On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic

Sundar Subramanian, Sanjay Shakkottai and Piyush GuptaINFOCOM 2007

Outline Introduction Network Model Randomway Algorithm Routing for non-uniform traffic patterns Extending non uniform traffic to networks with Holes Conclusion

Introduction Geographic forwarding based

techniques have been widely suggested as an efficient routing method for wireless and sensor networks not required to maintain extensive

routing tables make simple routing decisions based on

the local geographic position

Introduction The geographic forwarding strategies in non-uniform networks

may fail due to a forwarding node does not have any neighboring nodes that are closer to the destination may get stuck in routing “holes” or local minima

Introduction

Introduction

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Introductionswitching to a boundary tracing scheme

Introduction

Introduction Currently known schemes only

allow for small variations (within Θ(1/√n)) in node data rates (The capacity of wireless networks)

Wireless networks may demand widely varying data rates mixture of video flows short messaging

Introduction -GOAL

Randomized geographic routing scheme that can achieve a throughput capacity Construct a geographic forwarding based routing scheme that can support wide variations in the traffic requirements

Network Model Network Model

nodes are uniformly and randomly distributed over a unit toroidal region Nodes have a uniform circular transmission range

Network Model To model the effect of network

“holes” due to various factors physical obstacles clusters of failed nodes

Network Model

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Network Model

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Network Model

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Network Model Assume n/2 random source nodes and randomly choose destination nodes for each traffic source node

uniformly and independently The throughput capacity T(n) of a network is defined as the maximum data-rate

Randomway (n,K) Algorithm To have a few extra fields

Randomway (n,K) Algorithm(1) The source node for every traffic flow creates Rlog(n) copies of its packet to send It chooses Rlog(n) independent and uniformly distributed points To sets the NEXT-DEST field to the randomly generated location in each of these copies WAYPOINT-NUM is set to 4K + 1

Randomway (n,K) Algorithm(2) The Rlog(n) packets are routed from the source in a Greedy geographic manner to the location in NEXTDEST.

Randomway (n,K) Algorithm(3) If it is not the NEXT-DEST location

it searches within its neighboring nodes is closest to the NEXT-DEST location

if none of its neighbor nodes are closer to the NEXT-DEST

drop the packet

Randomway (n,K) Algorithm(4) If it is the NEXT-DEST location

If WAYPOINT-NUM > 1 sets WAYPOINTNUM = WAYPOINT-NUM – 1 Repeat the first step

If WAYPOINT-NUM = 1, sets NEXT-DEST = FINAL-DEST WAYPOINT-NUM = 0

If WAYPOINT-NUM = 0, the packet is received at the destination

Randomway (n,K) Algorithm

Randomway (n,K) AlgorithmFor general Geographic forwarding based

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Randomway (n,K) AlgorithmFor general Geographic forwarding based

Randomway (n,K) Algorithm

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Randomway (n,K) Algorithm

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Randomway (n,K) Algorithm

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Randomway (n,K) Algorithm

Randomway (n,K) Algorithm

Randomway (n,K) Algorithm

Randomway (n,K) Algorithm

Randomway (n,K) Algorithm H(j) be the number of source-destination pairs that generate a line that touches tile j

2(Rlog(n))4K+1√n The number of paths passing though any tile j is at most

H(j) (Rlog(n))∗ 4K+1 = √n(Rlog(n))8K+2

Randomway (n,K) Algorithm The number of packet routes is no more than√n(Rlog(n))8K+2 T(n) = Θ( 1 /√n(log n)P ) P <∞ is achievable

Routing for non-uniform traffic patterns In many scenarios the traffic

demands could be non-uniform Video flows, short messaging

To provide a constructive scheme (RANDOMSPREAD) to distribute the traffic flows uniformly over the region

Routing for non-uniform traffic patterns Create √n routes simultaneously to the destination Using a three meta-hop path

Routing for non-uniform traffic patterns

Routing for non-uniform traffic patterns

Routing for non-uniform traffic patterns Partition the packet-routes in the network

into 4 disjoint classes T1: Packet routes generated by type-a source

nodes to their corresponding destinations. T2: Outward lines radiating from source

nodes to their first intermediate way-point T3: Inward lines radiating into destination

nodes from their last intermediate way-points T4: The rest of the packet routes generated

between the first and the last intermediate way-points

Type-a traffic requirement: Θ( 1 /√n) Type-b traffic requirement: Θ(1)

Extending non uniform traffic to networks with holes The modification to the RANDOMWAY(n,K) is only at the source nodes

If a source is a type-b node with Θ(1) traffic requirement transmits √n / (R log(n))P packets simultaneously

4K+2 way points

Conclusion Presented algorithms for

throughput optimal routing in networks with holes and non-uniform traffic preserve the inherent advantages of

geographic scalability and fast convergence

Thank you!!