End-to-End Fair Bandwidth
Allocation in Multi-hop Wireless
Ad Hoc Networks
Baochun Li
Department of Electrical and Computer Engineering
University of Toronto
IEEE ICDCS 2005
Presented by Yeong-cheng Tzeng
Outline
I.
II.
III.
IV.
V.
VI.
Introduction
Objective and Constraints
Optimal Allocation Strategies
Achieve Allocation Strategies:
Algorithms
Performance Evaluation
Conclusions
I. Introduction

In wireless networks



Flows compete for shared channel bandwidth if they
are within the transmission ranges of each other
Contention in the spatial domain
In wireline networks


Flows contend only at the packet router with other
simultaneous flows through the same router
Contention in the time domain
I. Introduction

Design an topology-aware resource allocation
algorithm



Contending flows fairly share channel capacity
Increasing spatial reuse of spectrum to improve
utilization
Previous works - break a multi-hop flow into
multiple independent subflows


The inherent correlation between upstream and
downstream subflows are lost
The probability of dropping packets is increased
I. Introduction
II. Objective and Constraints

Objective


Maximize spatial reuse of spectrum
Constraint

Maintain basic fairness among contending
flows
II.A Preliminaries

Contending subflows


Contending flows


Two active subflows if one subflow is within the
transmission range of the other
If any of their subflows are contending subflows
Contending flow group



If multi-hop flows are contending flows
i.e. G(Fi)=G(Fj)={Fi,Fj}
G(Fi)=G(Fj) and G(Fj)=G(Fk), then G(Fi)=?G(Fk)
II.A Preliminaries

Subflow contention graph



Represents the spatial contention relationship
among contending subflows
Vertices correspond to subflows
Connected vertices correspond to contending
subflows
II.B Objective: Maximizing Spatial
Reuse of Spectrum

In single hop case, the objective of maximizing
spatial reuse of spectrum



Translated to maximizing the aggregate channel
utilization
Total effective single-hop throughput
max  i ui
II.B Objective: Maximizing Spatial
Reuse of Spectrum

The throughput decreases when we take the
end-to-end effect into consideration
II.B Objective: Maximizing Spatial
Reuse of Spectrum



The end-to-end throughput of multi-hop flows
is determined by the minimum throughput of its
subflows, i.e., ui=min(uij), j=1,…li
We define the total effective throughput as the
total end-to-end throughput of all multi-hop
flows, i.e.,  i ui
Our objective


To maximize the total effective throughput
Subtly different from the objective in the singlehop case
II.C Fairness: the case of multi-hop
flows

In wireline networks, an allocation strategy
(r1,…,rn) is weighted max-min fair, if
 Both  r  B and ri  i , i  1,...n hold for all n
n
k 1 k

contending flows
For each flow Fi, any increase in ri would cause
a decease in the allocation rj for some flow Fj
satisfying rj/wj < ri/wi
II.C Fairness: the case of multi-hop
flows
II.C Fairness: the case of multi-hop
flows


Generally, if ri.j is allocated to the subflow Fi.j, we
have uij=ri.j, thus ui=min(ri.j)
If we equalize channel allocations for all
subflows belonging to the same flow



i.e., rˆi  ri.1  ri.2  ...  ri.li
We have ui  ri. j  rˆi
From the viewpoint of channel allocation, we
define the fairness constraint as

rˆi / wi  rˆj / w j  
II.C Fairness: the case of multi-hop
flows

Definition: In a multi-hop wireless network, the
allocation strategy (rˆ1 ,..., rˆn ) is fair for contending
flows (F1,…Fn) in the same contending flow
group, if


Within any local neighborhood (that flows contend
n
for the same channel capacity B),  k 1 mk rˆk  B ,with
mi being the number of contending subflows of Fi in
this local neighborhood
rˆi / wi  rˆj / w j   over any time period [t1,t2]
II.D Basic Fairness

The allocation strategy (rˆ1 ,..., rˆn ) is to allocate
B to all subflows in the same contending
flow group, regardless of whether they
actually contend in the same local
neighborhood
li
n
n
ˆi i  B
  ri. j   rl

i 1 j 1
ui  rˆi  wi B
i 1

The total effective throughput is

( i 1 wi ) B
n
 i1 ui   i1 rˆi 
n
n

n
j 1
wjl j
n
j 1
wjl j
II.D Basic Fairness


For a flow Fi, each subflow
Fi.k only contends with its
immediate upstream flow Fi.k-1
and immediate downstream
flow Fi.k+1
If li ≥ 3, we may classify the
subflows into three
independent sets, where
subflows in each set may
transmit concurrently:


{Fi.j, j = 3k + 1, k ≥ 0}
{Fi.j, j = 3k + 2, k ≥ 0}
{Fi.j, j = 3k + 3, k ≥ 0}
II.D Basic Fairness

We define the virtual length of a flow Fi, vi, as follows:



wi B
The basic share of Fi: rˆ   w v
The total effective
throughput
n
i
n
j 1


3, l  3
vi   i
li , li  3

n
u 
i 1 i
i i
( i 1 wi ) B

n
j 1
wjv j
We claim an allocation strategy satisfies the constraint of
basic fairness, if the allocation of any flow is equal to or
higher than its basic share


Still satisfies the fairness constraint
Achieve a higher total effective throughput
III. Optimal Allocation Strategies

Develop an estimation algorithm to
calculate the optimal allocation strategies
that achieve our objective of maximizing
spatial bandwidth reuse, while satisfying


The fairness constraint
The basic fairness constraint
III.A. Satisfying the Fairness
Constraint

Clique


Weighted clique size, 


A complete subgraph in
the weighted subflow
contention graph, which
represents a set of
subflows that mutually
contend with each other
k
The sum of weights on
all vertices in a clique
Weighted clique number,
  max  , k  1,..., J
k
III.A. Satisfying the Fairness
Constraint


Assume that for each flow Fi, there are ni,k
subflows in the cliqueΩk (ni,k ≥ 0)
Since all subflows in the same clique contends for
the channel capacity B, for contending flows
(F1,…,Fn) in the same contending flow group, we
have





 r̂0  B
n
i 1
n
i 1
(ni ,k rˆi )  B, k  1,..., J
(ni ,k wi )rˆ0   k rˆ0  B, k  1,..., J ; rˆi  wi rˆ0
III.A. Satisfying the Fairness
Constraint

Channel allocation per unit weight r̂0  B 



ui  rˆi  wi B 
n
n
n
i1 ui  i1 rˆi  i1 wi B 
Proposition 1: Under the fairness
constraint, the upper bound of total
effective throughput is  w B  , where 
denotes the weighted clique number
n
i 1
i

III.B. Satisfying the Basic Fairness
Constraint

total effective throughput
capacity constraint
Basic share constraint

Let
xi  rˆi 
wi B
 j 1 w j v j
n
,1  i  n
xi: additional share
III.B. Satisfying the Basic Fairness
Constraint

A basic feasible solution
xi  0, i  1,..., n
Total effective throughput
n
  i 1 wi B
n
 j 1 w j v j
It is known that there exist polynomial-time
algorithms to solve such a linear programming
problem




Simplex algorithm
III.B. Satisfying the Basic Fairness
Constraint

Proposition 2: The solution to the above
linear programming problem constitutes
the optimal allocation strategy (rˆ1 ,..., rˆn ) ,
while supplying the basic fairness property.
Such an allocation strategy maximized the
total effective throughput
IV. Achieving Allocations Strategies:
Algorithms

We propose a two-phase algorithm to
achieve and implement near-optimal
allocation strategies


The first phase determines the allocation
strategy for subflows at each nodes
The second phase is fully distributed and
seeks to implement the calculated allocation
strategy for each of the subflows
IV.A. First Phase: The Centralized
Form

Need a centralized node



Process per-flow information
Construct the weighted subflow contention graph
Steps

Each Node collects information






Virtual length
Weight
Deliver information to centralized node
The centralized node constructs the weighted subflow
contention graph
Solve the linear programming problem
Broadcast the allocation strategy
IV.B. First Phase: The Distributed
Form

Steps

Construction of local cliques
Overhearing
 Exchange information with immediate neighbors


Intra-flow exchange of constraints
Local channel capacity constraint
 Local basic fairness constraint


Achieving locally optimal allocation strategies
IV.B. First Phase: The Distributed
Form
IV.B. First Phase: The Distributed
Form
IV.C. Second Phase: Scheduling

Use the calculated allocation strategy (allocated
share) as the weights



IV.C. Second Phase: Scheduling

Due to lack of centralized coordination:

Intra-node coordinations



Inter-node coordinations




Packet from different subflows are queued separately
Select the next packet to sent, obeying the allocated share
Determine the backoff timer
Think of all subflows on one node as one virtual flow
Adjust their contention window to proportional to node share
Others




Follow the standard RTS-CTS-DATA-ACK handshaking
protocol as 802.11
Each node is required to maintain a virtual clock, vi(t)
Each node is need a local table to keep track of service tags
Use RTS, CTS and ACK packets to piggyback service tags
IV.C. Second Phase: Scheduling

Scheduling algorithm


When a packet arrives at node i, it enqueues
in its own subflow queue
When a packet reaches the head of its queue,
three tags are assigned
Start tag: sij ,k  vi (tij ,k )
 Internal finish tag: I i j ,k  Si j ,k  Lij ,k / cij
 External finish tag: Ei j , k  Si j ,k  Lij ,k / ci

IV.C. Second Phase: Scheduling

Scheduling algorithm

Set backoff timer




j ,k
Sender estimates a backoff value Q   mT (Si  rm )  
Receiver estimates a backoff value R   mT ,m i (ri  rm )  
Backoff timer is uniformly distributed in
[0,CWmin+max(Q,R,0)]
When sender sends a packet successfully


Update its virtual clock as the external finish tag of the
previous packet
Select packet have the smallest internal finish tag
V. Performance Evaluation

Simulate results in two network scenarios



a simpler topology shown in Fig. 1;
a more elaborate topology shown in Fig. 6.
Compare the performance of 2PA with


standard IEEE 802.11 MAC
the two-tier fair scheduling algorithm



maximizes single-hop total effective throughput
guarantees basic fairness among single-hop flows
Others





Implement with a channel capacity of 2Mbps with Two Ray Ground
Reflection as the propagation model
Dynamic Source Routing (DSR) as the routing protocol
CBR of 200 packets per second with a packet size of 512 bytes
use identical weights of 1 for each flow
each simulation session is T = 1000 seconds
V. Performance Evaluation

Interested parameters

The number of packets successfully delivered
for each of the flows


The total number of successfully delivered
packets


to evaluate the allocated share to each of the flows
and subflows
to evaluate the extent of spatial spectrum reuse
The total number of packets lost
V.A. Scenario 1
V.B. Scenario 2
VI. Conclusion




Study the issue of end-to-end fairness in
multi-hop wireless ad hoc networks
Propose estimation algorithms
A two-phase algorithm is presented to
approximate the optimal allocation
strategies
Evaluation performance is effective