On The Throughput-Optimal Distributed
Scheduling Schemes with Delay Analysis in
Multi-hop Wireless Networks
IEEE Student Paper Contest
Seoul Section 2009
Presenter: Nguyen H. Tran
Email: [email protected]
http://networking.khu.ac.kr
March 27, 2006
1
Outline
 Introduction
 Network Model and Examples
Pick and Compare Scheduling Mechanism
Proposed Algorithm
Open Issues
Conclusion
2
Introduction
In wireless networks, how to design an efficient
medium access scheme is an important issue.
In 1992, Tassiulas’ seminal paper triggers an
avalanche of works dealing with throughputoptimal scheduling algorithms.
We develop a low-complexity, distributed
scheduling scheme to achieve the optimal
performance for K-hop interference model
3
Wireless Network Model and Examples
Example:
Wireless Network
One-Hop Inferference Model:
N = Node set = {1, 2…, N}
L = Link set = {1, 2, …, L}
Sl = Interference Set for
link l L
General Interference Set Model:
Sl = l U {links that interfere with link l transmission}
4
Wireless Network Model and Examples
Example:
One-Hop Inferference Model :
Wireless Network
Set Sl
N = Node set = {1, 2…, N}
L = Link set = {1, 2, …, L}
Sl = Interference Set for
link l L
General Interference Set Model:
Sl = l U {links that interfere with link l transmission}
5
Wireless Network Model and Examples
Example:
Two-Hop Inferference Model :
Wireless Network
Set Sl
N = Node set = {1, 2…, N}
L = Link set = {1, 2, …, L}
Sl = Interference Set for
link l L
General Interference Set Model:
Sl = l U {links that interfere with link l transmission}
6
Wireless Network Model and Examples
Queueing Dynamics:
-Slotted System: t = {0, 1, 2, 3, …}
-One Queue for each link l:
Ql[t] = # packets in currently in queue l (on slot t)
Al[t] = # new packet arrivals to queue l (on slot t)
ml[t] = # packets served from queue l (on slot t)
ml[t]
Al[t]
Ql[t]
Ql[t+1] = Ql[t] – ml[t] + Al[t]
R[t] ={Feasible Schedules}
ml[t] {0, 1}
ml[t] = 1 only if Ql[t]>0 AND no other active links w Sl
7
Wireless Network Model and Examples
Queueing Dynamics:
-Slotted System: t = {0, 1, 2, 3, …}
-One Queue for each link l:
Ql[t] = # packets in currently in queue l (on slot t)
Al[t] = # new packet arrivals to queue l (on slot t)
ml[t] = # packets served from queue l (on slot t)
ml[t]
Al[t]
Ql[t]
Ql[t+1] = Ql[t] – ml[t] + Al[t]
R[t] ={Feasible Schedules}
ml[t] {0, 1}
ml[t] = 1 only if Ql[t]>0 AND no other active links w Sl
8
Max Weight Scheduling
Capacity Region:
L = {All rate vectors l = (l1,…, lL) supportable}
Capacity Region L
[Tassiulas, Ephremides 92]: Max Weight Match (MWM)
Maximize
Subject to: m[t] R[t]
wl[t]ml[t]
(Stabilizes Network, Supports all l interior to L)
9
Max-Weight Complexity and Suboptimal Algorithms
 Max-Weight Scheduling is a centralized and highcomplexity algorithm
K=1: polynomial time-complexity
K>=2: NP-Hard
 Some of distributed and suboptimal proposals: Maximal
Matching, Constant-Time Complexity…
Capacity Region L
g-scaled region gL
10
Goal
 We aim to design a scheduling algorithm for
K-hop Interference Model with Distributed
fashion yet still achieve Optimal Throughput.
Too Ambitious……..??
There is a solution: Pick and Compare
Algorithm
What is the price: increasing Queuing Delay
11
Pick-and-Compare Algorithm
At each time-slot [t]
12
Pick-and-Compare Illustration
13
Delay Analysis
Theorem:
Pick-and-Compare algorithm can achieve the
throughput-optimal performance if rate vector
l = (l1,…, lL) lies in the capacity region, and
we have:
14
Algorithm Description
Distributed Computation Model
m [t]
R
Each time-slot [t] is divided into control phase (CP) and
data transmission phase (DP)
Nodes are assumed to be synchronized and have unique
IDs
15
Proposal: Pick Algorithm 1
Randomized Feasible Allocation Algorithm:
RTS
O(1)
n
m
node m choose n with probability
P{m [t]=m*[t] }≥
R
u
16
v
Proposal: Pick Algorithm 1
Randomized Feasible Allocation Algorithm:
CTS
O(1)
n
m
node m choose n with probability
COL
P{m [t]=m*[t] }≥
R
u
17
CTS
v
Proposal: Pick Algorithm 1
Randomized Feasible Allocation Algorithm:
m [t] ={(m,n), (u,v)}
O(1)
m
n
P{m [t]=m*[t] }≥
R
Remark:
Exponential growth of delay in
network size
u
18
v
Proposal: Pick Algorithm 2
Randomized Maximal Matching Algorithm:
RTS
K
4∆
O(e
log2 N)
n
m
node m choose n with probability
P{m [t]=m*[t] }≥
R
u
19
v
Proposal: Pick Algorithm 2
Randomized Maximal Matching Algorithm:
CTS
K
4∆
O(e
log2 N)
n
m
node m choose n with probability
COL
P{m [t]=m*[t] }≥
R
u
20
CTS
v
Proposal: Pick Algorithm 2
Randomized Maximal Matching Algorithm:
K
4∆
O(e
log2 N)
m
ACK(m,n)
n
P{m [t]=m*[t] }≥
R
u
21
ACK(u,v)
v
Proposal: Pick Algorithm 2
Randomized Maximal Matching Algorithm:
m [t] ={(m,n), (u,v)}
K
4∆
O(e
log2 N)
n
m
node m choose n with probability
RTS
RTS
P{m [t]=m*[t] }≥
R
u
22
v
Proposal: Pick Algorithm 2
Randomized Maximal Matching Algorithm:
m [t] ={(m,n), (u,v), (i,j), (p,q)}
K
4∆
O(e
log2 N)
n
m
i
P{m [t]=m*[t] }≥
R
j
Remark:
Polynomial growth of delay in
network size
p
q
u
23
v
Compare Algorithm
24
Results
25
Simulation Results
26
Open Problems
27
THANK YOU!!
28