending packets to specific IP addresses, significantly reducing tracking and routing overhead. Fundamentally speaking, update message exchange is mostly based on users visibility range, which is mainly affected by proximity; i.e., avatars are interested in nodes within a specific distance around them. Therefore MMOG applications require a routing scheme that can deliver messages to specified locations in the virtual space. Such location based routing motivates the use of geographical routing, which has been introduced and successfully used in the context of wireless networks; however, in its current form it is not well suited for MMOGs which run on wired networks. In this article, we propose a scalable MMOG networking architecture based on hierarchical multi-grid geographical routing that is well suited for MMOG networks. We present our concept and design of hierarchical geometrical routing based on locality sensitive hashing, demonstrate its performance, and discuss both the strengths and shortcomings of our approach. 1. INTRODUCTION Collaborative Virtual Environments (CVE) are network applications that incorporate interfaces such as computer graphics, sound, and haptics to generate a synthetic world and simulate the experience of real-time interaction among multiple users in the virtual world. Massively Multiplayer Online Game (MMOG) are CVEs that deal with a massive number of online players, sometimes in the hundreds of thousands. As players move freely in these environments and interact with each other, update messages need to be exchanged in real time in order for the players to remain in sync. Since there are a large number of players, a large volume of update messages could potentially be exchanged over the Internet. Most of the existing MMOGs use a Client/Server (C/S) approach or a hybrid architecture combining C/S with Peer-to-Peer (P2P) communications. However, the existence of a server in both techniques suggests a bottleneck and also a single point of failure, both impacting scalability. A fully P2P architecture, where the peers themselves contribute in the communications task without a central server, would alleviate this problem. However, such a P2P architecture would also pose the challenge of decentralizing several tasks that are normally handled by the server. Entity tracking and location awareness is among the most important of these challenges. In MMOGs, an entity (player, bot, object, etc.) needs to send updates to a specific area in the environment known as that entity s area of effect. In a C/S approach, the entity sends its update to the server, which in turn sends the update to all other entities that are in the same zone, or, if it wants to be more efficient, to all entities in the first entity s area of effect. The server can do this because it keeps track of the location of all entities in the zone. In a P2P scenario; however, entities have no centralized database to keep the mapping between the nodes locations and IP addresses. Hence, if IP routing is used similar to a C/S approach, an entity would require to first make a location query to find out about the IP addresses of the nodes that are currently in its area of effect. Considering the continuous movements of entities in the MMOG, the results of such a query will soon become invalid and so the query must be updated with a high frequency. 1

2 Such a location query service will therefore consume a large amount of bandwidth and processing resource from the peers. This suggests that perhaps IP routing is not an appropriate solution for a fully P2P scenario. In this paper, we propose the use of geometrical routing, at the application layer, as an alternative networking architecture for MMOGS. Geometrical routing, as introduced in the context of wireless ad-hoc networks, is a general term for a group of in-line routing algorithms where a packet is sent to a specific location in space, and not to a specific IP address. Each intermediate hops will route incoming packets to a point that is closer to the packet destination than itself. This frees the nodes from knowing about entities in their area of effect before sending updates to them. Another reason that motivates the choice of geometrical routing is to minimize the latency stretch introduced in multi-hop routing. Because update messages are exchanged based on avatars interest that mostly depend on their visibility and virtual distance in the MMOG, the message transfer hop-count can be reduced if the overlay routing preserves locality upon forwarding messages to their destinations. Since geometrical routing has a locality preserving characteristic, as a packet is forwarded to nodes that are closer to the destination in each routing hop, packets destined for close neighborhoods won t be relayed from faraway nodes, satisfying update exchange requirements in MMOGs. Through the rest of this article we will discuss several aspects of geometrical routing and propose solutions that best fit MMOG applications. We will introduce the idea of hierarchical geometrical routing as an effective way to reduce hop count in wired networks where, unlike wireless networks, transmission range is not limited. Moreover, we propose the use of multiple grids to alleviate the problem of long routing distances along the grid edges. The details of the design are discussed in section 3 while section 4 addresses dynamics of the environment and how to support it. Section 5 shows the results of our experimental evaluations, and section 6 draws conclusions on the results. Before we continue to the next section, two conventions used in the paper should be noted. The first one is the use of the term multicast, which, in this paper, always refers to applicationlayer multicast and not IP multicast, unless stated otherwise. The second one is that, when we talk about coordinates, position, motion, and mobility, we are referring to these terms in the virtual space (inside the game), and not in the physical space, unless stated otherwise. With this in mind, let us begin by discussing background and the related work. 2. Background and Related Work 2.1 Overlay Networks Layer 3 IP routing is the simplest basic form of routing available over the Internet that is used by most popular Internet applications such as web browsing, , file transfer, etc. However, there are many cases when an application prefers to implement its own customized routing using an overlay network that it establishes over the Internet. While in network layer routing the specific path is usually determined by routers, in application layer routing each end node has to decide where to forward a message so that it goes through the best path according to the application s specific requirements. There are a number of reasons behind the use of overlay routing. Here we discuss three main reasons. First, overlay networks have been proposed as a way to improve Internet routing to achieve higher-quality data transfer [21]. The key design goal in overlay design is to develop techniques to allow end-hosts and applications to cooperatively gain improved reliability and performance from the Internet. At a glance, overlay nodes examine the condition of the connections and traffic demand among themselves and, based upon the 2

3 situation, decide on how they should let the packets flow. Another reason behind the use of overlay routing is to avoid IP address searching queries. Overlay networks can be constructed in order to permit routing messages to destinations not specified by an IP address. As mentioned in the previous section, MMOG applications could benefit from this approach by delivering update message to specified locations in the online game. Working directly with IP address would be inefficient in this case as it requires either a central indexing mechanism or the use of an IP address query mechanism, which is not practical due to large amount of overhead imposed by the search packets flooded all over the network. Note that in a static environment, nodes can cache the addresses in order to avoid repeated queries, although this also results in large routing tables for large scale networks. However, this will not work in MMOGs because nodes frequently change their virtual location and are not static. Finally, the lack of a practicality of IP multicasting is another reason to use overlays. IP Multicast has not been widely used over the internet due to several practical obstacles [5]. This has motivated applications to build their own multicast mechanism, at the application lauer, and use it in the place of network layer multicast. Again, MMOGs can benefit from this for their large communication groups. In today s overlays, a Distributed Hash Table (DHT) is the most popular structured scheme for distributed P2P communication, especially for file sharing systems. A DHT can be used to route messages to a node having a specific logical address and without knowing the IP address in advance. However, current DHTs use a random identifier space and therefore do not respect node s virtual locality when routing data. Although they work well for file sharing applications where the concept of virtual locality does not exist, they lead to lower performance for MMOG applications where message exchange among peers is not random. Some DHT networks such as Pastry do specify a Proximity Neighbor Selection (PNS) routing table construction method with respect to the physical underlying network in order to minimize latency. However, this proximity is calculated according to the physical rather than the virtual distance. Moreover, locality is achieved in a static manner as nodes join the network - it is not useful in MMOGs where nodes frequently change their virtual position. A number of previous works have discussed the idea of DHT based ID assignment and routing for MMOG application [13][2][6][9][13][17][22]. Some of them have proposed ways to modify the uniform ID assignment in DHT and change it to a more localized structure; however, the resulting schemes still do not consider preserving locality over the ID space. Moreover, most of the current DHT based routing substrates are known to have a large latency stretch even in the presence of proximity routing schemes a fact that will adversely affect MMOGs sensitive to latency. Furthermore, such schemes must also deal with the change in the IDs whenever nodes move, join, or leave the game. This potentially high level of mobility and churn would make the approach inefficient. On the other hand, geometrical routing does not suffer from any of the above shortcomings because knowing the positions of target nodes is not required and there is no need for location services. Let us have a closer look at some details of geometrical routing. 2.2 Geometrical Routing The idea of using position information for routing was first proposed in the 1980s in packet radio networks and interconnection networks. Geographical routing [10], also called geometric or geometrical routing, geo-routing, or position-based routing, is a routing principle that relies on the geographic position information where source nodes send messages to the geographic location of the destinations instead of using network addresses. Geometrical routing can be used to forward messages towards their destinations without having the 3

4 knowledge of the network topology or a prior route discovery. It is suitable for scenarios where, most of the time, it is difficult to determine the overlay topology due fast and/or frequent changes in nodes, and in scanarios where a large volume of global topology discovery messages, which would impose a considerable overhead on the system and seriously affects the system scalability, must be kept. Geometrical routing has therefore been designed to be highly scalable with low overhead, based on the assumption that each forwarding node has the following information: (1) The coordinates (x, y, z) of its position (2) The location of its immediate neighbors. This usually implies the exchange of a small number of packets between neighboring nodes (3) The location of the destination Based on the above information, the forwarding node can determine which one of its neighbors can bring the packet closer to the destination than itself; this set is called the forwarding set (it can be more than one neighbour) for this destination. The forwarding node would then pick the best candidate from the forwarding set as the next hop for the packet. As nodes only keep their physical first hop neighbors in their routing tables, O(1) messages need to be sent for route discovery and O(1) entries need to be stored in each routing table. Making a proper forwarding decision has been the subject of several works in the geometrical routing literature [7]. Several geometrical routing schemes have been proposed in the context of wireless networks. Greedy forwarding (GF) scheme proceeds by picking a node from the forwarding set that is typically the closest one to the destination. The compass routing [14] algorithm is also a memory-less algorithm that forwards packets from a source S to a destination T through neighbor V that forms the smallest angle with the destination. Randomized Compass routing [3] is also a variation of compass routing in which the next hop is chosen randomly from the neighbors with the smallest angle above and below the line ST that connects the source to the destination. In the Most Forwarding within Radius (MFR)[20] approach, nodes forward the packet to the hop that maximizes progress along the x-axis. GEographical DIstance Routing (GEDIR) [20] resembles a greedy algorithm, with the difference that packets are sent to the neighbor that is closest to the destination node, despite the distance of the current forwarding node from the destination. It should be noted that none of the above deterministic algorithms can ensure routing convergence. They can fail if a message reaches a local minimum with respect to destination where no closer hop to the destination is found. This might happen in a void point where the forwarding set of an intermediate hop is empty with respect to a specified packet s destination. The forwarding node would therefore find no neighbors closer than itself to the destination. Voids can be avoided by algorithms such as Face-1 or Face-2 [4]; however, neither may be used as a standalone routing method due to their unsatisfactory performance. Therefore, methods such as Greedy Perimeter Stateless Routing (GPSR) [11] Geographic-Forwarding-Geocast (GFG) [19], GOAFR+ [15], and Geographic-Forwarding-Perimeter-Geocast (GFPG) [19] advocate a combination of greedy and face routing to improve the routing delivery rate while keeping the routing performance high. Voids in wireless networks happen as a result of barriers or sparse regions where the neighborhood radius is not big enough. However this limitation does not exist in wired networks and voids may only happen in sparse regions around the receiver. Therefore, the wise selection of neighbors as discussed later in the article can alleviate the void problem in wired geometrical routing and there is no need for the previously mentioned algorithms that limit the routing performance and make it more complex. In addition to this difference, other differences between wireless and wired MMOGs must be taken into account, which are discussed in section3. 4

5 2.3 Three Dimensional Routing Although related research so far has addressed mostly routing algorithms in two dimensional spaces (2D), some applications involve nodes distributed in the 3D space, as shown in figure 3. Therefore, while many aspects of geographic routing have already been solved for 2D networks, little is known about 3D networks. AB3D [1] is among the few works on 3D geometrical routing, although it is still based on mapping 3D into 2D and therefore doesn t introduce a thorough 3D solution. In this article we present a new 3D geometrical routing technique for wired networks. The use of geometrical routing for wired networks has been briefly discussed in a some works [16]. However, our proposed approach differs in two important aspects: we primarily introduce the concept of hierarchical geometrical routing where the flat greedy routing scheme is no longer used; and we address the dynamic issues related to the movement of users and propose appropriate solutions for churn and mobility. Our approach towards building a geometrical routing architecture will make use of Locality Sensitive Hashing (LSH) [8]. In our proposed solution, the hashing space is divided into a number of sub-spaces called buckets. The locality sensitive hash function is a mapping from the high-dimensional point to the bit-string representing the bucket to which the point belongs. The hashing is performed in a way that closer nodes are most probably hashed to the same bucket. Therefore, LSH is considered a locality preserving mapping. Geometrical routing of packets can then be performed by using LSH to find the answer to a query in a large dataset. 2.4 Hybrid Approaches While the above approaches are fully distributed, other research have suggested hybrid approaches that combine P2P and C/S. For example, the work in [12] focuses on using application-layer multicast with a centralized approach to group management. Therefore there is a central entity that stores information about all the users in a distributed application. The central entity employs a process by which it identifies a fully meshed global graph that contains properties of the nodes and links in the overlay network. The central entity creates and manages one distribution tree for each group. A distribution tree is built such that the data flows directly between the peers in a group without going through the central point. While such hybrid approaches have the advantage of easier implantation and deployment compared to a fully distributed approach, they still suffer from the server bottleneck and, more importantly, a single pint of failure. As the number of players increases and the gaming environment becomes highly dynamic, a large volume of topology information traffic needs to be collected by the central server, turning it into a potential bottleneck. In the following section we present the design of our proposed architecture. We discuss how LSH is applied separately at multiple stages in the hierarchical routing architecture, and we propose the idea of multiple bucket set hashing to avoid the problem of proximity conservation violation along the bucket edges. 3. The Proposed Architecture Inspired by the concept of geometrical routing as introduced in wireless networks, we aim to design a geometrical routing scheme for MMOGs that differs in the following aspects: 1- Wireless nodes are only capable of communicating directly with only those nodes in their vicinity through radio communication. Fundamentally, such wireless geometric routing is locality-preserving because 5

6 the network does not permit long-distance hops due to the limited range of neighborhood. However, this would also apply to non-local messages where it results in increased hop-count. 2- The limited transmission range affects the neighborhood definition where neighbors are always physically limited to be within a fixed radius round a node. This neighborhood definition doesn t allow wireless networks to support hierarchical routing where messages can have long jumps in the first steps of the routing to reach the destination faster and in a fewer number of hops. Wired networks need not limit the nodes to have neighbors within this limited distance range. Therefore, MMOG networks have the possibility of using hierarchical routing as the transmission range of the nodes is not physically limited. 3- Localization of MMOG update messages, typically bounded to an entity s virtual area of effect, can increase the routing efficiency. Such virtual localization does not necessarily exist in wireless networks. 4- Wired networks cannot take advantage of a free broadcast channel. The use of this broadcast channels facilitates the neighbor discovery process in wireless networks. Neighbor discovery and neighbor selection process will be more complicated in wired networks where information cannot be easily multicasted, at the physical layer, to the neighbors. To achieve geometrical routing, we perform hierarchical routing over the geometrical space over a grid rather than an unstructured pattern. This grid can facilitate the choice of hierarchical neighbors by specifying the region where each neighbor should be located. Moreover, neighbor selection and routing on a grid provides the nodes with the opportunity to make sure that routing will converge. Therefore, complex convergence issues, prevalent in wireless geometrical routing, need not be addressed for MMOGs. However, it should be noted that the establishment and maintenance of the grid imposes an overhead in the system. Hierarchical geometrical routing over a grid requires the hierarchical partitioning of the space where close points are mapped to the same region. A representative neighbor is then selected from each level of the hierarchy coming towards the point where that node is selected. This is referred to as hierarchical neighborhood. 3.1 Locality Sensitive Hashing As mentioned before, we use Locality Sensitive Hashing (LSH) for finding nearest neighbours in our routing algorithm. LSH is a method of performing probabilistic dimension reduction of high-dimensional data. The basic idea is to hash the input items so that similar items are mapped to the same buckets (partitions) with high probability. One of the main applications of LSH is its fast and efficient nearest neighbor search algorithm. With the use of LSH for game map partitioning, we can later redefine the routing of update messages to specified areas of interest as routing queries to nearest neighborhood of those locations. LSH functions therefore become a group of functions, H, containing specific hash functions h, that map the points in an d-dimensional space to points in one dimension, satisfying the following requirements: For any points p and q that are close to each other, there is a high probability P1 that they fall into the same bucket P H [h(p) = h(q)] P1 for p q R1 (1) ; where R1>0 is a threshold that should be specified by the hash function. For any points p and q that are far apart, there is a low probability P2 < P1 that they fall into the same bucket P H [h(p) = h(q)] P2 for p q cr1 (2) 6

7 ; where c > 1 is a parameter called approximation factor for the LSH function. It should be noted that (R, cr, P1, P2) are parameters that determine the sensitivity of the hash function. LSH-based nearest neighbor search algorithms have two main parameters: the width parameter k, and the number of hash tables L. In the first step, we define a new family of hash functions G, where each function g G is obtained by concatenating k randomly selected functions h 1,...,h k from the family of hash functions F, therefore each function g i maps every single point p according to the following relation : g i (p) = [h 1 (p),...,h k (p)] i=1 L (3) Given a query point q, the algorithm iterates over L number of hash functions gs. For each g considered, it retrieves the data points that are hashed into the same bucket as q. The process is stopped as soon as a point within a specified distance from q is found. In our approach, we will have a fixed choice of h 1,...,h k known by all the nodes that will be explained later. As in the scenario of dividing the space into a number of regions, each region is a hash bucket. A point is likely to be located in the same bucket as its nearest neighbor. The number of buckets is smaller than the universe of possible avatars in the related region and so this ratio becomes much smaller as we go up in the hashing hierarchy. Given a query point, we determine which bucket the point is located in and pass the query to the closest neighbor to that bucket. We will also add the following two techniques to LSH in order to improve the routing performance: Hierarchical hashing Regular nearest neighbor search has two basic steps. The first step is searching for the right bucket and the second step is the linear search inside the found bucket for the desired point. Considering the fact that linear search among a large dataset is not efficient, the number of points inside a bucket is preferred to be small. However, this will increase the number of buckets for a fixed number of data points. Our solution to this problem is the use of hierarchical hashing where data points are hashed into different sets of buckets with different resolutions. The search would then be performed among higher level bucket sets while each higher level bucket consists of a number of lower level buckets. The hierarchical locality sensitive hashing would therefore allow us to considerably expedite the search process. Multi-table hashing Although hierarchical routing on a grid offers several advantages, it sometimes makes the packets go through unnecessary long routes when nodes are located along grid edges. This occurs when nodes are hashed to different buckets even though they are close. Therefore, neighborhood proximity is not preserved in these locations. Our solution to avoid this is to use a multi-grid approach where multiple hashing tables are used in order to preserve the overall neighborhood proximity. The packets will then be forwarded with respect to one of the grids at each routing hop on the condition that they always move down in the grid hierarchy. Therefore, the packets always get closer to their destinations with respect to the grid hierarchy in every single step while they might switch between the grids. This will guarantee the routing convergence. The family of hash functions that has been used for hashing are range check functions that return the index of the interval in which the input is located. We also categorize the range functions that apply to x, y and z coordinates. x y z F={ h i (p),h i (p),h i (p) i 1.. N } (4) 7

8 x i x h (p) = (i+ 1) p (5) y i y h (p) = (i+ 1) p (6) z i z h (p) = (i+ 1) p (7) x y z g(p) = [ h n (p),h n (p), h n (p) ] (8) In the above relations, the points are hashed to buckets according to their spatial locations. The hash functions divide the cubical 3D game world into 8 equally sized cubes in the first iteration. Eight cubes are used since we have chosen to divide each axis (x, y, and z) by two. The hashing procedure is performed according to the same relations in the lower hierarchy levels and each smaller cube will also be divided into 8 smaller cubes. The previously mentioned hashing functions perform a uniform hashing on the whole game space. However, if the density of avatars and objects is not the same in the 3D map of the game, we may need to have hashing that is map-dependent. In this case, LSH can be adaptively performed to avoid unnecessary number of buckets where most of them are empty. As the non-uniform choice of hashing depends on the game specific density of avatars in game space, we will proceed with the uniform hashing case. However, it should be noted that the whole concept is also applicable to the non-uniform hash functions. Figure 1 shows the hierarchical LSH-based divisions of the 3D space in two levels. The first level of the tree is related to the first step where the game space (assumed as a single cube) is divided into 8 smaller cubes that have been labeled from 0 to 7. The second level of the tree shows the second step where each of these cubes is also divided into 8 smaller cubes. The label of the smaller cubes is derived by concatenating the label of their parent cube with numbers 0 to 7. Although not shown in the figure, the hashing hierarchy can still be continued into lower levels with the same hashing and labeling rules. Figure 1 hierarchical locality sensitive hashing in two levels 3.2 Routing Algorithm Having divided the virtual environment into a hierarchical set of buckets, we now use an efficient strategy to route the packets to their destination. Routing is the process of sending a message from one of the tree leaves to the other. Each intermediate hop tries to forward the message to a node that is closer to the destination branch of the message. Routing is basically performed in two steps, the first step is guiding the packet to the right bucket, and the second step is routing the packet to its destination within that bucket. Therefore, whenever a node receives a packet, it will initially try to route it to the right bucket. The packet would then be received by a single entity or the whole bucket based on unicast or multicast needs. To route the packet through the shortest path, it should follow a systematic path over the branches where it tries to get one 8

9 step closer to the destination with each hop. To support this, each node keeps enough neighbors in the tree where it can forward the packet through the right branch. This is possible if for N levels of hierarchy the node keeps neighbors that are in a common branch with itself in levels one through N in the tree as well as the one neighbor with no common branch. This way it can always send the forwarding packet one branch closer to the destination by considering how many branches does the forwarding packet has in common with it. It will then choose a next hop that has one more branch in common with the forwarding packet. For example, in Figure 1, if the node in bucket 73 has a packet that belongs to any of the buckets 70-77, it can directly forward the packet to that bucket. The packets that lie with buckets are forwarded to bucket 15 and the packets that belong to buckets 0-7 are forwarded to bucket 2. Figure 1 shows the eligible neighbor set for a node located in bucket number 73 that has been marked with an arrow in the figure. The neighbors are colored in grey. Node 73 keeps a representative from buckets that are in the same branch with it. These are considered as its level1 neighbors. It also selects six other neighbors from the other braches 0-6. Figure 1 only demonstrates the neighbors selected from branches 0 and 1 where nodes from bucket 02 and bucket 15 have been selected. These are considered as level 2 neighbors for bucket 73. It should be noted that the network tree might have more levels than 2. However, the neighbor selection rule would still remain the same. For example, for three levels, each node needs to know 7 neighbors from its own branch, 7 neighbors from the other level 2 branches, and 7 neighbors that are located in other level 1 branches. The routing table size would therefore be of O(K) where K is the number of hierarchy levels. More precisely, the routing table size would be 7*K +L as 7 neighbors are needed in each hierarchy level and L represents the number of leaf sets in the routing table. The leaf set for a node s routing table consists of a number of nodes that are closest entities to that node. The leaf set is used for linear search inside the bucket. The N number of hierarchy levels is usually selected in the order of O (log 8 ) so that few nodes exist in each bucket. N Therefore for N number of users, the size of the routing table will be in the order of O (log 8 ). Upon reception of a packet, the forwarding node checks to see how many bits the destination bucket has in common with itself. If they are located in the same bucket, the packet will be forwarded to a member in the leaf set that is closest to it. Otherwise the packet will be forwarded to member A in row k+1 if the number of common bits are k. Here, member A belongs to a bucket number that has k+1 bits in common with the destination bucket number; therefore, the packet gets one step closer to its destination by being forwarded to member A in the routing table. As mentioned before, the above algorithm fails to preserve proximity along bucket edges. For example, in Figure 1, the nodes in buckets labeled 07 and 10 might be pretty close while they are connected by two hops. Multiple hash tables may be used to solve the neighborhood problem across the bucket edges. In this approach, each node is mapped to two independent buckets. Therefore, if proximity is violated in the first mapping, there is a high chance that it will be preserved in the second mapping that is independent from the first one. We have selected two sets of hierarchical hash buckets: one for n=1 and the other for n=2. The number of sub divisions across search axis would be 2 and 3 for n=1 and n=2 respectively. As these two numbers have no common factor, it can be concluded that the grid boundaries for each set of buckets won t collide. Therefore, we can take advantage of both grids in the neighborhood proximity preservation. 9

10 When the routing is performed with respect to two routing tables, the previously explained forwarding decision will be repeated for the second routing table and member B will be chosen in level K. The packet will then be forwarded to either A or B whichever has the lower level in the hierarchy. If the packet is meant to be forwarded to the leaf set, then the closest member of the leaf sets from both routing tables will be chosen. The Proposed routing procedure is shown in pseudo code form in Table 1. The procedure is executed whenever a packet with destination location P and destination buckets D 1 and D 2 with respect to the two grids arrives at a node at location M that is in buckets A 1 and A 2 with respect to the first and second grids. Notations: Table 1 Routing algorithm pseudo code R i (j) : the entry in the i th routing table R at column j. L i (j): the i-th closest nodes in the leaf set L of the i th routing table shl(a;b): the length of the prefix shared among A and B, in digits. Algorithm (1) if ( (D 1 =A 1 ) or (D 2 =A 2 ) { (2) // route the packet to the closest leaves (3) Forward to L i (j) s.th. P- L i (j) is minimum, D i =A i (4) } (5) else { (6) //Route the packet with respect to the grid that brings it closer to its destination (7) Let x=shl(d 1,A 1 ); (8) Let y=shl(d 2,A 2 ); (9) If (R 1 (x) null or R 2 (y) null ) { (10) If (x=y) { (11) forward to Z s.th P-Z minimum, Z { R 1 (x), R 2 (y)} (12) }else If ( (x > y) and R 1 (x) null ) { (13) forward to R 1 (x) (14) }else{ (15) Forward to R 2 (y) (16) } (17) } (18) else { (19) //rare case where all routing table entries are null (20) Forward to Z s.th. (21) max(shl(d 1,Z 1 ), shl(d 2,Z 2 )) (max(x,y)), Z-P < M-P, Z R 1 U R 2 (22) // where Z belongs to buckets Z 1 and Z 2 with respect to the first and second grid (23) } (24) } Multicast routing is an essential need in update distribution as most of the update messages are addressed to a continuous area of interest. The previously proposed routing scheme can easily be adjusted to perform multicast to a bucket. Whenever nodes receive a packet that has been multicasted to a bucket other than their own bucket, they will forward it to the closest possible bucket until the packet reaches the bucket for which it has been destined. When a node inside that bucket receives the packet it forwards it to its leaf set inside the bucket where it will also be forwarded to the leafs own leaf sets. Nodes do not forward the packets that they have received before, to prevent the multicast packets to be repeatedly forwarded by the same node. The other important issue to be addressed in the routing is the maintenance of the routing table. This requires the nodes to frequently exchange update messages to know about their neighbors locations. Whenever a node moves, its location might change with respect to the bucket set. It should therefore check to see whether its previous neighbor set is still valid for the new location. Moreover, the routing table of all those nodes that had this node as their neighbors might also need to be updated. In MMOGs where nodes move frequently, real- 10

11 time update of the routing tables seems to be a challenge. In the following section we propose a solution to the localized update of the routing tables without the need for global information exchange. 4. Selective Updating: Handling Mobility and Churn To support players movements, joining, and leaving operations, we must update the routing tables upon frequent changes in the players locations. Routing table updates can be performed in either global or selective ways. While global updating of the routing tables is much simpler, it imposes a large overhead on the network given the massive number of players. We have therefore chosen selective updating that is much more efficient when the users move fast and require frequent updates in the routing tables. In the selective updating approach, a node tries to send routing table updates to those whose routing tables should change upon its movement. It also gets help from its neighbors to choose new entries for its routing table while informing the old neighbors about the changes. As mentioned before, different levels of neighborhood are defined for a node. It should be noted that neighbors in different levels need to be treated differently during the update procedure. Level1 neighbors are defined as the nodes whose positions are within the same bucket as that node. Level2 neighbors are nodes whose buckets immediately surround that node s bucket. Similar definitions are used for higher level neighbors. Based on these definitions, we will explain our approach to update the routing tables in three specific situations when nodes join the network, move in the network, or leave the network JOIN Procedure A joining node is assumed to know one of the nodes in the network that acts as a bridge in helping it to connect to the right point in the network. The joining node first contacts its known points and sends a query with its joining coordinates to any existing node. This query will eventually reach a leaf neighbor whose position is closest to the joining node. This node is most probably in the same bucket as the joining node, or a bucket close to it. Therefore, their routing tables can have lots of entries in common. The closest node to the joining node will then respond to the join query by sending a list of its routing table entries to the joining node. The joining node then connects to each neighbor on the routing table list and organizes its own routing table. The neighbors also update their routing tables to account for the joining node MOVE Procedure When a node moves, position updates are sent to all its currently connected neighbors as well as those who have this node in their routing tables. The nodes that have the moving node as their neighbor will then check to see if they need to choose a new neighbor or their current routing tables still works fine. The neighbors of the moving node will perform different procedures based on their level of neighborhood. If the update recipient is a level 1 neighbor, it checks to see whether the moving node is still in the same bucket as before. If so, it will then look to see if any of its leaf set members are good candidates to become a leaf set member of the moving node, and informs the moving node about any such found candidates. If the recipient is a level2 neighbor, it will check if the moving node has changed its level1 bucket during the movement. Nothing needs to be done if level1 bucket has not been changed. In the case of change in level1 bucket, two different scenarios might happen. In the first scenario, the moving node moves into the same bucket as the level2 neighbor. The neighbor will then inform it of a set of new possible level1 neighbors. The moving node will also get disconnected from those neighbors that are no longer eligible and connects to new neighbors that it finds based 11

12 on the information it acquires itself or from its neighbors. The second scenario that might happen is when the moving node enters another level1 bucket other than the one where the update recipient resides. Nothing needs to be done by level2 neighbor in this case. The moving node will also disconnect any boundary neighbor that has left its bucket. A similar procedure applies to level3 neighbors when nodes move across the edges of level2 buckets. The nodes rarely change buckets with respect to higher level buckets. However, we can still apply the same policy to higher level neighbors if required. Figure 2 demonstrates the neighborhood update procedure in a hashing space of two dimensions in three levels of hierarchy. Let us present the procedure by discussing the scenario for a random member specified by a star sign in Figure 2-a. Figure 2-b shows the location of the star nodes with respect to its neighbors where level one neighbors are represented by black dots, level 2 and 3 neighbors are black diamonds and black triangles respectively, and black squares represent level3 neighbors. Figure 2-c demonstrates the scenario when the star node moves inside its own bucket. It will inform its level1 neighbors, who will help it to change some of its level1 neighbors and choose better neighbors. White circles represent the former neighbors that have been replaced by new ones. Figure 2-d demonstrates the scenario when the star node changes its level 1 bucket. Here, the star node needs to update its level1 neighbors based on the information it receives from its former level2 neighbor that is now located in the same bucket with it. A similar scenario happens in Figure 2-e and Figure 2-f where the star node changes its level2 and level3 buckets. In all these cases, former neighbors are shown in white circles while current neighbors are represented in black circles. a) The 2D game space and avatars b) Hierarchical neighborhood for star node c) Star node moves within its own bucket d) Star node moves out of its level1 bucket 12

13 e) Star node moves out of its level2 bucket f) Star node moves out of its level3 bucket Figure 2 The change of neighborhood in different movement scenarios 4.3. LEAVE Procedure The leaving node simply disconnects. As topology discovery messages are regularly exchanged among the nodes, the neighbors will discover the absence a node as soon as it does not respond to topology discovery messages. The neighbors then try to find other replacements. 5. Experimental Evaluation In this section, we present experimental results obtained with the simulation of the proposed architecture. The simulation software has been implemented in C++, and has been done for various network sizes of up to 10,000 nodes. Each MMOG node is assigned a 3D location in a cube that represents the whole game space. Players are distributed round 50 center points that are uniformly distributed over the xy plane. The number 50 has been chosen so that clusters do not have that much of overlap while each cluster has a fairy large number of users. Users are expected to be located close to the z=0 plane (mostly on the virtual ground) and clustered around some central points of interest, while a few users are flying (airplanes, avatars, etc ) above. Therefore we have a clustered but overall uniform population over the XY plane while the population density decreases as z index increases due to the fact that most objects are located near the ground rather than up in the sky. Figure 3 shows the typical distribution of players that have been used in the simulations Z axis Y axis Y axis (a) 50 X axis X axis (b) 13

14 Z axis Z axis X axis (c) Y axis ( d) Figure 3 Typical player Distribution over the game map: (a) 3D, (b) xy plane, (c) xz plane, (d) yz planes The nodes are assumed to send their updates to a spherical area around themselves. The Radius of this sphere is referred to as Area of Interest (AoI) radius. We consider the dimension of the game map to be in the range [0..100] along the three axis. The AoI radius has been assumed to be randomly selected from the range [1..3] for each player. The choice of LSH hierarchy order depends on the number of the typical density of players on the game map. The higher orders results in an increase in number of hashing buckets and subsequently decreases the number of nodes that will be located in each bucket. This will in turn help expedite the second phase of routing that guides the packet inside its bucket. However, the increase in the number of hashing buckets increases the size of routing tables and neighborhood discovery and update messages. A rough estimate for the N size of the routing table is O (log 8 ) in order for the buckets to host only a few nodes. In the simulations we have chosen the hierarchy order to be 5 as a compromise among the previously mentioned factors; i.e., not to have too many buckets, while still having a reasonable number of hierarchies to cover the non-uniform user distribution in dense areas. In the following sections, we will use a number of simulation results in order to demonstrate various features of the routing algorithm Routing performance Figure 4 demonstrates the results of the simulation for hop counts. Data is recorded in a 1 sec interval for a randomly selected node that regularly updates the nodes inside its AoI with the rate of 100 kpbs. In the figure, we can see an average hop-count of 2.6 hops with the highest hop-count of 5 hops. Most entities in the AoI are located within hop distance of 4. The number of messages sent in one hop is smaller than the number of messages sent in two and three hops. This is due to the fact that the area that is covered by the players located within the one hop is smaller compared to the area covered by the players within 2 hops. The number of messages that have passed 3 hops to reach their destination is also larger than the number of messages that pass two hops with the same reason. However, most of the entities farther than 4 hop counts are located out of the AoI sphere and the number of sent messages that go over 4 hops decreases substantially in Figure 4. 14

15 Number of Samples Hop Count Figure 4 message hop count distribution 5.2. Scalability The first experiment shows the number of routing hops as a function of the number of MMOG players, which is important since latency plays an adverse role in MMOGs. For scalability measurements, we changed N the number of players from 100 to and the number of hashing hierarchy is chosen to be log in each 8 case. In each of the trials, we have measured the average hop count value for the messages generated by a random player. Figure 5 demonstrates the average number of hop counts versus the number of players. As N mentioned before, the size of the routing table is O (log 8 ). The maximum number of hops required to route a packet to a specific node is N log +L where 8 N log 8 depends on the network size and represents the hops that the packet passes to reach its bucket, where L is the number of hops that the packet should traverse inside its bucket to reach its final destination. Therefore, L is not much dependant on the network size and has a typical value of 0 or 1. Figure 5 shows the fact that the average number of hop counts grows significantly slower compared to log N 8. This is mainly due to the locality preserving features of the routing algorithm where scaling the network won t result in the localized traffic to traverse longer distances. 15

16 4.5 4 Log(N) Average Hop Count Average hop count Number of players Figure 5 Average hop count versus number of nodes 5.3. Movement The final experimental evaluation has been performed to demonstrate the validity and performance of the dynamic neighborhood update scenario when players frequently change their place in the game environment. The simulation scenario in this case consists of nodes that change their location with the random speed in the range of [ ] units/sec and a random movement direction. We have applied the dynamic neighborhood update policy and measured the topology consistency (the ratio of the valid neighbors to all the neighbors in the routing table) from the view point of one of the nodes. We have also limited the bandwidth of the topology update messages to 5 kpbs. Figure 6 shows the distribution of topology consistency value for a randomly selected node in the simulated network Topology Consistency Time(Sec) Figure 6 Topology consistency for a random node As can be seen in the figure, topology consistency is well maintained in an average of 95% of the situations. In the remaining 5% of the situations, packets are forwarded to neighbors that are no longer in their 16

17 previous locations. This will only result in extra hops in the transfer of the packets while the messages will still be delivered. In order to provide a more general view of the topology consistency value, the distribution of topology consistency has been plotted in Figure 7 for the whole network. The simulation scenario has been kept the same as the previous case. As can be seen in the figure, topology consistency value mainly lies above 0.8 for most nodes in the network while the average is around This further demonstrates the performance of the dynamic neighborhood update scheme Distribution of Topology Consistency Topology Consistency Figure 7 Distribution of Topology consistency through the whole network 6. Summary and Conclusion In this paper we have applied geometrical routing to MMOGs in a wired environment.. The idea of using a geometrical routing architecture for MMOG update exchange is primarily motivated by the requirement of sending updates to specified locations. However, since the concept of geometrical routing has been introduced in the context of wireless networks, important design changes are required to make it suitable for MMOGs. The first design change is the possible use of hierarchical routing in MMOGs where transmission range is not limited. The second change is the localization of MMOG update messages within their limited interest range in order to increase the routing efficiency. These constraints motivate the use of a hierarchical, proximity aware architecture for MMOGs. We have therefore proposed a hierarchical multi-grid geometrical routing scheme based on locality sensitive hashing to address both requirements. The use of locality sensitive hashing is primarily due to the its locality preserving features, though locality sensitive hashing fails to maintain proximity along grid edges, and we have therefore used a multi-grid approach to avoid this problem. Finally, we have discussed the dynamic issues related to player mobility and churn in MMOGs which causes changes in the routing hierarchy. We have exploited the concept of hierarchical neighborhood to propose an efficient way of neighborhood update when nodes join, change their location, or leave the network. Simulation Results demonstrate the fact that the proposed algorithm has a satisfactory performance in terms of update exchange and is capable of maintaining a consistent topology under churn and users movement. 17

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