Mobile Ad Hoc Routing Using Rough Set Theory

V. Mary Anita Rajam, V. Uma Maheswari and Arul SiromoneyDepartment of Computer Science and Engineering,

College of Engineering Guindy,Anna University, Chennai – 600 025, India

Contact email: asiro@vsnl.com

Abstract

Mobile ad hoc networks are formed dynamically withoutany infrastructure and each node is responsible for routinginformation among them. Rough set theory is a mathemati-cal tool to deal with vagueness and uncertainty. In this pa-per a routing protocol for mobile adhoc networks that usesrough set theory is proposed. The performance of the pro-tocol is compared with that of an existing routing protocol.

1. Introduction

A mobile ad hoc network [3] is a group of wireless mo-bile nodes that can dynamically form a temporary network.Nodes form an ad hoc network where there is no infrastruc-ture or centralized administration for communication or it isexpensive or inconvenient to set up one. Each node in an adhoc network is responsible for routing information amongthem and hence acts as a node as well as a router.

Some examples of ad hoc networks are computers ofpeople in conferences or meetings or lectures communicat-ing among themselves, military applications and emergencyservices.

Since each node in an ad hoc network is responsible forrouting, each node should maintain necessary informationabout the next hop or the path through which the data has tobe routed to the destination. A number of routing protocols(e.g. Destination Sequenced Distance Vector (DSDV) [7],Dynamic Source Routing (DSR) [1], Ad hoc On DemandDistance Vector (AODV) [8]) have been proposed for adhoc networks.

Dynamic Source Routing (DSR) [1] is a routing pro-tocol, in which each node has a route cache to store theroutes that are either used by the node or learnt by lookinginto the packets that pass by. When a source node wantsto send a data packet, it uses the route present in its routecache to route the packet to the destination. If there is no

route in the route cache, the source node initiates a routediscovery. During route discovery, the source node broad-casts a route request packet. If any intermediate node thatreceives the route request has a route to the required des-tination in its route cache, it will send a route reply to thesource, else the intermediate node appends its own addressto the route record and re-broadcasts the route request. Ifthe route request reaches the destination node, the destina-tion node sends back a route reply to the source node. Ifan intermediate node while forwarding a data packet, findsthat the link to the next hop does not exist, then it sends aroute error to the source node and the source node updatesits route cache accordingly.

Destination Sequenced Distance Vector (DSDV) [7] isa table driven routing protocol developed for ad hoc net-works. In DSDV, each node maintains a routing table whichholds information regarding how to reach all other nodes inthe network. This includes the number of hops to reach eachnode, the next hop on the route to that node and a sequencenumber to distinguish between stale routes and valid routes.

Ad hoc On demand Distance Vector(AODV) [8] is simi-lar to DSDV in that they both use routing tables which con-tain the next hop, number of hops and sequence numbersfor nodes of the network. However, AODV does not keepan entry for all nodes in the network. Instead each nodeonly stores information regarding routes which that node iscurrently involved in, or has been involved in. For eachdestination there is only a single entry in the routing ta-ble. Freshness of routes is maintained by sequence numbersmaintained by each destination. When a node using AODVdesires to send a packet, it looks up its routing table, if ithas a valid route to the destination, then it sends the packet,otherwise the node must initiate a path discovery process asin DSR. AODV uses route requests and route replies simi-lar to that of DSR. A route reply packet is unicasted backalong the desired route with each node making an entry inits routing table.

Rough set theory, introduced by Zdzislaw Pawlak [5]is a mathematical tool to deal with vagueness and uncer-

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tainty. Elements that exhibit the same characteristics areindiscernible and form the elementary sets. In this paper avariant of DSR protocol is proposed that uses the conceptof rough sets. Each mobile node maintains an informationsystem that assists in routing packets. Information aboutroutes are added to the information system when learnt orused. When packets are routed, the information system isused to decide on the next hop to which the packet is to besent. The performance of the proposed routing protocol iscompared with the performance of DSR protocol.

The remainder of the paper is organized as follows. Thefollowing section gives the definitions with respect to roughsets. Section 3 describes the proposed routing protocol, sec-tion 4 evaluates the performance of the proposed routingprotocol and section 5 gives the conclusions.

2. Definitions

Consider a universe U of elements. An information sys-tem I is defined as I = (U,A, V, ρ) where A is a non-empty, finite set of attributes; V =

⋃a∈A Va is the set of

attribute values of all attributes, where Va is the domain(the set of possible values) of attribute a; ρ : U × A →V is an information function such that for every elementx ∈ U , ρ(x, a) ∈ Va is the value of attribute a for ele-ment x. Let d /∈ A be known as the decision attribute, thenI = (U,A∪{d}, V, ρ), is known as a decision system, whereA is known as the set of condition attributes. This definitionis based on the definition of Rough Set Information Systemin [5, 6, 4].

The information system (decision system) can also beviewed as an information table (decision table), where eachelement x ∈ U corresponds to a row, and each attributea ∈ A (A ∪ {d}) corresponds to a column. The value ofthe entry in the information table at row x and column a isρ(x, a).

Let M be the set of mobile nodes. A route is a paththrough mobile nodes in M and is denoted as a sequenceof mobile nodes m1m2 . . . mk, mi ∈ M, i = 1, . . . , k.The route cache of mobile node m stores routes that mknows. A new route is not added to the route cache if italready exists in the route cache, or is a subpath of a routealready in the route cache. We note that any route in theroute cache is a path starting from m itself, and is denotedas mm1m2 . . . mk, mi ∈ M, i = 1, . . . , k. Any route inthe route cache is a simple path, where no node repeats, thatis, mi �= mj ∀mi,mj ∈ M, i �= j.

Let each mobile node m ∈ M have an information ta-ble Im associated with it. Consider a particular mobilenode m ∈ M and let its information table Im be denotedas I = (U,A, V, ρ). Let A = M . Every m ∈ A isa boolean attribute, with Vm = {0, 1}. Consider a rowx ∈ U corresponding to the route mm1m2 . . . mk, mi ∈

M, i = 1, . . . , k. We note that ρ(x,mi) = 1, for each mi

in the route, and is 0 for all other m ∈ A. When a routemm1m2 . . . mk, mi ∈ M, i = 1, . . . , k is to be added tothe route cache, a row corresponding to this route is alwaysadded to the information table. However, we note that theroute is added to the route cache itself only if it is not iden-tical to or a subpath of any other route already in the routecache.

Consider a particular destination mt ∈ M . Let d ∈ Mbe an attribute that corresponds to the next hop that shouldbe taken by a packet from this mobile node m to reach thedestination mt in a route. We note that Vd = M , andρ(x, d) = m1, where x ∈ U is the row corresponding tothe route mm1m2 . . . mk, mi ∈ M, i = 1, . . . , k, and mt

is one of the mi.Let B = {mt}, B ⊆ A. Consider the decision system

IB = {U,B ∪ {d}, V, ρ}. We note that the universe U isthe same as that of the information system I . In this paper,IB is used in the following manner to determine the nexthop that is to be taken by a packet to reach the destinationmt. For some m ∈ Vd and k ∈ Vmt

, let Xm,k denote theset Xm,k = {y ∈ U | (ρ(x, d) = m) ∧ (ρ(x,mt) = k)}.In other words, the set Xm,k consists of the elements inU of the decision system IB that have m as the next hopand the destination node mt has the value k in the corre-sponding route (that is, the destination node mt is presentor not present in the corresponding route according to kbeing 1 or 0). Let |X| as usual denote the count of el-ements in a set X . The value mn ∈ Vd is such that|Xmn,1| ≥ |Xmi,1| ∀mi ∈ Vd,mi �= mn. In other words,the value mn of the decision attribute d, is the node that isused as the next hop by the most number of entries that havethis destination mt in the corresponding route.

3. Routing

In the proposed routing protocol(DSR+), each mobilenode maintains an information table I . Whenever a routeis learnt or used by the node a row is added to the informa-tion table.

When a source node sends a data packet, it uses the nexthop given by the information table, if available, or the routein the cache, or initiates a route request and finds a route.

In each of the intermediate nodes through which the datapacket is sent, the intermediate node uses the next hop givenby its information table, if available. If it is not possible todetermine the next hop from the information table, the routein the route cache in that node, if any, is used, else a freshroute discovery is done by initiating a route request.

When a next hop is to be found from the informationsystem, only the rows that have the given destination areconsidered. If the given destination is a next hop, then thenext hop itself is chosen as the destination. Else, the node

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that is used by most of the entries as next hop to reach thedestination is chosen as the next hop.

When an intermediate node is forwarding a data packetand it does not find the link to the next hop, it sends a routeerror with the information about the dead link to the sourcenode. When the source node receives the route error, itdeletes in each path of the cache the subpaths starting fromthe deadlink. This is done in the information tables in thesource nodes and the intermediate nodes that forwarded theroute error.

DSR+ is similar to DSDV and AODV in that it has in-formation about the next hop through which packets areto be routed to a particular destination. Both AODV andDSR+ have information about next hops only for routesthat have been used or learnt compared to DSDV whichhas entries in routing tables for all nodes in the networksand has an overall picture of the network. AODV main-tains only a single routing table entry for a particular desti-nation. DSR uses source routing whereas DSR+ routes hopby hop. DSR, DSR+ and AODV have route discovery pro-cedures for learning unknown routes. In all four protocolsthere are mechanisms by which the other nodes are madeknown about link failures.

4. Performance Evaluation

4.1. Simulation environment

The network simulator ns2 [2] is used for the experi-ments. The random waypoint mobility model is used in arectangular field. Constant bit rate traffic sources are used.The radio model in the simulator is based on the LucentTechnologies WaveLAN 802.11. providing a 2Mbps trans-mission rate A transmission range of 250 m is used. Thelink layer modeled is the Distributed Coordination Func-tion (DCF) of the IEEE 802.11 wireless LAN standard. A15 node network in a field with dimensions 670x670 is used.The source-destination pairs are spread randomly over thenetwork. 512 byte data packets are used. Simulations arerun for 500 simulated seconds.

4.2. Performance Metrics

The performance is evaluated using the following met-rics:

(i) Packet delivery ratio: The ratio of the data packetsdelivered to the application layer of the destination to thosesent by the application layer of the source node.

(ii) Average end-to-end delay: The average delay fromwhen a packet is sent by the source node until it is receivedby the destination node.

(iii) Number of Route requests: The total number ofroute requests sent by different nodes during the simulation.

4.3. Simulation results

For each scenario, the source destination pairs and theinitial positions of the nodes are changed randomly. Thefollowing table shows the packet delivery ratio, end-to-enddelay and the number of route requests generated when thenumber of source-destination pairs are varied from 5 to 12.Each value in the table is the average of the values got in10 simulation runs. It is seen that there is not much of dif-ference in the packet delivery ratio. The number of routerequests is less for DSR+ than DSR when the number ofconnections is less.

No. Pkt. Delivery Avg. No. ofof Ratio (%) Delay (secs) RREQ

Conn. DSR+ DSR DSR+ DSR DSR+ DSR5 98.12 98.09 0.064 0.074 39 41.36 98.28 98.39 0.086 0.116 50.4 50.77 97.53 97.84 0.092 0.157 77 78

10 95.84 95.89 0.44 0.4 201 19411 96.79 96.99 0.264 0.203 134 12612 96.26 96.48 0.431 0.331 176 174

Figure 1. Average end to end delay vs. num-ber of connections

In figure 1, the average end to end delay is shown. It isseen that the end to end delay for DSR+ is less compared toDSR when the number of connections is less. When thereis an increase in the number of connections, the end to enddelay of DSR+ becomes more than that of DSR. This meansthat the packets reach the destination in less number of hopswhen the number of connections is less. The number ofroute requests that are used to find new routes is also nothigh for DSR+ when the number of connections is less asseen in figure 2. So with less overhead the packets reachthe destinations in less number of hops when the number ofconnections is less.

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Figure 2. Number of Route Requests vs.number of connections

5. Conclusions

An extension to the mobile ad hoc routing protocol DSRis proposed in this paper as an application of notions fromrough set theory. The behaviour is simulated using the net-work simulator ns2 and analysed. Other extensions to roughset theory that are useful in mobile ad hoc networks are be-ing explored.

References

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[3] D. B. Johnson, D. A. Maltz, and J. Broch. Dynamic sourcerouting protocol for multihop wireless ad hoc networks. InC. E. Perkins, editor, Ad Hoc Networking, pages 139–172.Addison- Wesley, 2001.

[4] J. Komorowski, Z. Pawlak, L. Polkowski, and A. Skowron.Rough sets: A tutorial. In S. K. Pal and A. Skowron, edi-tors, Rough Fuzzy Hybridization: A New Trend in Decision-Making, pages 3–98. Springer-Verlag, 1999.

[5] Z. Pawlak. Rough sets. International Journal of Computerand Information Sciences, 11(5):341–356, 1982.

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[7] C. Perkins and P. Bhagwat. Highly dynamic destination-sequenced distance-vector routing (DSDV) for mobile ad hocnetworks. In Computers Computer Communications Review,pages 234–244, Oct. 1994.

[8] C. Perkins and E. Royer. Ad-hoc on demand distance-vectorrouting for mobile computers. In Proceedings of the Secondinternational workshop on Mobile Computing Systems andapplications, pages 90–100, 1999.

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