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Capacity of wireless ad-hoc networks
By Kumar ManvendraOctober 31,2002
Outline
Problem definition What is meant by the “capacity” ? Why is it relevant ?
What are the issues involved ? Example scenarios with various
simulation environments Performance results
Open problems Summary Future Work References
Problem Definition Capacity of Ad-Hoc Wireless Networks
A measure of the amount of data that can be transmitted simultaneously in an ad-hoc wireless network
Alternative explanation: Lack of congestion losses and misrouting of packets
Problems Overall capacity decreases with increase in non-
local traffic and number of nodes because they have to forward each other’s packets
Spatial reuse doesn’t seem to help that much
Factors influencing Capacity Traffic Pattern
Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size
Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-
hoc network
Need to explain the issues involved
Gupta and Kumar[3] showed that for static nodes, as number of nodes per unit area,n, increase …the throughput per source-destination pair decreases like 1/SQRT(N)
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of NodeInterference Range of Node 4
5
Inter-nodal distance = 200 ms
Example #1 : Capacity of a chain of nodes
MAC interference among a chain of nodes
1 2 3 4 6
Radio Range of Node(200 ms) Interference Range of Node 4
5
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of Node(200 ms) Interference Range of Node 4(550
ms)
5
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of Node
5
Radio Range of Node(200 ms) Interference Range of Node 4(550
ms)
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of Node
5
Assuming radios of non-neighboring nodes do not interfere with each other
Radio Range of Node(200 ms) Interference Range of Node 4(550
ms)
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of NodeInterference Range of Node 4
5
Assuming radios of non-neighboring nodes do not interfere with each other
Total Max. Channel Utilization = 1/3
Example #1 : Capacity of a chain of nodes
1
MAC interference among a chain of nodes
2 3 4 6
Radio Range of NodeInterference Range of Node 4
5
Assuming interference range interfere with non-neighboring nodes
Total Max. Channel Utilization = 1/4
Simulation Performance Results – single chain of nodes
64 B
500 B
1500 B
With Longer Chains, Utilization levels go substantially low.
For a 1500 Byte packet size, it is as low as 15%
Simulation Performance Results – single chain of nodes
64 B
500 B
1500 B
With Longer Chains, Utilization levels go substantially low.
For a 1500 Byte packet size, it is as low as 15%
Mimics results from actual hardware testing also
1) 802.11 is incapable of discovering an optimal schedule of transmissions
2) Inherent unfairness because nodes at the end send in more packets than nodes in the middle can forward
3) Back-offs cause wastage
Analysis of Performance Results
With increase in the length , per node
Interference increases.
So, per node waste of bandwidth
increases.
For example, in the example above,
Node #1’s send rate is 0.48 while nodes further along the link can only forward at the rate of 0.26-0.35
2 3 6
Radio Range of Node Interference Range of
Node 4
1 4
Analysis of Performance Results
Waste in terms of back-off
Periods
For Example : Node #1 wasted back-off time is 5.4% of total time
1 2 3 4 6
Radio Range of Node Interference Range of
Node
5
Two communication patterns
Example #2 : Capacity of a regular lattice network
Scenario #1 Scenario #2
Scenario #1
Example #2 : Capacity of a regular lattice network
Internode Distance = 200 ms Interference radius = 550 ms
Every third row can operate Without interference to give a Maximum throughput of 1/4
Thus flow in such a lattice network is expected (theoretically) to reach 1/12
Performance Results for Lattice simulations
60 B
500 B1500 B
Same inefficiencies as in chain list :
Disproportionate traffic per node
And wasted back - off time( close to 0.75%)
Scenario #2
Example #2 : Capacity of a regular lattice network
Traffic flow direction
1) Optimal Scheduling possible with predetermined routes.
2) Overall throughput can be maximized (in theory) with one vertical flow in one time unit and horizontal flows in another
Performance Analysis
1500 B500 B
60 B
Possible Problem :
Since each node has a single queue per flow, if a packet to be sent horizontally is waiting for contention, the packet to be sent vertically might lose its chance to be sent
Wasted time due to Back-off as high as 2.25%
Example Scenario #3 : Random traffic random layout
Assuming total randomness of nodes placement and destination selection for each sending node.
Assuming pre-computed paths
Performance Results – comparison with lattices 1500 Bytes packets
horizontal
Horizontal and vertical
random
Random networks have somewhat less capacity than lattices because more packets routed through the center of the network, and not enough spatial reuse
Another Perspective :Load imposed due to network’s nodes
One-hop capacity depends upon the amount of spatial reuse possible in the network and depends upon
Number of nodes Inter-nodal distance Physical area covered in the network
Mathematical analysis : For packet rate ,R,….communication radius, r And expected physical path length L
One Hop Capacity of the network to send and forward packets C > n . R . (L/r)
Assuming uniform node density, D, and number of nodes ,n …Capacity, C is also equal to k(n/D) , where k is a constant.
Therefore, per node capacity , R(packet rate), is R < k(r/D)*(1/L) = (C/n) / (L/r)
Factors influencing Capacity Traffic Pattern
Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size
Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-
hoc network
Factors influencing Capacity Traffic Pattern
Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size
Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-
hoc network
Factors influencing Capacity Traffic Pattern
Random Locality of Communication Long Range Interference Multiple antennas End-to-end delays Packet Size
Node Properties Node distribution Static / Mobile nodes Communication Radius and area of the ad-
hoc network
Another Perspective :Load imposed due to network’s nodes
One-hop capacity depends upon the amount of spatial reuse possible in the network and depends upon
Number of nodes Inter-nodal distance Physical area covered in the network
Mathematical analysis : For packet rate ,R,….communication radius,
r And expected physical path length L
One Hop Capacity of the network to send and forward packets C > n . R . (L/r)
Assuming uniform node density, D, and number of nodes ,n …Capacity, C is also equal to k(n/D) , where k is a constant.
Therefore, per node capacity , R(packet rate), is
R < k(r/D)*(1/L) = (C/n) / (L/r)
Recap
Per Node Capacity = (Average One hope Capacity) /
(Expected Path Length)
R = (C/n) / (L/r)
or
Inference : As expected path length increases, the bandwidth available to each node decreases.Inference: Since capacity is determined by traffic patterns, the most capacity enhancing traffic pattern is strictly local because expected path length remains constant
Recap
Per Node Capacity = (Average One hope Capacity) /
(Expected Path Length)
R = (C/n) / (L/r)
or
Inference : As expected path length increases, the bandwidth available to each node decreases.Inference: Since capacity is determined by traffic patterns, the most capacity enhancing traffic pattern is strictly local because expected path length remains constant
Effects of Mobility If a wireless network with many users, authors
contend that optimal strategy is to allocate the bandwidth to the user who can best use it.
Assumptions of asynchronous applications and high threshold of tolerable delays
On the above assumption, per node throughput can be kept constant
distributing packets to as many nodes as possible (each with difference time variance)
transmitting only when nodes are close together so as to minimize interference
And hence, probabilistically , maximizing the overall throughput
Summary
Capacity in an ad-hoc wireless network depends upon the following :
Number of nodes Density Traffic pattern Mobility Communication radius/interference
References
Capacity of Ad-Hoc wireless networks , Li, Blake, Couto, Lee, Morris
Mobility increases the capacity of ad-hoc wireless networks, Grossglauser, Tse
The Capacity of Wireless Networks, Gupta and Kumar