Title: End-to-End Fair Bandwidth Allocation in Multi-hop Wireless Ad Hoc Networks
1End-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
2Outline
- Introduction
- Objective and Constraints
- Optimal Allocation Strategies
- Achieve Allocation Strategies Algorithms
- Performance Evaluation
- Conclusions
3I. 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
4I. 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
5I. Introduction
6II. Objective and Constraints
- Objective
- Maximize spatial reuse of spectrum
- Constraint
- Maintain basic fairness among contending flows
7II.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)
8II.A Preliminaries
- Subflow contention graph
- Represents the spatial contention relationship
among contending subflows - Vertices correspond to subflows
- Connected vertices correspond to contending
subflows
9II.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
10II.B Objective Maximizing Spatial Reuse of
Spectrum
- The throughput decreases when we take the
end-to-end effect into consideration
11II.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., uimin(uij), j1,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-hop case
12II.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 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 lt ri/wi
13II.C Fairness the case of multi-hop flows
14II.C Fairness the case of multi-hop flows
- Generally, if ri.j is allocated to the subflow
Fi.j, we have uijri.j, thus uimin(ri.j) - If we equalize channel allocations for all
subflows belonging to the same flow - i.e.,
- We have
- From the viewpoint of channel allocation, we
define the fairness constraint as -
15II.C Fairness the case of multi-hop flows
- Definition In a multi-hop wireless network, the
allocation strategy is fair for
contending flows (F1,Fn) in the same contending
flow group, if - Within any local neighborhood (that flows contend
for 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
16II.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
-
17II.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.k1 - 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 0Fi.j, j 3k 3, k
0
18II.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
19III. 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
20III.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 all vertices in a clique
- Weighted clique number,
21III.A. Satisfying the Fairness Constraint
- Assume that for each flow Fi, there are ni,k
subflows in the cliqueOk (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 -
-
-
22III.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
23III.B. Satisfying the Basic Fairness Constraint
total effective throughput
capacity constraint
Basic share constraint
xi additional share
24III.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
25III.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
26IV. 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
27IV.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
28IV.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
29IV.B. First Phase The Distributed Form
30IV.B. First Phase The Distributed Form
31IV.C. Second Phase Scheduling
- Use the calculated allocation strategy (allocated
share) as the weights -
-
-
32IV.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
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
33IV.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
34IV.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,CWminmax(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
35V. 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
36V. 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
packets - to evaluate the extent of spatial spectrum reuse
- The total number of packets lost
37V.A. Scenario 1
38V.B. Scenario 2
39VI. 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