Geographical Routing In Ad Hoc NetworkYang Fan

Abstract......................................................................................................................................................11. General Description...........................................................................................................................12. Grid's Location Service (GLS)..........................................................................................................2

2.1 The Core Conception of GLS....................................................................................................22.2 The Routing Table in GLS.........................................................................................................42.3 Location Query in GLS..............................................................................................................42.4 Bootstrapping in GLS................................................................................................................52.5 The Weak points of GLS...........................................................................................................6

3. Geographical Routing Using Partial Information – GRA.................................................................63.1 Routing Table Structure of GRA...............................................................................................63.2 Packet Format............................................................................................................................73.3 Voronoi Cells and Voronoi Views.............................................................................................73.4 Packet Forwarding in GRA........................................................................................................83.5 Route Discovery......................................................................................................................103.6 The Size of Routing Table in GRA.........................................................................................103.7 The Enhancement of GRA.......................................................................................................11

4. Predictive Location-Based QoS Routing (PLQR)...........................................................................114.1 Update Protocol of PLQR........................................................................................................114.2 Predictions...............................................................................................................................134.3 QoS Routing in PLQR.............................................................................................................144.4 Enhancements..........................................................................................................................14

5. The Author's Opinions.....................................................................................................................14

Abstract

In this paper, a finding geographical location algorithm and two geographical-based routing algorithms will be introduced. All of them have both up side and down side, but because of "closer to destination" benefited from geographical information, the algorithms present simple and straightforward.

Because each of the three algorithms is as a whole, so, the introductions will take such an order that each of them is described with a separate chapter. The last chapter is summing-up of all the algorithms and given some author's opinions.

1. General Description

Traditional routing algorithms in Ad Hoc network are address-based routing. These considerations may derive from IP routing algorithms. Because IP routing has experienced several decades of history, so, many of well-rounded logic could be directly used for reference, such as, the basic architecture of routing tables and the self-organized routing algorithms. But an address-based routing algorithm might sometimes be difficult to route packets to a special destination in such an Ad Hoc network that its topologies could be fast changed. The main reason is an Ad Hoc network itself absents a "trustable" entity for reference. Thus, it will be difficult to recognize a node "moving" with a traditional address.

Unlike the traditional routing algorithms, the algorithms introduced in this paper are geographical-based routing. The main advantages for geographical-based

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routing are it is possible for all the nodes of network "coarsely" know every destination by the main logic "closer to destination" even though they never "meet" before and it is also easy to know whether a destination has changed its position from the viewpoint of network. On some cases, we may even predict where a destination will be moving. Thus, an Ad Hoc network may become, on some level, "static" and some complications of routing logic can be reduced. Of course, each thing always has both positive and negative sides. The disadvantages for geographical-based routing are the route is not guaranteed to be the shortest.

A geographical-based algorithm typically consists of two parts. One is finding location information and the other is the logic of routing to a special destination. Therefore, we may take this order to construct our article. An algorithm of finding location information will be firstly introduced and then two typical geographical-based routing algorithms will be discussed. These three algorithms respectively are the "A Scalable Location Service for Geographic Ad Hoc Routing" created by MIT Laboratory for Computer Science, the "Predictive Location-based QoS Routing in Mobile Ad Hoc" created by University of Illinois at Urbana-Champaign" and the "Geographical Routing Using Partial Information for Wireless Ad Hoc Networks" created by University of California, Berkeley.

Basically, it is assumed that the geographical information is obtained from some additional technologies, such as, GPS.

2. Grid's Location Service (GLS)

A scalable location service for geographic Ad Hoc routing created by M.I.T is named GLS (Grid's Location Service). Its purpose is to realize a distributed location service in a large scaling Ad Hoc network. GLS assumes an Ad Hoc network can be as large as the area of a metropolitan.

2.1 The Core Conception of GLS

The core conception of GLS is to divide the whole area of an Ad Hoc network into some order-n squares. An order-1 square represents the area that a mobile node can directly reach each other without any routing. So, all the nodes in order-1 square are neighbors. Whereas, order-n square, just as its name implies, represents the area that a mobile node can reach by relaying n-1 times. Note an order-n square is not divided dependent on a special node but on the relation to the whole network area. The following Fig.1 shows the basic conception of GLS's partitions.

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Each mobile is identified by a unique number (ID). The IDs are generated from a mobile node's unique name, such as, host name and MAC address by employing a strong hashing algorithm.

A mobile node will select its location servers (LS as simple) in all the orders of partitions. The logic of selecting LSs is that one LS in each neighbor order-n square of a mobile node will be chosen. For example, if assumed an Ad Hoc network consists of 4 order-3 squares as shown by Fig.1, then a mobile node will select 3 LSs in its neighbor order-1 squares, 3 LSs in its neighbor order-2 squares and 3 LSs in its neighbor order-3 squares. Thus, an LS tree is constructed with a sparse layout, i.e., the farther to a destination the sparser of its LS. The following Fig.2 shows an example a mobile node B selects its LSs in an order-4 defined Ad Hoc network.

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The strategy of selecting LSs by a mobile node is to recruit nodes with IDs "closer" to its own ID. Here "closer" means a circled close. For example, 43 are "closer" to 17 than 12 does.

Note Fig.2 just assumes a mobile node can reach another through some middle nodes. Those nodes don't appear in Fig.2 for outstanding the conception.

2.2 The Routing Table in GLS

Each mobile node in GLS needs to maintain a routing table that records the routing information to all the nodes within its order-2 square. For example, node B in Fig.2 should record the routes to node 2, 7, 23, 41 and 63.

2.3 Location Query in GLS

When a mobile node wants to find the location of another node, it will send a request, encoding its own geographical information in the request, to the least node whose ID is greater than or equal to the destination. The receiver node will further forward the request and so on until the request encounters a LS of the destination. Then the LS will directly forward the request to the destination. Because the source's geographical information is in the request, so, the destination can directly respond to the source. A location query has completed at this stage. The following Fig.3 shows how a mobile node can find the location of another.

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To understand why each step brings the query to the best node in a larger square, we will first consider the query from node A (76) for the address of B (17), shown starting in the lower right of Figure 3. The abbreviated topology has no more than one node per square, so the query trivially begins at the best node, itself, in its order-1 square. The query moves to the best node (21) in A’s order-2 square, because 76 happens to know the positions for all the nodes in its order-2 square (see sect. 2.2). This is an artifact of the sparse layout, so the next step tells the important story: why 21 knows the location of the best node in the next higher order square.

Recall that 21 is the best node in its order-2 square. This guarantees that no nodes in that square have IDs between 17 and 21. Now, consider a node X somewhere in node 21’s order-3 square, but not in 21’s order-2 square. Recall that X had to choose a location server in node 21’s order-2 square. If X’s ID is between 17 and 21 then X must have chosen node 21 as a location server since there are no better nodes in node 21’s order-2 square. Thus, node 21 knows about all nodes in its order-3 square that lie between 17 and itself, including the minimum such node. In this case, that node is 20. At the next step, node 20 must know about all nodes in the order-4 square between 17 and itself. Since nodes 20 and 17 share the same order-4 square (the entire figure), node 20 knows about node 17, and the query is finished.

2.4 Bootstrapping in GLS

For illustrative purposes, an important bootstrapping issue have advisedly ignored. It has been assumed that nodes select their location servers appropriately

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and send their coordinates to them. This appears to assume that a node can scan an entire square (of arbitrary size) and choose the appropriate node to act as its server. In fact, nodes route update packets to their location servers without knowing their identities. Assume that a node B wishes to recruit a location server in some order-n square. B sends a packet, using geographic forwarding, to that square. The first node L in the square that receives the packet begins a location update process that closely resembles a query for B’s location; but this update will actually carry the current location of B along with it. Because the update will arrive at the least node greater than B before leaving the order-n square containing L, so, this is exactly the appropriate destination for the location update to go to. The final destination node simply records B’s current location and becomes a location server for B.

For example, if assumed that node B has chosen node 2, 23 and 46 as its LSs (node B happens to all the nodes in its order-2 square; seeing sect. 2.2) in Fig.2 and now it sends an update to one of its neighbor order-2 square containing node 26, we may see the update might arrive at node 14 through node 7. Because node 14 happens to know all the nodes within its order-2 square, so, it will forward the update to node 26 and because the latter knows no one node is better than itself, so, it will record node 17's geographical information.

By the way, the discussions above also imply that a mobile node should broadcast itself to its neighbors in the same order-1 square at the very beginning. Then all the neighbors will respond to the node with their neighbors so that the node knows all the nodes in its order-2 square.

2.5 The Weak points of GLS

The main weak points of GLS are if a packet arrives at one node that doesn't know any nodes closer than itself to the ultimate destination, then a query will simply be failed by responding with an error report. In the other word, GLS doesn't offer any strategy for recovering from dead ends, which usually occurs when all the nodes are not evenly distributed in a geographical area.

3. Geographical Routing Using Partial Information – GRA

GRA (Geographical Routing Algorithm) is created by University of California, Berkeley. As its name implies, GRA will mainly concentrate on routing packets from a source to its ultimate destination using partial information.

The basic assumptions of GRA are a mobile node exactly knows its neighbors that it can directly reach and coarsely knows the topology outside its own area. Then GRA will use these partial information to complete routing between a source to its ultimate destination.

3.1 Routing Table Structure of GRA

The routing table structure of GRA takes the following format described by Fig.4.

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The first column is the node's name, such as, node S and N. The second one is the geographical information of nodes. The third one is the neighbor node to the current node. This is an important conception in GRA. That means a node A can be best reach by node B if the latter is in the third column of node A. For example, node S' will be best reach by node N'. The last one is the time stamp as IP normally does with it. Thus, each routing table entry will be a 4-tuple (

).

3.2 Packet Format

The following Fig.5 is the packet format of GRA.

3.3 Voronoi Cells and Voronoi Views

GRA partitions the whole communicating region with Voronoi cells. The conception of Voronoi cell can be described with the following way. Let

be the set of nodes whose geographical location are known to node S at time t ( is also assumed). These nodes can be referred as centers at node S and the centers are called Voronoi cells.

Another conception is the Voronoi views. It actually is a known partition to a special node. The following Fig.6 shows an example of a Voronoi view from the viewpoint of a special node S.

If assumed nodes A, B, C and D happen to be in node S's routing table, then 4 Voronoi cells around node S can be constructed as shown by Fig.6. This is just the Voronoi view from node S. Because node E is not in node S's routing table, so, it is partitioned into center D. Of course, if node E is further known by node S later, the Voronoi view from node S will consist of 5 Voronoi cells. Note unlike GLS, a partition of GRA can be very large and the known node in each Voronoi cell doesn't guarantee to reach all the others in the same cell. For example, even though nodes D and E are in the same cell, they may still be unknown each other. We will later see that a "stable" GRA's network means every cell will only contain a node. A Voronoi view is represented by , where is a known node to node S at time t.

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3.4 Packet Forwarding in GRA

The basic logic of GRA's packet forwarding is "closer to destination". When a packet arrives at node S, it will search its routing table to find who is closer than itself to the ultimate destination. If assumed node fit to the condition, then node S will further forward the packet to node and so on until the packet arrives at the destination. GRA's routing has finished. Note if some middle node happens to know a shorter path to the destination, then the routing path will be corrected. But a remote node may not be necessary to know the existence of such a middle node.

From the routing procedure of GRA, we may see a geographical-based routing algorithm can largely reduce the routing complication (it is quite simple). This is because a node only needs to coarsely know the topology outside its own subarea. This closely resembles a postal system. For example, if assumed that we want to post some mail to Yvaskyla, we may first expect the mail will go through Tempare (we might only know such a middle node). But it may eventually go through Lahti because the main postal office knows this is more straightforward way.

It is however quite possible that a packet destination is equally close to two nodes and . On some cases, this phenomena may cause a routing loop. So, a name

order is assumed to resolve the tie.

If node S finds no one closer than itself to the ultimate destination when a packet arrives at it, then the packet will be "stuck" there. This will cause a route discovery algorithm (RDA as simple) to further find the destination. RDA will be extended to the next section. After RDA, the stuck packet can continue to the destination and all the nodes between the stuck node to the destination will update their routing tables.

The following Fig.7 gives an example network and Figs, 8 and 9 give some example of routing tables based on Fig.7.

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Example 1. Suppose node A gets a packet to destination C. From its routing table shown in Fig.8, node A can directly find node B is closer than itself to node C. So, node A will send the packet to node B. Because node B happens to know node C, so, it forwards the packet to destination C. The routing procedure completes.

Example 2. Suppose node A gets a packet to destination D. But from its routing table shown by Fig.8, node A finds no node closer than itself to node D. The packet will thus be stuck at node A. This will cause a route discovery. The route discovery process finds the path {A, B, C, D} to the destination D. In this process it also updates the routing tables of nodes A, B and C. The updated routing tables are shown in Fig.9.

Example 3. Suppose next node A gets a packet to destination E. From its routing table shown in Fig.9, node A finds node B is closer than node A to the destination E. Node A then forwards the packet to node B. Node B will find node D is closer than itself to the destination E. Then it will forward the packet to node D through node C (because it knows node D can only be reach through node C). When the packet arrives at node C, it finds itself closer than node D to the destination E. So, it directly forwards the packet to the destination E.

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Example 4. Observe Fig.10. The routing tables at each node are shown in the figure. Note the node positions are left out for convenience to the tie topic. Thus T2: (b,1) (a, a) is the routing table at node 2. (b,1) means if the surrogate destination is b then the packet will forward to node 1 and whereas (a, a) has the normal meaning except for the position information having been left out.

Both nodes 1 and 2 have a and b in their routing tables. Node 1 sends packets to a through 2 and node 2 sends packets to b through node 1. Suppose node 1 originates a packet for node d. Since it knows both nodes a and b are equidistant from node d, suppose it randomly chooses node a and forward the packet to node 2. Likewise node 2 is faced to the same choice. If node 2 randomly chooses node b then the packet may result in a cycle. From this example, we may see a name order is needed to resolve the tie.

3.5 Route Discovery

Several different algorithms can be used to find a path to the destination. Examples of such algorithms are breadth-first search (e.g., flooding) or a depth-first search. The key requirements for route discovery settle at that an acyclic path should be found from the stuck node to the ultimate destination. It can be verified that both the breadth-first search and the depth-first search will find an acyclic path for GRA.

After a is found, where S is the stuck node, D is the destination node, is some middle node between S and D and Path is some route discovery algorithm, an entry should be added to the routing table of . It can be imaged that if a mobile node is a newcomer to an Ad Hoc network and the network is using GRA for routing, then it will surely trigger several times of route discoveries to get its "static" routing table.

3.6 The Size of Routing Table in GRA

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It can be justified that the size of routing table in each GRA's node will be , where is the mean route discovery path length, n is the number of

nodes in an Ad Hoc network and is the same as (direct radio).

3.7 The Enhancement of GRA

Up to now, everything seems OK. But an observant reader will find GRA's network is a little "static". If some nodes in path have moved to be unreachable at time , then the route discovery has to be triggered again on some node even only one hop is spanned. So, additional requirements should be added to GRA. The requirement specifies neighbors should exchange "hello" messages to discover their neighboring topology and each node should also transmit its routing table as part of the "hello" message. This process closely resembles that a new node will announce itself to its neighbors by broadcasting when moving to a new area.

4. Predictive Location-Based QoS Routing (PLQR)

In this chapter, Illinois's solution for QoS routing in mobile Ad Hoc network will be introduced. For simplification, the solution can be named as PLQR (Predictive Location-based QoS Routing).

PLQR is based on the whole network track through an update protocol. The update consists of two types. Type 1 is a regular update similar to "hello" message exchanges and type 2 is an instant update when a considerable change occurs at a node. These are very traditional and are not so interesting. But an important conception introduced by PLQR is the predictability. As we know, the topology of an Ad Hoc network is very flashing. In the other word, it is so unstable that routing information built up with innumerable trials and hardships is so quickly invalid as written in water. Therefore, the predictability looks quite important in such a network. Meantime, we will see that geographical-based routing has a high advantage in this aspect, for it can directly indicate what motion means.

By the way, PLQR assumes a mobile node at least has two basic features. One is it can find its geographical location and the other is it can also detect its location change in position and directly. If GPS is exact enough, then these requirements are not difficult to be matched.

4.1 Update Protocol of PLQR

PLQR defines two types of updates. The details is explained below.

1. Type 1 update: A type 1 update is generated periodically. It can be generated with a constant frequency, i.e. the time between successive type 1 updates remains constant. Alternatively, the frequency of the type 1 update can vary linearly between a maximum ( ) and a minimum ( ) threshold, with the velocity v of the node. Consequently, the distance traveled between

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successive type 1 updates remains constant. This function is illustrated in Figure 11.

2. Type 2 update: A type 2 update is generated when there is a considerable change in the node’s velocity or direction of motion. From its recent history (i.e. from recent updates), the mobile node can calculate an expected location that it should be in at a particular instant. The node then periodically checks if it has deviated a distance greater than from this expected location. If it has deviated more than a distance from its expected location, a type 2 update is generated.

The generation of type 2 updates can be calculated referring to Fig.12. If

(1)

then a type 2 update should be generated. It is clear that

(2)

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4.2 Predictions

The predictions of PLQR are divided into two categories. One is location prediction and the other is delay prediction.

Location Prediction: The location prediction is done with the latest two updates respectively from a destination node D. With two updates, we can easily find two fixed points and then a predictive line can also be decided. This is shown with the following Fig.13.

From Fig.13, it is clear there're (with similarity of triangles and Pythagoras's theorem)

(3)

There however exists a potential problem. If node D is not moving in a linear fashion but suddenly taking a turn on some place during the period of time interval ( ) (It is clear the update at time becomes obsolete), then prediction can completely lose its exactness. Thus, before the next update arrives, all the packets to node will be lost. To solve the problem, it is specified that two updates with a very short interval will be sent. Thus, it is only possible that packets to the destination D will be lost during this very short period of time.

Delay Prediction: The delay prediction is used to compensate the exactness of the time interval for the location prediction. The delay prediction is simply done

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by comparing the two time values between a sender and a receiver for a most recent update. Thus, it is suggested a synchronized clock be assumed.

4.3 QoS Routing in PLQR

There exist two typical QoS routing strategies. One is differential service and the other is resource reservation. But these two strategies are difficult to be used in an Ad Hoc network with two reasons. One is flow scheduling as the base for differential service is not yet available and the other is an Ad Hoc network is too flashing to promise any resource reservations.

PLQR utilizes a source-based routing instead of these typical routing strategies. Each mobile node in PLQR will maintain an update table shown by the following Fig.14.

The QoS routing will be based on the proximity list, which is selected according to both the mobile nodes' geographical information and their resource parameters. Even though the Illinois's solution doesn't mention how can we exactly calculate the proximity list, the author thinks this should be a fussy calculation, for it is likely the geographical information of a mobile node can be contradicted with its resource parameters. The algorithms for fussy logic should be not very difficult in this case, but we have to carefully choose the knowns from a mobile node's geographical information and its resource parameters.

4.4 Enhancements

The main enhancement of PLQR is to add the direction information in updates and in-band updates piggybacked on data packets. The advantages for the former are to enhance the location prediction (but having to pay the price for enlarging the size of update packet) and for the latter are to randomly shorten the period of time for type 1 update. Furthermore, frequent updates may cause flooding in network. So, PLQR could be improved by MPR (Multiple-Point Relay) scheme as OSPF (Open Shortest Path First) does.

5. The Author's Opinions

In this paper, a location service and two routing algorithms in Ad Hoc network have been introduced. All of them are based on the geographical information of mobile nodes. In this chapter, the author will give some evaluations based on the author's self-consciousness.

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The author think all the algorithms introduced in this paper plumply hit their respective goal and present their differently simple and straightforward characteristic. Compared to some traditional routing algorithms, they reduce, on different levels, the complications of routing algorithms. This is the direct advantage benefited from geographical-based routing. Even though there exist some disadvantages, their advantages comparatively are much more significant. A wisdom says "Why do we need to pay 99% effort just for 1% potential problem if it is not so pivotal". Therefore, keeping simple with some trivial problems might be the best solution all the time.

Clearly, the prediction suggested by PLQR is an interesting topic. The prediction can give us a relatively longer stable period in an so-flashing Ad Hoc network. Partial information routing is also interesting to reduce the size of routing tables (It seems this is the compensation for PLQR). Whereas, GLS may be one of the simplest algorithms for location services.

Furthermore, it might be better if we could find some ways to combine these algorithms together. Of course, this will need another effort put on it. Meantime, we may also need to get some helps by improving hardware. For a current mobile, for example, it is clear that the memory is not enough to store the whole update table required by PLQR if an Ad Hoc network is a little large.

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