SLALoM: A Scalable Location Management Scheme for Large Mobile Ad-hoc Networks

SLALoM A Scalable Location Management Scheme for Large Mobile Ad-hoc Networks Christine T. Cheng *, Howard L. Lemberg, Sumesh J. Philip, Eric van den Berg and Tao Zhang * Institute for Math & its Applications, 4 Lind Hall, 2 Church St. SE, Minneapolis, MN 55455 Telcordia Technologies, 445 South St., Morristown, NJ 796 Department of CSE, University of Buffalo, 21 Bell Hall Box 62, Buffalo, NY 1426 Abstract - In a mobile wireless ad-hoc network, nodes move about and relay packets destined for other nodes. One of the biggest challenges in this area is the design of scalable routing protocols. Recently, a family of routing protocols has emerged that is potentially more scalable than the protocols that discover and/or maintain end-to-end routes. These protocols are location-based - the network maintains nodes approximate geographic locations and use the information to route packets. An important component of these protocols is the management of the location information at network nodes. In this paper, we present one such scheme called SLALoM which scales well in large, mobile ad-hoc networks. In particular, we prove that under a specific environment the overhead cost of SLALoM is asymptotically lower than [6], the only other location management scheme that has been analyzed theoretically. We also provide simulation results that show our scheme performs well in comparison to under a variety of scenarios not incorporated into the analysis. I. INTRODUCTION Mobile ad-hoc wireless networks have no fixed infrastructure. Nodes are mobile and relay packets destined for other nodes. Due to these networks constantly changing topology, one of the biggest challenges today is to design routing protocols that scale well as the number of nodes increases. Many schemes have been suggested (see [5] for survey), most of which are route-based. Nodes discover and maintain routes to destination nodes either in a pro-active or on-demand manner. However, this approach could be problematic in a highly mobile setting because links on a given route break frequently as nodes move about. As a result, maintenance of end-to-end routes can incur heavy signaling traffic, which is a major cause of limited network scalability for routing protocols. Recently, a family of routing protocols has been proposed as a potentially scalable solution for mobile ad-hoc networks. These protocols are location-based; i.e., the network maintains nodes geographic locations (as opposed to routes) and use these information to route packets. Studies show that, even with knowledge of the approximate locations of nodes only, location-based routing can significantly reduce signaling overhead compared with route-based methods [1], [4], [6]. Since maintenance of nodes approximate locations can be easier than maintenance of end-to-end routes, location-based routing protocols are likely going to be more scalable. A critical issue for location-based routing protocols is the management of location information at the nodes. For instance, should a node store the location of every other node in the network? If not, for how many nodes should it act as a location server? Should the node change the location information it keeps as it moves? How often should location information be updated? These questions must be answered carefully to minimize the overhead costs of the protocols. One of the earliest location-based routing protocols is DREAM [1]. In DREAM, a node typically has accurate location information for nodes close to it. If it has to send a message and the destination location is unknown, partial flooding is used to find the location. Some more recent schemes, e.g., GLS [4] and [6], call for nodes to maintain location of specific subsets of the nodes. In addition, the location server systems are designed so that when a destination node s location is not in their databases, nodes can learn about this information in a deterministic manner and thereby reduce signaling overhead. GLS designates location servers for each node so that property is achieved the distance traversed by a location query will be proportional to the path length between the source and destination node of a message. To maintain, the location servers are more densely distributed near the node. Consequently, when a node moves, GLS has to reassign location servers for the node, which could incur heavy overhead if nodes are highly mobile. divides the area in which the nodes move about into unit regions. Each node is assigned a home region and the nodes in this region act as the location servers for the node. has eliminated the need to change location servers when nodes move. In the process, however, it has sacrificed property. The location of a node is independent of its servers location. Thus, a query sent by a node near a far-awayfrom-home destination node may need to traverse a long way to discover the destination node s location. In this paper, we present a new location management scheme

for mobile ad-hoc networks called ScaLable Ad-hoc LOcation Management (SLALoM) - which combines the strengths of and GLS. Each node is assigned multiple home regions distributed uniformly over the area in which the nodes move about. (Again, the nodes in these home regions act as location servers for the node.) This could significantly reduce the distance location updates and query messages have to travel, and hence also reduce the total signaling traffic needed to maintain location information. On the other hand, more home regions for each node correspond to more location updates. We circumvent this problem by maintaining the invariant that home regions near a node will always know of the unit region it currently occupies while home regions far from the node will only know of a larger region that contains the node. Thus, whenever a node moves into a new unit region, it informs only its nearby home regions of its new location. It is only when the node has moved far enough that it updates its distant home regions of its new location. In Sec. II, we present SLALoM in detail. In Sec. III, we compute the overhead cost of our scheme using the theoretical framework set up in [6] and show that SLALoM s overhead cost is asymptotically better than GLS and s. In Sec. IV, we present our simulation results. II. DESCRIPTION OF SLALOM We assume that mobile nodes are capable of knowing their current location, using for example, the Global Positioning System (GPS), and are equipped with radios with transmission range. For ease of discussion, we will describe the scheme assuming the nodes move about in a square region of area. We show in Sec. IV that the scheme works well even when this assumption is relaxed. Our scheme divides the square into unit regions which we also call order-1 squares. It then combines of the order- 1 squares to form order- squares. A node s home region will consist of an order- square. With some exceptions, every node has a home region in each order- square. Hence, every node has home regions. Assigning home regions. Let be a square made up of unit regions so is congruent to an order- square. Number the unit regions in from to. We first consider an assignment of the nodes to square. Let be a function that maps roughly the same number of nodes to each unit square in. Let us denote by the assignment generated by. Using as a template, our scheme assigns every node a home region in each of the order- squares. However, because the original square sometimes cannot be tiled perfectly with squares congruent to, some nodes may not have a home region in the order- squares next to the boundary of the original square. Nonetheless, the following is true. REMARK Let and be nodes in the network. Regardless of where is located in the original square, there is a home region of that is within of. Fig. 1. squares although some of the order-! squares are cut-off. The grid-like arrangement of the shaded regions is an example of where a node s home regions may be located. The original square consists of order- squares and! order-! Each node knows the assignment and hence can determine home regions of any node. In particular, it can determine the closest home region of any node in constant time. Maintaining location. Let be an node in the network. Suppose it lies in the order- square "$# and "# is inside order- square. We say that a home region of is near if the home region lies in or it lies in one of the eight order- squares that neighbor. Otherwise, a home region is far from. The following invariant always holds for all home regions of know is in. In addition, all home regions near know is in " #. Our scheme requires the following functions to maintain this invariance (i) Whenever moves out of "&# and into "#(', it informs all of its previous nearby home regions of its departure from ")# and all of its current nearby home regions of its arrival at "*#+'. It must also obtain from its neighbors in "*# of the location server information it has to keep. (ii) If " #(' is in an order- square,' different from then must inform all of its previous far home regions of its departure from and all of its current far home regions of its arrival at '. To inform a home region means that an update packet containing the node s location is sent to that home region and a broadcast is made to all the nodes in that home region. Multiple home regions have to be informed at once. We do this efficiently by modeling the information dissemination as trees that span the home regions of. It is not difficult to construct these trees so that the construction is based on a few rules (and hence has no storage requirements at the nodes) and the edges that & connect the home regions of have length. Since has - home regions, the total length of the tree is. To send a message to its. nearby home regions, sends a unicast to its home region in "&#+' and from there, the node that received s message sends messages to the / other home

regions using the edges in the tree. If moves into *,' then the information dissemination to the / other home regions is broadened to the rest of the home regions. Finding a node s location. Suppose node wishes to send a message to node. First, finds the closest home region of using. It then sends a query packet to this home region to inquire of s location. Two cases arise (i) If the home region knows s order- square location, sends its message directly to this square. (ii) If not, suppose s order- square location is. Let be the order- square that is a neighbor of $ and lies between the current location of and &. Node will route its message to s home region in. The node that receives s message for will have node s order- square, which can then forward the message to. Finally, we mention that the forwarding of update and query packets to unit regions can be done using any geographicbased routing algorithm. In our simulations, we use MFR [3] (which forwards packets to the neighbor closest to the destination node) which allows us to compare our scheme s performance with. III. ANALYSIS OF SLALOM Woo and Singh [6] were the first to analyze the scalability of a location management scheme theoretically. Using a specific mobility model and MFR as a geographic routing algorithm, they computed the average number of packets sent within the network to maintain the locations of the nodes. They showed that the average overhead cost generated by is proportional to and where is the average velocity of the nodes and is the number of nodes in the network. We shall follow their analysis and show that, under the same assumptions, our scheme s average overhead cost is proportional to and and, hence, is likely to be more scalable in practice. We note that this analysis is dependent on how the network scales, as pointed out by Woo and Singh. If is fixed while is increased, the diameter of the network decreases and the average degree of the nodes increases. Routing using any reasonable algorithm will be faster in general. They propose instead to grow as a function of so that the average degree of the nodes in the network is kept constant. Later, we present a mobility model which will imply that should be grown linearly in. The overhead cost of a location management scheme can be divided into three parts Location update cost. This cost covers all the signaling messages nodes send to their home servers (both near and far) whenever they move to a new location. Location maintenance cost. This cost covers all the signaling messages nodes (a) send to their previous order- squares to inform them of their departure, (b) send to their current order- squares to inform their of their arrival and (c) collect as they are now location servers for the nodes currently registered in their order- squares. Location finding cost. This cost covers all the signaling messages sent for locating a mobile. Mobility Model We assume that nodes move randomly and indpendently of each other. Each node selects a direction to move, chosen uniformly between. Each node selects its speed, chosen uniformly between for some time, where is distributed exponentially with mean. After a mobile has traveled for time, it selects another direction, speed and time to travel. As a consequence of this model, the average degree of a node will be proportional to where is the area within a node s transmission range. To keep this fraction constant, must grow linearly with. In our scheme, the original area is partitioned into unit regions. Based on the above mobility model, the size of the unit region is chosen so that its average node density is approximately!, a constant. Thus, there are #"! unit regions, each with area $. Woo and Singh noted the following 1. The cost of broadcasting in an order- square by a node,, is proportional to the number of transmissions needed to cover the said square. The latter is in turn proportional to the area of the order- square divided by the area cov- " ered by a single transmission. Thus, &$ packets per order- square. 2. The distance a node has to cover to cross an order- square is proportional to the side of an order- square. Thus, the number of order- squares a node crosses per second, ')(, is proportional to $. NOTE By using a similar argument above, ', the number of order- sqaures a node crosses per second, can also be estimated by *' ( +" $ order- squares per second. Location update cost. Let us denote the location update cost per second per node as -,. Recall that each time a node moves into a new order- square, it has to inform its. nearby home regions of its current exact location. This entails. broadcasts in a unit region. Furthermore, if such a move also causes the node to move into a new order- square, then it has to inform all its far home regions of its current approximate location. This requires broadcasts in a unit region. We have., " *' (. /21 34' /65 packets/sec/node where /61 and /75 are the costs of sending a message to nodes in the near and far home regions respectively. We can estimate /61 (and /75 ) by 891 (8;5 ) where 891 is the total distance between the source node and its nearby (distant) servers and where is the average forward progress made towards a destination node in the course of one transmission. Woo and Singh sketched a way to compute the value of, which is dependent on and the average degree of a node in the network. To determine 891 and 8;5, we need to consider the total length of the edges of the tree used to span the home regions of a node.

' We mentioned that this tree will have total length. Furthermore, the tree behaves like a BFS-tree in that nearby home regions are close to the root while very far home regions are at the bottom of the tree. In particular, the. nearby home regions of the node are spanned by a subtree of length.. We now have., " *' (.., " packets/sec/node Location maintenance cost. Let denote the location maintenance cost per second per node. When a node moves to a new order- square, covers the cost of two broadcasts the first to inform the node s previous order- square of its departure and the second to inform its new order- square of its arrival. It also includes the cost of collecting server information, which will be proportional to the number of nodes registered in an order- square. Since each node s location is recorded in home regions, there are location information to store. But there are & " order- squares so each order- square has nodes registered at its site. If we assume that one data packet can contain bits then, & " *')( " packets/sec/node Location finding cost. Let denote the cost of locating a node per second per node. If wishes to find the location of a, it sends a unicast to a home region of closest to it. By construction, such a home region is at most away. If this home region is near then obtains the exact location of. Thus, " packets per second per node. On the other hand, if the home region is far from then obtains an approximate location of. Node then routes its message to a home region near, ". The node that receives the message at " then sends it to the exact location of. In this case, " 3 8 " 8 " 8, " &8 " " packets/sec/node The second term of the first equation arises because we added the extra steps the routing takes before reaching. The second equation follows from the fact that 8 " 8,. And since the distance of to any of its nearby home region is at most, the third equation follows. In this analysis, we shall make the assumption that packets arrive at each node at a rate of packets/sec according to a Poisson process. Total Overhead Cost. Combining the results above, we have the total overhead cost for the network. THEOREM. The average total overhead cost of SLALoM is packets per second, which is minimized when " (. That is, when is chosen appropriately, the average total overhead cost of our protocol is packets per second. IV. SIMULATION RESULTS In our simulations, we implemented both SLALoM and in order to evaluate how SLALoM behaves and how it compares to in practice. In particular, we focused on scenarios not incorporated into the analysis provided in Sec. III. We investigated how well the two schemes perform and compare in (a) geographical areas that are not perfect squares, (b) small to medium networks where the asymptotic analysis cannot fully reveal the signaling overhead of the schemes and (c) network measures not covered by the overhead cost of routing. Our simulations were implemented using the Network Simulator ver.2 (NS2) [2] and mobility extensions to NS from the Carnegie Mellon University. To speed it up, we used a perfect MAC layer that resolves all collisions and has infinite bandwidth. The number of nodes varied from to. As the number of nodes increased, the size of the area in which the mobiles move about was also increased from rectangular playgrounds of m m to m m so that the network density is kept relatively constant. Each order-1 square has a fixed size of m m. The radio transmission range of each mobile node is m. As discussed in Sec. II, the order-2 square size should increase with the number of nodes to reduce the overall signaling overhead. For the results here, however, each order-2 square consists of 4 order-1 squares regardless of the number of mobiles in the network. This will lead to the worst-case total signaling overhead of SLALoM. The nodes in the simulation moved according to the mobility model in Sec. III. Each node chose a speed uniformly at random from to m/s. For each run, we generated location query packets per second where the originator of the query and the object of the location query were chosen uniformly at random. The MFR geographic routing was used in the simulation for forwarding packets to a given geographical location. With MFR, a node forwards packets to the neighbor that is geographically closest to the destination node. We used the following metrics for the comparison. 1. Signaling Delay the average hop-count distance traversed by signaling packets. Signaling delay directly impacts the connection setup or packet delivery delays experienced by applications running over an ad-hoc network. More importantly, it could also have a significant impact on the performance of location-based routing protocols. The higher the delay, the more difficult it will be to maintain up-to-date information on mobiles locations. 2. Location Query Loss Ratio the percentage of packets lost during a location query. The reasons that a location query packet is dropped include packet loss while the packet is on its way to the location servers, packet drop by the location servers and packet loss on the way back to the originator of the query. Location servers drop query packets when they do not have have the information requested. Packets are lost on the way to the servers or back to the originator often because nodes cannot locate the servers and/or the sending nodes respectively.

1 9.6.55 Delay (in hops) 8 7 6 5 4 3 2 Query Packet Loss Ratio.5.45.4.35.3.25.2.15.1 1.5 5 1 15 2 25 3 5 1 15 2 25 3 Fig. 2. Average Signaling Delay Fig. 3. Location Query Loss Ratio 3. Total Signaling Traffic the total number of signaling packets generated in the network per second. The signaling packets include location update and location query packets. Fig. 2 shows the signaling delays. The average signaling delay of increases quickly with the size of the network, since location queries can travel far. On the other hand, the average signaling delay of SLALoM stays relatively unchanged as the network size increases. In Fig. 2, the average signaling delay of SLALoM is slightly higher than 3 hops. This can be explained by the fact that since each order-2 square consists of order-1 squares, round-trip location queries go through about hops and location updates to nearby home regions go through about hops. Fig. 3 shows the location query loss ratio. In the simulation, the response to a location query is sent back to the originator of the location query using the location information carried in the query packet. The query loss ratio of appears to increase with the size of the network much faster than that of the SLALoM. This is primarily because the signaling delay of has become significantly higher than that of SLALoM as the network size increases. As a result, it is more likely, in than in SLALoM, that the originator of the query has moved out of the unit region where it initiated the query by the time the query response is returned. Fig. 4 shows the total signaling traffic. It appears that for small to moderate sized networks, the two schemes have comparable total signaling traffic. It is important to note that the signaling traffic of SLALoM can be readily reduced by increasing the size of order-2 squares. Increasing the size of order-2 squares allows SLALoM to trade off the total signaling overhead with signaling delay. V. CONCLUSION We have presented SLALoM, a scalable location management scheme for a mobile ad-hoc network. We have shown theoretically that when nodes move about uniformly at random in a square region and MFR is the geographic routing algorithm, Total Signaling Traffic (packets/second) 5 45 4 35 3 25 2 15 1 5 5 1 15 2 25 3 Fig. 4. Total Signaling Overhead Traffic SLALoM scales well with increasing network size. That is, the overhead cost of SLALoM is proportional to and - which is better than, the only other location management scheme that has been analyzed theoretically. Using simulations, we have also shown that under a variety of scenarios not incorporated into the theoretical analysis, SLALoM performs quite well. REFERENCES [1] S. Basagni, I. Chlamtac, V. Syrotiuk, and B. Woodward. A distance routing effect algorithm for mobility. In Proceedings of Mobicom 1998, pages 76 84, October 1998. [2] K. Fall and K. Varadhan. Ns notes and documentation, technical report. UC Berkeley, LBL, USC/ISI, and Xerox Parc., 1997. http//www.isi.edu/nsnam/ns. [3] T. C. Hou and V. Li. Transmission range control in multihop packet radio networks. IEEE trans. on commun., COM-34, 138 44, 1986. [4] J. Li, J. Jannotti, D. De Couto, D. Karger, and R. Morris. A scalable location service for geographic ad-hoc routing. In Proceedings of the Mobicom 2, pages 12 13, August 2. [5] E. M. Royer and C.-K. Toh. A review of current routing protocols for ad hoc mobile wireless networks. IEEE Personal Communications, April 1999. [6] S.-C. M. Woo and S. Singh. Scalable routing in ad hoc networks. Technical Report TR.1, Department of ECE, Oregon State University, March 2. submitted for publication.