Wireless Network Capacity Jamar Parris Xi Liu. Areas Covered Fixed Nodes Mobility of Nodes

Wireless Network Capacity

Jamar Parris

Xi Liu

Areas Covered

Fixed Nodes Mobility of Nodes

Focus

All wireless networks Causes issues:

Medium access issues No centralized control complicates matters

Physical layer issues Transmission power must be high enough to reach

receiver whilst causing minimal interference to others.


Useful Information

Packets sent in multi-hop fashion Packets can be buffered at intermediate

nodes Several nodes can transmit simultaneously

provided no interference from others Two types of networks considered:

Arbitrary Networks Random Networks


Arbitrary Networks

Node locations, destinations, traffic demands, range are all arbitrary.

2 models used to describe successful transmission from hop to hop: Protocol Model Physical Model

Adds a signal to interference ratio Adds a ambient power level


Arbitrary Networks

Assume 1 bit meter is when one bit is transported the distance of 1 meter

Multiple credit not given for same bit carried to several destinations e.g. multicast

Sum of products of bits and distances over which they are carried indicates transport capacity


Arbitrary Networks – Results

Transport capacity under Protocol Model is

This depends on: Nodes being optimally placed Traffic pattern optimally chosen Transmission range being optimally chosen.


Transport & Throughput Capacity If the capacity were to be equally divided,

each node would get Now if source and destination pair were 1m

away Throughput and Transport Capacity would be

equal It should be noted that transport capacity

increases when the signal power decays more rapidly with distance


Random Networks

Each node randomly chooses destination Destination chosen independently as the

node closest to a randomly located point All transmissions use the same range Nodes are randomly located either on the

surface of a sphere or in a plane


Random Networks

Sphere: Every node in a cell is within range of every other

node in its own cell or adjacent cells If two cells are not interfering neighbors than their

transmissions cannot collide. Number of interfering neighbors are bounded so

that each cell has chance to transmit. Each cell contains at least one node to make

relaying feasible.


Sphere


Random Networks

Also uses Protocol & Physical Model Uses Different Criteria for successful transmission Under Protocol Model - Results

Results same for both the sphere and plane Throughput Capacity is

Throughput constriction is caused by the need for all nodes to share the channel with other nodes

Under Physical model, throughput capacity is


Relay Nodes

Idea is to add additional nodes who only relay packets and are not themselves sources

This allows for an increase in throughput However, number of relay nodes to have an

significant increase in capacity can be large. For example, with 100 nodes, to make

capacity equal to five times its value when there are no relay nodes, you need 4476 relays.


Trade-Offs

Throughput versus range Increasing range of each node would reduce hops

traversed. However, since nodes close to receiver need to be idle to avoid collision, throughput would actually decrease.

Actually reducing range to as small as possible is what’s needed.

However, range can only get so small before the network loses connectivity


Inferences of the paper

Maybe you should group nodes into cells and then designate one node to carry the burden of relaying multi-hop packets.

Maybe connect base stations by wired links to improve capacity.

If we assign a base station in each cell to communicate with other distant base stations wirelessly, base stations inherit same capacity limitation.


Inferences of Paper

According to tests, subdividing the channel W into W1, W2, etc. did not change anything.

As number of nodes increase throughput will also decrease.


Issues with this paper

Interference is not factored in Access to wireless channel not coordinated Mobility not included Link failures not included

Hence adapted and distributed traffic routing not included.

Claims that the above will only reduce capacity. Not all of these is necessarily true


Mobility of Nodes

Follows the same model, only nodes are mobile as opposed to fixed

Network Topology changes over time Incurs delay, good for applications that can

tolerate delays of minutes to even hours. E-Mail Database Synchronization


Mobility of Nodes

Transmit only when nodes are close to each other.

Reduces number of hops each packet must take, increasing throughput.

Each node has an infinite stream of packets to send to its destination.

The S-D association does not change over time, only the nodes themselves move.


Two Scenarios Used

Mobile Nodes without Relaying

Mobile Nodes with Relaying


Mobile Nodes without Relaying The problem with fixed nodes is that

throughput reaches zero because number of relay nodes packet must go through increases

In this scenario, we expect that any two nodes can be expected to be close to each other from time to time.

Improve capacity by not relaying at all and only let sources transmit directly to destinations.


Results

If the range is large (i.e. transmissions over long distances are allowed). many S-D pairs are within range.

Interference however will limit the number of concurrent transmissions over long distances

Makes throughput interference limited Also, if range is small, only a small fraction of S-D

pairs will be close enough to transmit a packet. Makes throughput distance limited. Throughput per session decreases as n gets larger

if only direct transmissions are allowed.


Mobile Nodes With Relaying

Problems with no relaying: Find a way to communicate only locally to

overcome interference limitation Find a way to ensure that there are enough

sender-receiver pairs to transmit to overcome distance limitation

Proposed Solution: Direct communication not enough, so introduce

relaying.


Basic Idea

Spread the traffic stream between the source and destination to a large number of intermediate relay nodes

Each packet goes through one relay that buffers the packet until final destination delivery is possible

For each S-D, every other node except S & D can serve as relay nodes

Goal is packets of every source node will be distributed across all nodes in the network


Basic Idea

This ensures that every other node in the network will have packets buffered destined to every other node not including itself

Hence, a sender-receiver pair always has a packet to send unlike in the case without relaying

How many times must a packet be relayed in order to spread traffic uniformly?


Number of Hops per packet

It turns out only one The probability of an arbitrary node to be

scheduled to receive a packet from source S in equal for all nodes and independent of S

Each packet therefore has to make only two hops Source to relay Relay to destination Total achievable throughput is


2 Phases

Phase 1 Scheduling of packet transmissions from source to relays

or from source to final destination in one hop if possible Phase 2

Scheduling of transmissions from relay to final destination or from source to destination if possible.

When a receiver is identified, sender checks to see if it has any packets for which receiver is the destination, if it is, it transmits.

In either phase, direct transmission is allowed since it is possible for a sender receiver pair to be a source destination pair as well.


Phase 1 & Phase 2


Centralized vs. Distributed Implementation This model allowed for central coordinated

scheduling, relaying and routing. Authors believe algorithm can be

implemented in a distributed manner as well In this case:

At each instant, node can randomly and independently determine if they want to be a sender or potential receiver

Each sender seeks out a receiver close to it and attempts to send data to it


Distributed Implementation

Same phases as in centralized Multiple senders may attempt to send to

same receiver Author’s analysis showed that probability of

success is reasonable even with many users


Problem

Since capacity in both phases are identical, delay experienced from source to destination can be infinite even for a finite number of nodes if capacity in phase 1 fully used.

Author Fix? Allow both source to relay and relay to destination

transmissions to occur concurrently but give priority to relay to destination transmissions.


Sender Centric versus Receiver Centric So far, sender selects the closest receiver to

send to What if receiver selects the closest sender

from which to receive? At first, it may seem that results should be the

same, but in fact this is not the case Problems occur if several receivers select the

same sender


Two possible outcomes

If the sender can only select one receiver to send to, sender-receiver pairs need to be eliminated,

If sender can generate multiple signals for several receivers, we need to account for the fact the desired signal is only a fraction of unit power.

Authors found no elegant want to integrate these complications into the proof


Receiver centric approach preferable If there is a single receiver This is due to the fact that the selected

sender always has the strongest signal In the receiver centric approach, interference

is smaller. Signal to interference ratio is larger in receiver

centric approach Throughput is also slightly higher than in the

sender centric approach


Throughput Comparison

Sender Centric Receiver Centric


Downlink & Uplink Throughput

Downlink: from source to all relays Uplink: from relays to destination Due to multi-user diversity, throughput of downlink is

high due to fact that at any one time a relay node is likely to be close to source

The same also applies for uplink This is in essence a statistical multiplexing effect

due to a large number of network users


Implications & Conclusions

Make use of delay tolerance of applications to improve throughput in a mobile wireless network

Impossible to support a high throughput per source-destination pair using direct communication, they are too far apart most of the time

This idea must be combined with a two hop strategy to achieve high throughput

Drastic improvement in throughput over fixed nodes in previous paper


Problems with this model

Nodes have entirely random mobility patterns. What if mobility is constrained? Delay increases as the system gets larger but at the

same time so does throughput No constraint on delay imposed This implies that with a constraint on delay imposed

the maximum achievable throughput must decrease. Must balance throughput and delay


Capacity of Ad Hoc Network

Examine the capacity at a detailed level Single Cell Capacity Capacity of a Chain of Nodes Capacity of a Regular Lattice Network Capacity of Random Network

Some conditions that per-node capacity scales Local traffic pattern

Capacity of A Single Cell

All nodes can hear each other Four-way handshake

2Mbps Expect to see 1.8Mbps for 1500B data packet if

control overhead is counted 1.7Mbps if IFS is counted

Capacity of A Chain of Nodes - Analysis

1 2 3 4 6

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

5


1 2 3 4 6

Radio Range of NodeInterference Range of Node 4

5


1 2 3 4 6

Radio Range of NodeInterference Range of Node 4

5

Total Max. Channel Utilization = 1/4

Capacity of A Chain of Nodes – Simulation

64 B

500 B

1500 B

Node 1 sends as fast as its MAC allows

With Longer Chains, Utilization levels go substantially low.

For a 1500 Byte packet size, it is as low as 15% (1/7) of 1.7Mbps

1) It is possible to achieve ¼ under 802.11 MAC

2) 802.11 failed to find an optimal schedule

3) Backoff waste

1 2 3 4 6

Radio Range of Node Interference Range of

Node

5

Discrepancy

Backoff wastage: large backoff at node 1 (5.4%)

Two communication patterns

Scenario #1 Scenario #2

Capacity of A Regular Lattice Network

Scenario #1

Internode Distance = 200 m Interference radius = 550 m

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



Expected: (1/12) * 1.7 =

0.14 Mbps Observed:

0.1 Mbps Discrepancy:

Same as in chain

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

3) Per-flow throughput is expected to be (1/24)


Slightly less than half of the per-flow throughput without cross traffic

Possible Problem :

Head of queue block


Capacity of Random Network

Expect to see similar total capacity to lattice network

No dramatically loss1) Hole in area2) Center is more

susceptible to congestion

Traffic Pattern

Random traffic pattern The capacity available to each node is

O(1/sqrt(n)) Scalable traffic pattern

Exactly local traffic: fixed distance Power law distance distribution: if the distance

distribution decays more rapidly than the square of distance

The basic idea is that the average path length in scalable traffic pattern should be kept constant

Impact of Interference on Multi-hop Wireless Network Performance Framework to answer questions about the

capacity of specific topologies with specific traffic pattern

Assumptions No mobility Fluid model Centralized scheduler

The basic idea is to model as a standard network flow problem with wireless constraints

Network Flow Model Connectivity graph

Each vertex represents a wireless node Directed edge from A to B if B is within range of A

Linear programming that solves the MAXFLOW problem

Conflict Graph (Contention Graph) Each edge in the connectivity graph (link)

represented by a vertex in conflict graph An undirected edge between two vertices

(links) if one link will interfere with the other If there are an edge between two links, then the

two links cannot transmit together

Clique Constraints Cliques in conflict graph

At most one link in a clique can be active at any instance

Augment MAXFLOW LP to get upper bound

Properties of Clique Constraints Finding all cliques takes exponential time Even if all cliques are found, no optimality is

guaranteed More cliques added, more tight the bound Tradeoff between computation and

performance

Independent Set Constraints All links belong to an independent set can be

active together No two independent sets can active at the

same time Augment MAXFLOW LP to get lower bound

Properties of Independent Set Constraint Lower bound is always feasible

LP can output a schedule Finding all independent sets takes

exponential time The lower bound is optimal is all independent sets

are found Lower bound will increase if we add more

independent sets If upper and lower bound converge, the

optimality is guaranteed

Some Generalizations

Multiple radio on orthogonal channels Multiple, non-interfering links between nodes

Directional antenna Appropriate edges in connectivity graph Conflict graph can also accommodate

Multiple sender/receiver Multi-commodity flow problem for LP

Routing

Shortest path is not enough Channel quality should be considered May introduce congestion

Interference-aware routing Prefer routes that use up minimum amount of

spectrum resource Advantageous sometimes even with 802.11 MAC

Limitations

Computation cost 2-5 minutes for ~100 nodes

No guarantee to get optimal schedule in polynomial time

Change in conflict graph Slow vs. fast change

Fairness is bad

Capacity of Multi-Channel Wireless Networks Multiple channels share a fixed bandwidth Consider multiple channels and multiple

interfaces in networks # of channel c, # of interface m per node

What if we use less interfaces than channels m < c Intuitively, capacity degradation may occur

Results

The capacity is dependent on the ratio c/m, and not on the exact value of either c or m

For Arbitrary network:

There is always a capacity loss

Results

No degradation when c/m = O(log n) If c = O(log n), then m = 1 suffices

For Random network:

Capacity of Power Constrained Ad-hoc Network Consider model with low spectral efficiency

Arbitrary large bandwidth Power constrained

Two applications UWB Sensor network

The result is that throughput increases with node enter the network

Intuition

SINR = Signal / (Noise + Interference) Noise = noise density * bandwidth

In bandwidth-constrained scenario, SINR is dominated by interference

In low spectral efficiency, SINR is mainly affected by ambient noise

Question:

What are the fundamental limitations of wireless network?

Summary – Factors Influencing Capacity Node placement Traffic pattern Static / Mobile Available Bandwidth Multi-Channel Infrastructure support Directional / Omnidirectional antenna

Thanks!

Question? Suggestion?

Reference

P. Gupta and P. R. Kumar, " The capacity of wireless networks,'' IEEE Transactions on Information Theory , vol. IT-46, no. 2, pp. 388-404, March 2000

Capacity of power constrained ad-hoc networks , Arjunan Rajeswaran, Rohit Negi, IEEE Infocom 2004, Hong Kong, March 2004.

Jinyang Li, Charles Blake, Douglas S. J. De Couto, Hu Imm Lee, and Robert Morris, Capacity of Ad Hoc Wireless Networks, Proceedings of the 7th ACM International Conference on Mobile Computing and Networking (MobiCom '01), Rome, Italy, July 2001, pages 61-69

Kamal Jain, Jitendra Padhye, Venkata N. Padmanabhan, and Lili Qiu. Impact of Interference on Multi-hop Wireless Network Performance. In Proc. of ACM MOBICOM, San Diego, CA, September 2003

Matthias Grossglauser and David Tse. Mobility Increases the Capacity of Mobile Ad-hoc Wireless Networks. IEEE/ACM Transactions on Networking, Vol. 10, No. 4, Aug. 2002

Pradeep Kyasanur and Nitin Vaidya. Capacity of Multi-Channel Wireless Networks: Impact of Number of Channels and Interfaces In Proc. of ACM MobiCom 2005, Aug. - Sept. 2005

Abbas El Gamal, James Mammen, Balaji Prabhakar, and Devavrat Shah. Throughput-Delay Trade-off in Wireless Networks. Proc. of IEEE INFOCOM, March 2004.

Documents

Wireless Network Capacity Jamar Parris Xi Liu. Areas Covered Fixed Nodes Mobility of Nodes