Capacity of wireless ad-hoc networks By Kumar Manvendra October 31,2002.

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



1 2 3 4 6

Radio Range of Node(200 ms) Interference Range of Node 4

5


1


2 3 4 6

Radio Range of Node(200 ms) Interference Range of Node 4(550

ms)

5


1


2 3 4 6

Radio Range of Node

5


ms)


1


2 3 4 6

Radio Range of Node

5

Assuming radios of non-neighboring nodes do not interfere with each other


ms)


1


2 3 4 6


5

Assuming radios of non-neighboring nodes do not interfere with each other

Total Max. Channel Utilization = 1/3


1


2 3 4 6


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


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


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

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

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

Capacity of wireless ad-hoc networks By Kumar Manvendra October 31,2002.

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