View
39
Download
1
Category
Preview:
DESCRIPTION
Measuring and Modeling the Impact of Wireless Interference. Lili Qiu UT Austin Rice University Nov. 21, 2005. Introduction. Wireless interference affects network capacity. 1 Mbps. 1 Mbps. 1 Mbps. A. B. D. C. Throughput = 2 Mbps. 1 Mbps. 1 Mbps. 1 Mbps. A. B. D. C. - PowerPoint PPT Presentation
Citation preview
1
Measuring and Modeling the Impact of Wireless Interference
Lili QiuUT Austin
Rice UniversityNov. 21, 2005
2
IntroductionWireless interference affects network capacity
1 Mbps 1 Mbps
Throughput = 2 Mbps
Throughput = 1 Mbps
A B DC
1 Mbps
1 Mbps 1 Mbps
A B DC
1 Mbps
3
Capacity of Wireless Networks• Many research on computing capacity of
multi-hop wireless networks
• Most of it focuses on asymptotic performance bounds– Gupta and Kumar 2000:
• O(1/sqrt(N)) under optimal node placement• O(1/sqrt(NlogN)) under random node placement
4
Community Networking Scenario
Asymptotic analysis is not useful in this case
4 houses talk to the central ITAP. What is the maximum possible throughput?
5
Capacity of Wireless Networks
• A framework to compute network capacity of specific topologies with specific traffic patterns– Our Mobicom 03 paper, joint work with
Jain, Padhye, and Padmanabhan
6
Assumptions• Fluid model of data transmission
• Data transmissions can be finely scheduled by an omniscient central entity– The derived network capacity is under optimal
scheduling and optimal routing– Applications
• Assess the efficiency of the existing network protocols
• Help network provision (e.g., what-if analysis)
7
Interference Models• Protocol model
– Transmission is successful if d(i,j) R(i) and any node k with d(k,j) R’(k) is not tranmitting
– Binary interference model
• Physical model– Transmission is successful if SNR(i,j)
threshold– Non-binary interference model
8
Overview of Our Framework1. Model the problem as a standard network
flow problem• Described as a linear program
9
Step 1: Network Flow Model• Create a connectivity graph
– Each vertex represents a wireless node– Draw a directed edge from vertex A to vertex B
if B is within range of A
• Write a linear program that solves the basic MAXFLOW problem on this connectivity graph
• Several generalizations possible– Discussed later in the talk.
10
Example: Network Flow Model
A (Sender) C (Receiver)B
Linear Program:
Maximize Flow out of A
Subject to:
1. Flow on any link can not exceed 1
2. At node B, Flow in == Flow out.
Answer: 1 (Link 1, Link 2)
A B C
Connectivity Graph
Link capacity = 1
21
4 3
11
Overview of Our Framework1. Model the problem as a standard network
flow problem• Described as a linear program
2. Represent interference among wireless links using a conflict graph
12
Step 2: Model Interference using Conflict Graph
• A conflict graph that shows which wireless links interfere with each other
• Represent each link in the connectivity graph by a vertex in the conflict graph
• Draw an edge between two vertices if the wireless links interfere with each other
• Several generalizations possible– Discussed later in the talk.
13
Example: Conflict GraphConnectivity Graph
A B C
1
4
2
3
1 2
3 4
Conflict Graph
14
Overview of Our Framework1. Model the problem as a standard network
flow problem• Described as a linear program
2. Represent interference among wireless links using a conflict graph
3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper
bound on optimal throughput
15
Step 3: Clique Constraints• At most one of the vertices in a clique can
be active at any given instant– Total utilization of links belonging to a clique is
100%
• MAXFLOW LP can be augmented with these clique constraints to get a better upper bound
• Speed-up convergence: consider maximal cliques in the conflict graph– A maximal clique is a clique to which we can not
add any more vertices
16
Example: Clique Constraints
Link capacity = 1
Linear Program:
Maximize Flow out of A
Subject to:
1. Flow on any link can not exceed 1 * link utilization
2. At node B, Flow in == Flow out.
3. Sum of utilizations of links 1, 2, 3 and 4 (a clique) can not exceed 100%
1 2
3 4
Clique = {1, 2, 3, 4}
A B C
1
4
2
3
Answer = 0.5 (Link1, Link 2)
17
Properties of Clique Constraints
• Finding all cliques can take exponential time– Moreover, finding all cliques does not guarantee
optimal solution (due to odd holes and odd anti-holes)
• The upper bound is monotonically non-increasing as we find and add new cliques– As we add each clique, the link utilizations are
constrained further
• More computing time can provide better solution
18
Overview of Our Framework1. Model the problem as a standard network flow
problem• Described as a linear program
2. Represent interference among wireless links using a conflict graph
3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper bound on
optimal throughput
4. Derive constraints on utilization of wireless links using independent sets in the conflict graph • Augment the linear program to obtain lower bound on
optimal throughput
19
Step 4: Independent Set Constraints
• All links belonging to an independent set can be active at the same time
• No two independent sets are active at the same time
• MAXFLOW LP can be augmented with constraints derived from independent sets to get a lower bound
• Speed up convergence: consider maximal independent sets in the conflict graph– An independent set to which we cannot add
any nodes
20
Example: Independent Set Constraints
Link capacity = 1
Linear Program:
Maximize Flow out of A
Subject to:
1. Flow on any link can not exceed 1 * link utilization
2. At node B, Flow in == Flow out.
3. Sum of utilizations of all independent sets can not exceed 100%
4. Utilization of a link can not exceed the sum of utilization of independent sets it belongs to.
1 2
3 4
Independent sets: {1}, {2}, {3}, {4}
A B C
1
4
2
3
Answer = 0.5 (Link1, Link 2)
21
Properties of Independent Set Constraints
• Lower bound is always feasible – LP also outputs a transmission schedule
• Finding all independent sets can take exponential time– If we do find all independent sets, the resulting lower bound is
guaranteed to be optimal
• Lower bound is monotonically non-decreasing as we find and add more independent sets– More computing time provides better answers
• If upper and lower bounds converge, optimality is guaranteed
22
Putting It All Together1. Model the problem as a standard network flow
problem• Described as a linear program
2. Represent interference among wireless links using a conflict graph
3. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper bound on
optimal throughput
4. Derive constraints on utilization of wireless links using independent sets in the conflict graph • Augment the linear program to obtain lower bound on
optimal throughputIterate over steps 3 and 4 to find progressively tighten bounds on optimal throughput
23
Putting It All Together (Cont.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120
IterationsN
orm
aliz
ed T
hrou
ghpu
t
Upper Bound
Lower Bound
Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing
24
What-if Analysis
Scenario Aggregate Throughput
Baseline 0.5
Double range 0.5
Two ITAPs 1
Two Radios 1
Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing
25
Physical Interference
• Represent wireless links as vertices in conflict graphs
• Directed conflict graph
• Weight on edge X->Y represents the fraction of the maximum permissible noise at the receiver of link Y when link X is active
• Schedulable sets instead of independent sets
• Non-schedulable sets instead of cliques
26
Other Generalizations• Multiple senders and/or receivers
– Write LP to solve multi-commodity flow problem
• Non-greedy sender– Create a virtual sender– Include a “virtual link” of limited capacity from the virtual
sender to the real sender in the connectivity graph– This link does not conflict with any other links– LP maximizes flow out of virtual sender
• Single path routing– Integer linear programming
• Multiple radios on orthogonal channels– Represent with multiple, non-interfering links between
nodes
• Directional antennas– Include appropriate links in the connectivity graph– Conflict graph can accommodate any interference pattern
27
Other Generalizations (Cont.)
• Multirate radios• Create multiple virtual links corresponding to a
physical link, one for each data rate• Only one of the virtual links corresponding to a
physical link can be active at a time• The edge weights (under physical interference
model) reflect the specific noise tolerance for each rate
• Other objectives• Any linear function (e.g., fairness or revenue)
can be used
28
Limitations• Linear programs can take a long time to
solve– Especially when single path routing is used
• There is no guarantee that optimal solution will be found in less than exponential time
• Upper bound might not converge to optimal even if we find all cliques– Graphs with odd-holes and anti-holes
29
Summary• A flexible framework for deriving capacity of
specific topologies with specific traffic patterns– Computes upper and lower bounds on optimal
throughput – Accommodate various models of network
connectivity and interference, routing constraints, traffic demands
• How to get a conflict graph for a given network?– IMC 05 paper, joint work with Padhye, Agarwal,
Padmanabhan, Rao, and Zill
30
Estimate Wireless Interference• What is the metric to quantify wireless
interference?– Interference is not a binary relationship
• How to estimate wireless interference?– Using heuristics– Using empirical measurement
31
Pairwise Interference Metric• Two links, A->B and C->D
– Throughputs U1 and U2 when operating individually
– Throughputs U1’U1’ and U2’U2’ when operating simultaneously
• Link Interference Ratio (LIR) = (U1U1/ / +U2U2/ / ) / (U1 + U2)– LIR = 1 implies no interference– LIR < 1 implies interference– Not just binary: full range of values between 0 and 1.
• Challenge: Estimate LIR for all link pairs without requiring O(n4) experiments
32
Existing Heuristics• Heuristic 1
– All links in the multi-hop network interfere with each other
– Pessimistic Model• Heuristic 2
– Links which share an endpoint interfere with each other
– Optimistic Model• Heuristic 3
– Links AB and CD interfere if
33
Evaluation of Heuristics• Experimental Setup
– A testbed of 22 nodes, 802.11 wireless cards,RTS/CTS disabled, 75 random links selected,1000 byte UDP packets for 30 seconds
34
Proves 1st
heuristic wrong
Proves 2nd heuristic wrong
Median LIR of 75 links
Experimental results showed3rd to be pessimistic model
Existing heuristics are inaccurate. We need to look for methods to empirically measure wireless interference.
35
Impact of Interference on Unicast Transmissions: #1
• Carrier sense– A and C can hear each other. – Only one transmits at a time.
A B
C D
36
Impact of Interference on Unicast Transmissions: #2
• Collision of data packets– Transmissions from A and C collide at B– Reception of data fails at B
A B
C D
37
Impact of Interference on Unicast Transmissions: #3
• Collision of data and ACK packets– ACK from D collides with data from A– Reception of data fails at B
A B
CD
38
Impact of Interference on Unicast Transmissions: Other
Cases4. Data/ACK collision prevents reception of
ACK5. ACK/ACK collision
39
Impact of Interference on Unicast Transmissions
1. Carrier sense2. Data/Data collision3. Data/ACK collision prevents reception of
data4. Data/ACK collision prevents reception of
ACK5. ACK/ACK collision
40
Key Idea• Only consider carrier sense (#1) and data
packet collisions (#2)– Ignore ACKs
• Broadcast packets are sufficient for measurements– Consider only sender pairs, instead of link pairs– O(n2) experiments instead of O(n4)
41
Methodology
Measure A’s receive rate @ B = M
Measure C’s receive rate @ D = N
Measure A’s receive rate @ B = M//
Measure C’s receive rate @ D = N//
Broadcast Interference Ratio (BIR) = (B1/ + B2/) / (B1 + B2)
A
C
D
B
= 1 no interference< 1 interference
Pairwise InterferenceIndividual Broadcasts
Hypothesis: BIR is a good approximation of LIR
BIR for all pairs can be calculated with O(n2) experiments
BIR Captures1. Carrier sense2. Data/Data collisions
BIR Ignores1. Data/ACK collisions2. ACK/ACK collsions3. AutoRate
42
Evaluation: Baseline Scenario
Median LIR and BIR of 75 pairs CDF of |LIR-BIR|
802.11a, full power, 6Mbps, no RTS/CTS. 75 link pairs selected at random.
Average of 5 runs
Median error is zero!
43
Evaluation: Other Scenarios
Three other scenarios 5 days apart
44
Summary of results• BIR is a good approximation for LIR in
various scenarios – Low power– 802.11 a/b/g– Autorate
• BIR experiments need to be repeated regularly as link interference patterns change over time.
45
Future work• More evaluation:
– On different testbeds
– Different power levels
• Interference among larger groups of links (not just pairs)
• Further reduce measurement overhead– Combine heuristics with measurements– Leverage passive measurement
46
Thank you!
Recommended