On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar...
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![Page 1: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/1.jpg)
On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic
Sundar Subramanian, Sanjay Shakkottai and Piyush GuptaINFOCOM 2007
![Page 2: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/2.jpg)
Outline Introduction Network Model Randomway Algorithm Routing for non-uniform traffic patterns Extending non uniform traffic to networks with Holes Conclusion
![Page 3: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/3.jpg)
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
![Page 4: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/4.jpg)
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
![Page 5: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/5.jpg)
Introduction
![Page 6: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/6.jpg)
Introduction
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Introductionswitching to a boundary tracing scheme
![Page 8: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/8.jpg)
Introduction
![Page 9: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/9.jpg)
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
![Page 10: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/10.jpg)
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
![Page 11: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/11.jpg)
Network Model Network Model
nodes are uniformly and randomly distributed over a unit toroidal region Nodes have a uniform circular transmission range
![Page 12: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/12.jpg)
Network Model To model the effect of network
“holes” due to various factors physical obstacles clusters of failed nodes
![Page 13: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/13.jpg)
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
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Randomway (n,K) Algorithm To have a few extra fields
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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
![Page 19: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/19.jpg)
Randomway (n,K) Algorithm(2) The Rlog(n) packets are routed from the source in a Greedy geographic manner to the location in NEXTDEST.
![Page 20: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/20.jpg)
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
![Page 21: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/21.jpg)
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
![Page 22: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/22.jpg)
Randomway (n,K) Algorithm
![Page 23: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/23.jpg)
Randomway (n,K) AlgorithmFor general Geographic forwarding based
X
![Page 24: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/24.jpg)
Randomway (n,K) AlgorithmFor general Geographic forwarding based
![Page 25: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/25.jpg)
Randomway (n,K) Algorithm
X
X
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Randomway (n,K) Algorithm
X
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Randomway (n,K) Algorithm
X
![Page 28: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/28.jpg)
Randomway (n,K) Algorithm
![Page 29: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/29.jpg)
Randomway (n,K) Algorithm
![Page 30: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/30.jpg)
Randomway (n,K) Algorithm
![Page 31: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/31.jpg)
Randomway (n,K) Algorithm
![Page 32: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/32.jpg)
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
![Page 33: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/33.jpg)
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
![Page 34: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/34.jpg)
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
![Page 35: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/35.jpg)
Routing for non-uniform traffic patterns Create √n routes simultaneously to the destination Using a three meta-hop path
![Page 36: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/36.jpg)
Routing for non-uniform traffic patterns
![Page 37: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/37.jpg)
Routing for non-uniform traffic patterns
![Page 38: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/38.jpg)
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)
![Page 39: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/39.jpg)
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
![Page 40: On Optimal Geographic Routing in Wireless Networks with Holes and Non-Uniform Traffic Sundar Subramanian, Sanjay Shakkottai and Piyush Gupta INFOCOM 2007.](https://reader036.fdocuments.in/reader036/viewer/2022062413/5a4d1b1a7f8b9ab059992f73/html5/thumbnails/40.jpg)
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
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Thank you!!