End-to-End Fair Bandwidth Allocation in Multi-hop Wireless Ad Hoc Networks Baochun Li Department of Electrical and Computer Enginee ring University of Toronto IEEE ICDCS 2005 Presented by Yeong-cheng Tzeng
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
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 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.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