Geographical Routing Using Partial Information for Wireless Ad Hoc Networks

Rahul Jain, Anuj Puri, and Raja SenguptaDepartment of EECSUniversity of California, BerkeleyIEEE Personal Communications,

February, 2001

Problem Statement

Goal: Solve the routing problem in wireless ad hoc network using the position information.

How: When S want to send a packet to a node D, it takes the pos(D) and find one of its neighbors which geographically is closet to D; then it forwards the packet to D.

Problem: What if S is the closer to D than its neighbors?

Solution: Use Route Discovery Protocol

Assumptions

Each node has fixed power for trans-receivers, i.e. the neighbors of each node is fixed. We model the network with a graph

is a undirected connected graph. Initially each nodes knows the geographical positions of

itself and its neighbors. When Sending (forwarding) a message, we know the

geographical position of the destination.

),( ENG

G

Definitions

Let be the set of nodes whose locations are known to node S at time t. Call these nodes centers.

Voronoi cell: Let be any set of points in A Voronoi cell with center is defined as follows:

Voronoi view: The Voronoi view at node S at time t is:Voronoi view: The Voronoi view at node S at time t is:

},...,,{ 21 ks SSSC

},...,,{ 21 kSSS

iS

}|,)(|min|)(:|{)( SjjiiS CSSposzSposzzSV kj1

}:)({ siisS CSSVV

iS

Routing Table Structure

Node Node Position Neighbor Node (Next)

Time stamp

S pos(S) S TS

N pos(N) N TN

... … … …

S’ pos(S’) N’ TS’

… … … …

Each entry is a 4-tuple (Si, , pos(Si), NextS(Si), TSi)

The Algorithm

//let for some

If (S == D)

// packet reached its destination

else if (Si != S)

next_node = NextS(Si);

else

//packet is stuck

Initiate route_discovery(S, D);

next_node = Nexts(D);

)()( SiVsDpos CsSi

Route Discovery Protocol

route_discovery(S,D) finds an acyclic path Path(S,D) = <k0, k1, …, kl> from S to D, and it updates the routing table of node ki with an entry (D, pD, ki+1).

Example1

Example1 (Initial Routing Table)

Node Routing Table

A {(A, (1.5, 1.5), --), (B, (2,2), B)}

B {(B, (2,2), --), (A, (1.5, 1.5), A), (C, (3,1), C)}

C {(C, (3,1), --), (B, (2,2), B), (D, (2.5, 0), D), (E, (4,0), E)}

D {(D, (2.5, 0), --), (C, (3,1), C)}

E {(E, (4,0), --), (C, (3,1), C)}

A sends a packet to C: ABCA sends a packet to D: stuck

Example1 (Updated Routing Table)

Node Routing Table

A {(A, (1.5, 1.5), --), (B, (2,2), B), (D, (2.5), B)}

B {(B, (2,2), --), (A, (1.5, 1.5), A), (C, (3,1), C), (D, (2.5, 0), C)}

C {(C, (3,1), --), (B, (2,2), B), (D, (2.5, 0), D), (E, (4,0), E)}

D {(D, (2.5, 0), --), (C, (3,1), C)}

E {(E, (4,0), --), (C, (3,1), C)}

Assume: route-discovery(A, D)= <A, B, C, D>

Path-Finding Phase

The route can be discovered right up to destination node D (Full route discovery), or it can be discovered up to a node Y which has node D as a cell center (partial route discovery).

The following algorithm can be used to find an acyclic

path to the destination:

Breath First Search

Depth First Search

Convergence of Routing Tables

Definition: The Voronoi view of node S is complete if VS(S) contains only node S

If the routing table has enough information s.t.

no packet becomes stuck, then the Voronoi

views are complete.

Size of Routing Table

Claim: The average routing table size in a n-node network G when all the nodes have complete Voronoi views is , where

L is the mean route discovery path length.

))log(( nL

Multiple Route Discoveries Issue

Example

• S1 sends RD1 for the destination D at t1

• S2 send RD2 for the destination D at t2

RD1: s1x1x2y2 D

RD2: s2x2x1y1 D

ACK1 reaches x2, then ACK2

x2 puts (D, --,y2,--) first, then (D, --, x1, --)

And x1 puts, (D, --, y1, --), then (D, --, x2, --)

Cycle in the routing tables

Mobility in Ad Hoc Networks

The routing table might be inconsistent .

Improved Version of the Protocol

1. If S receives a “hello” message n i, it puts an entry (ni, pos(ni), ni) in its routing table

2. If S does not hear from a neighbor n i for a while, it removes all entries of the form (di, pi, ni) from its routing table

3. If Table(S) contains the entry (di, pi, ni) and S receives Table(ni) which contains the entry (di, pj, -), then S updates its entry to (d i, pj, ni ,-)

4. If Table(S) contains the entry (di, pi, ni ) and S receives Table(ni) which does not contain an entry (d i,--, --), then S removes the entry (di, pi, ni )

5. After any change to its routing table, S broadcasts the new Table(S)

Average Number of Neighbors

Mean Routing Table Size

GRA protocol packets per node

Time to Converge (in seconds)