1. Ulas C. Kozat Leandros Tassiulas Mibocom’03
Throughput Capacity of Random Ad Hoc Networks with Infrastructure Support
Ulas C. Kozat
Leandros Tassiulas
Mibocom’03
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2. Motivation
Throughput capacity with support of infinite capacity infrastructure network
Per-source node capacity
Compared with random ad hoc network without infrastructure
Assumption
Random network in a disk
# of ad hoc nodes / access point  Upper bounded
W bits/sec with fixed transmission range
N ad hoc nodes form a connected topology graph  release later
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3. Outline System Model Condition Conclusion Strong Connectivity
Weak connectivity
Partition, reduce transmission power, less interference, more simultaneous transmission
Sufficient and necessary conditions of transmission power
Constant bit rate cannot be achieved
Achievable capacity
Conclusion
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4. Two-tier Illustration
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5. System Model N, K Transmission is fixed Interference Model
number of ad hoc nodes and access points
lim N∞(N/K)=α
Transmission is fixed
Can be arbitrarily small as long as connectivity is maintained
Weakly or strongly
Interference Model
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6. Interference Model Protocol model
successful transmission  no other transmitters within a distance (1+D)r of the receiver, where r is the distance from the sender to the receiver
receiver
sender r
(1+D)r m j
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7. Outline System Model Condition Conclusion Strong Connectivity
Weak connectivity
Sufficient and necessary conditions of transmission power
Constant bit rate cannot be achieved
Achievable capacity
Conclusion
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8. Capacity Improvement with Infrastructure Layer
Per node throughput
Key: Make h(N, K) = Θ(1) Access to GW is not the bottleneck
Strong Connectivity rT>=sqrt(logN/πN)
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9. _____W______ (C+1)*{log(N+K)+1}
Intuition
_____W______ (C+1)*{log(N+K)+1}
λ(N,K)>=
=W / logN
Interference Cell <=C 1.
3. Θ(1)
2. Θ(log(N+K))
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10. The left  task1 and 3
Each Voronoi cell includes at least one access point
The number of destination nodes per access point within a Voronoi cell is Θ(1)
# Access points in a cell is Θ(log(N+K))
# destination nodes in a cell is O(log(N+K))
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11. Outline System Model Condition Conclusion Strong Connectivity
Weak connectivity
Sufficient and necessary conditions of transmission power
Constant bit rate cannot be achieved
Achievable capacity
Conclusion
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12. Weak Connectivity
Each ad hoc node should be connected to at least one access point with high probability
K GW
ACi(Xi): capture area
Aє: disk area є=rT
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13. Probability for being connected to AP
Lower bound
Upper bound 1-P(disconnected)
 - ∞
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14. Weak Connectivity Condition
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15. Unachievable of Θ(1) πrT2>c3/K  rT>c4/sqrt(N/π)
Under weak connectivity, per node transport capacity of Θ(1) cannot be achieved with p=1 
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16. Outline System Model Condition Conclusion Strong Connectivity
Weak connectivity
Sufficient and necessary conditions of transmission power
Constant bit rate cannot be achieved
Achievable capacity
Conclusion
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17. Achievability of Capacity
Nuances: Non-uniform distribution
Aє(N)=g(N)/N,
Lim x∞x2 (Aє(N))’=-∞
Upper bound of per node throughput
Each cell includes Θ(g(N)) ad hoc nodes.
g(N)/N needs to be defined
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18. Conclusion Per source throughput in Hybrid Network Weak connectivity
Is Θ(sqrt(N/logN)) better than random ad hoc network without infrastructure
Gain is from hop reduction
Weak connectivity
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