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

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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

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Outline

• Introduction
• Objective and Constraints
• Optimal Allocation Strategies
• Achieve Allocation Strategies Algorithms
• Performance Evaluation
• Conclusions

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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

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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

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I. Introduction
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II. Objective and Constraints

• Objective
• Maximize spatial reuse of spectrum
• Constraint
• Maintain basic fairness among contending flows

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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)

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II.A Preliminaries

• Subflow contention graph
• Represents the spatial contention relationship
  among contending subflows
• Vertices correspond to subflows
• Connected vertices correspond to contending
  subflows

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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

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II.B Objective Maximizing Spatial Reuse of
Spectrum

• The throughput decreases when we take the
  end-to-end effect into consideration

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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., 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

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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 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

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

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II.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

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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

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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.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

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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

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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

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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 all vertices in a clique
• Weighted clique number,

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III.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
• 
  

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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

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III.B. Satisfying the Basic Fairness Constraint

• Let

total effective throughput
capacity constraint
Basic share constraint
xi additional share
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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

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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

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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

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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

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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

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IV.B. First Phase The Distributed Form
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IV.B. First Phase The Distributed Form
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IV.C. Second Phase Scheduling

• Use the calculated allocation strategy (allocated
  share) as the weights

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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
  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

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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

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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,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

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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

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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
  packets
• to evaluate the extent of spatial spectrum reuse
• The total number of packets lost

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V.A. Scenario 1
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V.B. Scenario 2
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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