A General Model of Wireless
Interference
L. Qiu, Y. Zhang, F. Wang, M.
Han, R. Mahajan
Mobicom 2007
A Model for ?
• Misleading title
– Nothing new about wireless interference
• Indeed, a model for predicting the
throughput/goodput of wireless networks
• Motivation
– Helpful in evaluating design/protocols (e.g.
channel assignment)
– Direct measurements alone is insufficient
• Lacks predictive power and scalability
Problem Statement
• Given characteristics of
– RSS between each pair
(RSSm,n)
– Background noise (Bn)
– Traffic demand between pairs
(dm,n)
• What is the pairwise
throughput/goodput?
• My dumb solution
– Calculate SINR at every node
– Throughput = B*log2(1+SINR)
Bn
RSSm,n
• Problems
– Non-constant RSS
– Ignoring Underlying MAC
Contributions
• State of the Art: only handle restricted traffic
– Only two senders or two flows
– Only broadcast traffic
– Only saturated demands
• Contributions
– Interference among an arbitrary number of senders
– Both broadcast and unicast traffic
– Both saturated and unsaturated demand
State of the Art
This paper
Its limit
Reality
Dumb solution
Limit of analytical methods
Overview of the Model
given
network
RF profile
measurement
pairwise
RSS
traffic
demand
sender
model
throughput
receiver
model
goodput
• How it works
– Measure pairwise RSS via broadcast probes
• One node broadcast at a time, others measure RSS  O(n)
probes
– Saturated broadcast sender/receiver models
• Markov-chain model
– Extend to unsaturated broadcast
– Extend to saturated/unsaturated unicast
Broadcast Sender: Overview
• Estimate how much a sender can send
– MAC: 802.11 DCF
• Markov chain (simplification #1)
– State i: a set of active nodes Si
– Stationary probabilities: i (fraction of time that the system is in state i)
– Throughput of node m: tm = ∑i|mSi i
00
0…1
01
0…0
0..10
.
11
10
1…1
. .
.
Broadcast Sender: Overview (Cont.)
• State transition probability
–
–
–
–
–
Staying idle: P00(n|Si)
Idle to active: P01(n|Si)
Active to idle: P10(n|Si)
Staying active: P11(n|Si)
Assume node independence (simplification #2)
• Compute stationary probabilities i by solving LP
– Highly efficient for sparse M
Broadcast Sender: Transition Probabilities
P01 (m | Si )
 Pr[ medium is clear & counter  0 & m has data]
 Pr[medium is clear]
 Pr[counter  0 | medium is clear]
 Pr[m has data | medium is clear & counter  0]
1
 C(m | Si )  __________ ___________  Q(m)
CW (m) OH (m)
where Q(m)  1 under saturated demands
P00 (m | Si )  1  P01 (m | Si )
Tslot
P10 (m | Si ) 
T (m)
P10 (m | Si )  1  P10 (m | Si )
T DIFS / t slot
CW min / 2
Simplification #3
Under the assumption that both transmission
and idle times are exponential (simplification #4)
Broadcast Sender: Clear
Probability
• C (m | S i )  Pr[ I m|S   m ]
i
• How to estimate Im|Si?
– Im|Si=Wm+Bm+∑sSi\{m} Rsm
– Assume each term is lognormal variable
(simplification #5)
– Approximate the sum using a lognormal
variable by matching mean and variance
Broadcast Sender:
Handle Similar Packet Sizes
• Synchronization occurs when packet sizes used by
different nodes are similar
– When several nearby nodes transmit together, they will end
transmission together
– Independence assumption fails
• Handle synchronization
– Construct synchronization graph Gsyn
• Two nodes are connected iff C(m|{n})  0.1 and C(n|{m})  0.1
– Find all synchronization groups
• Each connected component in Gsyn is a synchronization group
(simplification #6)
– If m and n in the same synchronization group
• mSj and n Sj’ M(i,j) = 0
• P10(mn|Si) = Tslot/T(m) instead of (Tslot/T(m))|G|
Broadcast Sender:
Handle Unsaturated Demands
• Estimate Q(m): probability m has data to send when its
backoff counter is 0 and channel is clear at m
• Under saturated demands, Q(m) = 1
• Under unsaturated demands, compute Q(m) iteratively to
ensure that demands are not exceeded
Initialize Q(m) = 1
Solve the Markov chain
Update Q(m)
Brief overview of other parts
• Broadcast Receiver
– Estimate packet loss rate
• Extending to unicast: challenges
– Binary backoff
• Sending rate depends on loss rates
– DATA losses due to collisions with ACKs
• Model ACK sending rate, which in turn depends on
DATA sending rate and loss rates
– Traffic demand
• Account for retransmissions
Simulation Evaluation:
Saturated Broadcast
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
Ours (RMSE=0.0050)
UW (RMSE=0.1664)
Actual
1.2
1
Ours (RMSE=0.0028)
UW (RMSE=0.1450)
Actual
Goodput
Throughput
2 saturated broadcast
0 2 4 6 8 10 12 14 16 18 20
Sender ID
(a) throughput
0.8
0.6
0.4
0.2
0
0
100 200 300 400 500
Sender-Receiver Pair ID
(b) goodput
More accurate than UW 2-node model
Simulation Evaluation:
Saturated Broadcast
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.6
Ours (RMSE=0.0460)
Actual
Ours (RMSE=0.0189)
Actual
0.5
Goodput
Throughput
10 saturated broadcast
0.4
0.3
0.2
0.1
0
0 10 20 30 40 50 60 70 80 90 100
Sender ID
(a) throughput
0
500 1000 1500 2000 2500
Sender-Receiver Pair ID
(b) goodput
Accurate for 10 saturated broadcast
Testbed Evaluation
UW traces: 2 senders, 30 mW, broadcast, saturated
(a) throughput
(b) goodput
More accurate than UW-model for 2-sender
Summary
• A model for predicting the throughput of
wireless networks
• Validated by simulation and testbed
evaluation
State of the Art
This paper
Less
simplifications
Dumb solution
Its limit
RTS/CTS,
different MAC
Traffic modelling,
human behavior
Limit of analytical methods
Reality