Heterogeneity Increases Multicast Capacity In Clustered Network

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Heterogeneity Increases Multicast Capacity In
Clustered Network

• Qiuyu Peng Xinbing Wang Huan Tang
• Department of Electronic EngineeringShanghai
  Jiao Tong University, China
• April 12, 2011

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Outline

• Introduction
• Motivations
• Objectives
• Models and Definitions
• Main Result and Intuition
• Multicast Capacity Achieving Scheme
• Conclusion and Future Work

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Motivation

• Capacity of wireless ad hoc network is not
  scalable in a static
• ad hoc wireless network with n nodes, the
  per-node capacity is
• limited as .
• Interference is the main reason behind.

1 P. Gupta and P. R. Kumar, The capacity of
wireless networks, in IEEE Transaction on
Information Theory, 2000.
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Motivation

• Multicast traffic pattern is a generalized
  version of unicast traffic in ad hoc network
  Each source sends identical packets to multiple
  destinations.
• The per-node throughput is limited as
  if each multicast session composes of 1
  source and k destinations.

2 X.-Y. Li, S.-J. Tang, and O. Frieder.
Multicast capacity for large scale wireless
ad hoc networks, in Proc. ACM Mobicom 2008.
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Motivation

• The network models studied in previous works are
  homogeneous and uniformly distributed.
• Most realistic networks are characterized by
  various clustered heterogeneity.
• Spatial Heterogeneity 3
• Pattern Heterogeneity 4

3 G. Alfano, M. Garetto, E. Leonardi, Capacity
Scaling of Wireless Networks with
Inhomogeneous Node Density Upper Bounds, 2009.
4 M. Ji, Z. Wang, H. Sadjadpour, J. J.
Garcia-Luna-Aceves, The Capacity of Ad Hoc
Networks with Heterogeneous Traffic Using
Cooperation 2010.
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Motivation

• Network with multicast traffic pattern can also
  be regarded as clustered network since nodes of
  the same multicast session compose of a cluster.
• Sensor Network
• Military Battle Field

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Objectives

• The network heterogeneities investigated in prior
  works are inadequate for exploring the clustering
  behavior of such network.
• What are the new features of such network?

Heterogeneous Cluster Traffic (HCT) Clients of
the same cluster (data flow) are likely to be
deployed around a cluster head specified by an
Inhomogeneous Poisson Process (IPP).
Heterogeneous Cluster Size (HCS) Clusters may
have different size (cardinality) and HCS is
employed to describe the population variation for
each multicast data flow.
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Objective

• What are the impacts of heterogeneous cluster
  traffic and size
• on multicast capacity in static network?
• Heterogeneous cluster traffic increases network
  capacity for all the clusters.
• Heterogeneous cluster size does not influence the
  network capacity.

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Outline

• Introduction
• Models and Definitions
• Network Topology
• Transmission Protocol
• Capacity Definitions
• Main Result and Intuitions
• Multicast Capacity Achieving Scheme
• Conclusion and Future Work

Multicast Hierarchical Cooperation Presentation
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Network Topology

• There are clusters and each with
  number of clients.
• Both and scale with and
  .
• The edge of the deployed region is
  , which also scales with .

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Network Topology

• How to Model HCT (I/II)
• Each Cluster Client is distributed according to
  an inhomogeneous poission process around their
  cluster head specified by a dispersion density
  function .

H Cluster head C Cluster client
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Network Topology

• How to Model HCT (II/II)
• Given a probability density function , we
  must provide a quantitative value of its degree
  of heterogeneity.
• The expectation describes average node density
• The variance can describe HCT and a novel
  variable distribution variance is proposed

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Network Topology

• How to Model HCS
• The size of these clusters is not identical
  and for each cluster
• , its size
  .

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Transmission Protocol

• Protocol Model

Definition Let denote the distance between
node i and node j, and the common
transmission range, then a transmission from i to
j is successful if for any other node k
transmitting simultaneously.
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Capacity Definition

• Asymptotic Capacity
• Definition Let
  denote the sustainable rate of data flow for
  cluster . Assume that
  .
• Then is defined as
  the asymptotic network capacity
• if there exist two constants
  , such that

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Outline

• Introduction
• Models and Definitions
• Main Result and Intuitions
• Main Results
• Intuition
• Multicast Capacity Achieving Scheme
• Conclusion and Future Work

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Main Results(I/II)

• Given the distribution variance , the
  capacity is upper bounded as follows

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Main Results(II/II)

• Given a specified distribution variance , a
  set of dispersion density function can
  satisfy the requirement.
• Uniform Cluster Random Model is the right point
  process that can achieve the capacity upper bound
  in order sense.

• Uniform Cluster Random Model
• The dispersion density function is as
  follows
• where is
  defined as cluster radius. It means
• clients of each cluster are randomly and
  uniformly distributed in a
• disk of radius R centered at its cluster
  head.

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Intuitions

• Fully Cluster Overlapping
• HCT is relative slight and each cluster is fully
  overlapped with nodes from other clusters.
• Each node is required to serve for approximately
  clusters and it is identical to
  uniform case.

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Intuitions

• Trivial Cluster Overlapping
• HCT is relative severe and each cluster can be
  viewed as an isolated one.
• Each node is required to serve for a constant
  number of cluster so
• capacity can be achieved.

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Intuitions

• Partial Cluster Overlapping
• The degree of HCT is neither too severe nor
  slight therefore each cluster is overlapped with
  only some of the clusters.
• Each node is required to serve for a smaller
  number of clusters than the case of fully cluster
  overlapping.
• The Network Capacity is larger than
  , which is the achievable capacity of uniform
  network.

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Outline

• Introduction
• Models and Definitions
• Main Result and Intuitions
• Multicast Capacity Achieving Scheme
• Conclusion and Future Work

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Capacity Achieving Scheme

• Why designing scheduling policy for UCRM?
• UCRM, which is a special type of node
  distribution function, can achieve maximized
  capacity given a fixed theoretically.
• To test the theoretical result is applicable in
  real world scenario. Capacity achieving scheme is
  required to approach such upper bound.

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Capacity Achieving Scheme

• Case
• In this case,
  . There are at most a constant
  number of clusters inside a disk of radius R
  centered anywhere and a simple TDMA scheme can
  achieve capacity for each cluster.
  

Trivial Cluster Overlapping
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Capacity Achieving Scheme

• Case
• In this case,
  and the traffics in each cluster is not so
  aggregated because is relative smaller.

Scheduling Policy becomes complex
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Capacity Achieving Scheme

• Case
• Illustration of highway, access point and routing
  protocol.

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Outline

• Introduction
• Models and Definitions
• Main Result and Intuitions
• Multicast Capacity Achieving Scheme
• Conclusion and Future Work

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Conclusion

• We provide a close formula for the relationship
  between the achievable capacity and the
  distribution variance and the corresponding
  scheduling policy to achieve such capacity.
• Based on the formula, we find that HCT can
  increase the network capacity while HCS does not
  have impact on the network capacity.

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Future Work

• For HCS, we find it can not increase network
  capacity. However, it may increase the achievable
  capacity for small cluster because small cluster
  may rely on the information highway constructed
  by the bigger clusters.
• We can investigate the lower bound of the network
  capacity given a specified .
• We can also discuss the impact of base stations
  on the network capacity in our heterogeneous
  cases.

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Thank you for listening