End-to-End Fair Bandwidth Allocation in Multi-hop Wireless Ad Hoc Networks

Baochun LiDepartment of Electrical and Computer Engineering University of Toronto IEEE ICDCS 2005

Presented by Yeong-cheng Tzeng

OutlineI. Introduction

II. Objective and Constraints

III. Optimal Allocation Strategies

IV. Achieve Allocation Strategies: Algorithms

V. Performance Evaluation

VI. 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 si

multaneous flows through the same router Contention in the time domain

I. Introduction Design an topology-aware resource allocation alg

orithm Contending flows fairly share channel capacity Increasing spatial reuse of spectrum to improve utiliz

ation Previous works - break a multi-hop flow into mul

tiple independent subflows The inherent correlation between upstream and down

stream 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

Two active subflows if one subflow is within the transmission range of the other

Contending flows 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 subf

lows

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 ii

u

II.B Objective: Maximizing Spatial Reuse of Spectrum The throughput decreases when we take the en

d-to-end effect into consideration

II.B Objective: Maximizing Spatial Reuse of Spectrum The end-to-end throughput of multi-hop flows i

s 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.,

Our objective To maximize the total effective throughput Subtly different from the objective in the single-ho

p case

iiu

II.C Fairness: the case of multi-hop flows

In wireline networks, an allocation strategy (r1,…,rn) is weighted max-min fair, if Both and hold for all n c

ontending 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

1

n

kkr B

, 1,...i ir i n

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 subflow

s belonging to the same flow i.e., We have

From the viewpoint of channel allocation, we define the fairness constraint as

. ˆi i j iu r r .1 .2 .ˆ ...

ii i i i lr r r r

ˆ ˆ/ /i i j jr w r w

II.C Fairness: the case of multi-hop flows Definition: In a multi-hop wireless network, the a

llocation strategy is fair for contending flows (F1,…Fn) in the same contending flow group, if Within any local neighborhood (that flows contend f

or the same channel capacity B), ,with mi being the number of contending subflows of Fi in this local neighborhood

over any time period [t1,t2]

1̂ ˆ( ,..., )nr r

1ˆ

n

k kkm r B

ˆ ˆ/ /i i j jr w r w

II.D Basic Fairness The allocation strategy is to allocate

B to all subflows in the same contending flow group, regardless of whether they actually contend in the same local neighborhood

The total effective throughput is

.1 1 1

ˆiln n

i j i ii j i

r rl B

1̂ ˆ( ,..., )nr r

11 1

1

( )ˆ

nn n ii

i i ni ij jj

w Bu r

w l

1ˆ

n

i i i j jju r w B w l

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:

The basic share of Fi: The total effective throughput

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

3, 3

, 3i

ii i

lv

l l

11

1

( )n

n iii ni

j jj

w Bu

w v

1

ˆ ii n

i ij

w Br

w v

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

A complete subgraph in the weighted subflow contention graph, which represents a set of subflows that mutually contend with each other

Weighted clique size, The sum of weights on al

l vertices in a clique

Weighted clique number,

k

max , 1,...,k

k J

III.A. Satisfying the Fairness Constraint Assume that for each flow Fi, there are ni,k subflow

s 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

,1ˆ( ) , 1,...,

n

i k iin r B k J

, 0 0 01ˆ ˆ ˆ ˆ( ) , 1,..., ;

k

n

i k i i iin w r r B k J r w r

0̂r B

III.A. Satisfying the Fairness Constraint Channel allocation per unit weight

Proposition 1: Under the fairness constraint, the upper bound of total effective throughput is , where denotes the weighted clique number

1

n

iiw B

0̂r B

ˆi i iu r w B

1 1 1ˆ

n n n

i i ii i iu r w B

III.B. Satisfying the Basic Fairness Constraint

Let 1

ˆ ,1ii i n

j jj

w Bx r i n

w v

Basic share constraint

xi: additional share

total effective throughput

capacity constraint

III.B. Satisfying the Basic Fairness Constraint A basic feasible solution

Total effective throughput

It is known that there exist polynomial-time algorithms to solve such a linear programming problem Simplex algorithm

0, 1,...,ix i n

1

1

n

iin

j jj

w B

w v

III.B. Satisfying the Basic Fairness Constraint Proposition 2: The solution to the above

linear programming problem constitutes the optimal allocation strategy , while supplying the basic fairness property. Such an allocation strategy maximized the total effective throughput

1̂ ˆ( ,..., )nr r

IV. Achieving Allocations Strategies: Algorithms We propose a two-phase algorithm to achie

ve and implement near-optimal allocation strategies The first phase determines the allocation strat

egy for subflows at each nodes The second phase is fully distributed and seek

s 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 contentio

n 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 Packet from different subflows are queued separately Select the next packet to sent, obeying the allocated share

Inter-node coordinations 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 proto

col 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: Internal finish tag: External finish tag:

, ,( )j k j ki i is v t

, , , /j k j k j k ji i i iI S L c

, , , /j k j k j ki i i iE S L c

IV.C. Second Phase: Scheduling Scheduling algorithm

Set backoff timer Sender estimates a backoff value Receiver estimates a backoff value 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 previ

ous packet Select packet have the smallest internal finish tag

,( )j ki mm T

Q S r

,

( )i mm T m iR r r

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 to evaluate the allocated share to each of the flows

and subflows The total number of successfully delivered pa

ckets 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