1. Wireless Network Capacity
Jamar Parris
Xi Liu

2. Areas Covered
Fixed Nodes
Mobility of Nodes

3. 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.
Fixed Nodes
Mobility of Nodes

4. 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
Fixed Nodes
Mobility of Nodes

5. 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
Fixed Nodes
Mobility of Nodes

6. 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
Fixed Nodes
Mobility of Nodes

7. 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.
Fixed Nodes
Mobility of Nodes

8. 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
Fixed Nodes
Mobility of Nodes

9. 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
Fixed Nodes
Mobility of Nodes

10. 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.
Fixed Nodes
Mobility of Nodes

11. Sphere
Fixed Nodes
Mobility of Nodes

12. 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
Fixed Nodes
Mobility of Nodes

13. 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.
Fixed Nodes
Mobility of Nodes

14. 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
Fixed Nodes
Mobility of Nodes

15. 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.
Fixed Nodes
Mobility of Nodes

16. 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.
Fixed Nodes
Mobility of Nodes

17. 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
Fixed Nodes
Mobility of Nodes

18. 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.
Database Synchronization
Fixed Nodes
Mobility of Nodes

19. 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.
Fixed Nodes
Mobility of Nodes

20. Two Scenarios Used Mobile Nodes without Relaying
Mobile Nodes with Relaying
Fixed Nodes
Mobility of Nodes

21. 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.
Fixed Nodes
Mobility of Nodes

22. 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.
Fixed Nodes
Mobility of Nodes

23. 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.
Fixed Nodes
Mobility of Nodes

24. 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
Fixed Nodes
Mobility of Nodes

25. 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?
Fixed Nodes
Mobility of Nodes

26. 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
Fixed Nodes
Mobility of Nodes

27. 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.
Fixed Nodes
Mobility of Nodes

28. Phase 1 & Phase 2
Fixed Nodes
Mobility of Nodes

29. 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
Fixed Nodes
Mobility of Nodes

30. 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
Fixed Nodes
Mobility of Nodes

31. 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.
Fixed Nodes
Mobility of Nodes

32. 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
Fixed Nodes
Mobility of Nodes

33. 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
Fixed Nodes
Mobility of Nodes

34. 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
Fixed Nodes
Mobility of Nodes

35. Throughput Comparison
Sender Centric Receiver Centric
Fixed Nodes
Mobility of Nodes

36. 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
Fixed Nodes
Mobility of Nodes

37. 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
Fixed Nodes
Mobility of Nodes

38. 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
Fixed Nodes
Mobility of Nodes

39. 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

40. 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

41. Capacity of A Chain of Nodes - Analysis1 2 3 4 6
Radio Range of Node
(200 m)
Interference Range of Node 4 5

42. Capacity of A Chain of Nodes - Analysis1 2 3 5 6 4
Radio Range of Node
Interference Range of Node 4

43. Capacity of A Chain of Nodes - Analysis
Total Max. Channel Utilization = 1/4 1 2 3 5 6 4
Radio Range of Node
Interference Range of Node 4

44. Capacity of A Chain of Nodes – Simulation
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
It is possible to achieve ¼ under MAC
failed to find an optimal schedule
Backoff waste
500 B
1500 B
64 B

45. Discrepancy Backoff wastage: large backoff at node 1 (5.4%) 1 2 3 4 6
Radio Range of Node
Interference Range of Node 5

46. Capacity of A Regular Lattice Network
Two communication patterns
Scenario #1
Scenario #2

47. 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

48. Capacity of A Regular Lattice Network
Expected:
(1/12) * 1.7 = 0.14 Mbps
Observed:
0.1 Mbps
Discrepancy:
Same as in chain

49. Capacity of A Regular Lattice Network
Traffic flow direction
Scenario #2
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)

50. Capacity of A Regular Lattice Network
Slightly less than half of the per-flow throughput without cross traffic
Possible Problem :
Head of queue block

51. Capacity of Random Network
Expect to see similar total capacity to lattice network
No dramatically loss
1) Hole in area
2) Center is more susceptible to congestion

52. Traffic Pattern Random traffic pattern Scalable 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

53. 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

54. 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

55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

61. Routing Shortest path is not enough Interference-aware routing
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 MAC

62. 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

63. 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

64. 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

65. Results No degradation when c/m = O(log n)
If c = O(log n), then m = 1 suffices
For Random network:

66. 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

67. 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

68. Question:
What are the fundamental limitations of wireless network?

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

70. Thanks!
Question?
Suggestion?

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