Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity Scaling in Mobile Wireless Ad Hoc Network with Infrastructure Support Wentao Huang 1
Xinbing Wang1
Qian Zhang 2
1 Department
of Electronic Engineering Shanghai Jiao Tong University
2 Dept. of CS and Engi HK Univ of Science & Technology
June 24, 2010
ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Outline 1
Introduction Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
2
Model and Assumptions Basic Assumptions Mobility Model
3
Uniformly Dense Networks Our Results Basic Ideas of Proof
4
Non-uniformly Dense Networks Weak Mobility Trivial Mobility ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Outline 1
Introduction Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
2
Model and Assumptions Basic Assumptions Mobility Model
3
Uniformly Dense Networks Our Results Basic Ideas of Proof
4
Non-uniformly Dense Networks Weak Mobility Trivial Mobility ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Capacity of Ad Hoc Network Capacity of wireless ad hoc network not scalable: in a static ad hoc wireless network with n nodes, the per-node [1] throughput is limited as O √1n . Interference is the main reason behind.
[1] P. Gupta and P. R. Kumar, The capacity of wireless networks, IEEE Trans. on Information Theory, 2000. ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Mobility Increases Capacity In mobile ad hoc wireless networks with n nodes, the per-node throughput remains constant Θ(1)[2] . Full mobility is assumed: The stationary distribution of each node is uniform over the whole network. A Store-carry-forward communication scheme exploit node mobility to carry traffic across network.
[2] M. Grossglauser and D. N. C. Tse, Mobility increases the capacity of ad hoc wireless networks, IEEE/ACM Trans. Networking, 2002 ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Mobility Increases Capacity In mobile ad hoc wireless networks with n nodes, the per-node throughput remains constant Θ(1)[2] . Full mobility is assumed: The stationary distribution of each node is uniform over the whole network. A Store-carry-forward communication scheme exploit node mobility to carry traffic across network.
[2] M. Grossglauser and D. N. C. Tse, Mobility increases the capacity of ad hoc wireless networks, IEEE/ACM Trans. Networking, 2002 ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Partial Mobility
Even if node mobility does not cover the whole network area, it still helps. If mobility range is limited to f (n) portion of the network diameter, per-node capacity is Θ(f (n))[3] .
[3] M. Garetto, P. Giaccone, and E. Leonardi, Capacity scaling in delay tolerant networks with heterogeneous mobile nodes, in ACM MobiHoc, 2007. ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
Infrastructure Increases Capacity
In static ad hoc network with n wireless nodes and k base stations, the per-node capacity is Θ(k/n)[4] . Assume base stations have unlimited bandwidth and √ Θ(n) > k > Θ( n).
[4] B. Liu, Z. Liu, and D. Towsley, On the capacity of hybrid wireless networks, in IEEE Infocom, 2004. ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
The General (Unanswered) Problem
Main Question What is the capacity if the network features both mobility and infrastructure? How to achieve capacity?
ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Outline 1
Introduction Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
2
Model and Assumptions Basic Assumptions Mobility Model
3
Uniformly Dense Networks Our Results Basic Ideas of Proof
4
Non-uniformly Dense Networks Weak Mobility Trivial Mobility ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Assumptions
n wireless nodes moving over closed connected region Independent, stationary and ergodic mobility processes Uniform permutation traffic: each node is origin and destination of a single traffic flow with rate λ(n) Omni-directional antennas and a single wireless channel with bandwidth Wbps k = nK static inter-connected base stations Bandwidth between base stations are c(n)bps, and kc = nϕ
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Protocol Model Definition Let dij denotes the distance between node i and node j, and RT the common transmission range, then a transmission from i to j at rate W is successful if: dij < RT dkj > (1 + ∆)RT for any other k transmitting simultaneously.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Asymptotic Capacity
Definition Asymptotic per-node capacity λ(n) of the network is said to be Θ(g(n)) if there exist two positive constants c and c0 such that: limn→∞ Pr {λ(n) = cg(n) is feasible} = 1 limn→∞ Pr {λ(n) = c0 g(n) is feasible} < 1
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Home-point Based Mobility Every node has a “home-point” and tends to move around it.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Home-point Based Mobility
The shape of the spatial stationary distribution of each node’s presence is an arbitrary, non-increasing function s(d) of the distance from the home-point.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Distribution of Home-points Clustering home-points characterizes the heterogeneous node density. Uniform model
Clustered model
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Scaling the Network Size Network size grows as more nodes are joining.
Assume that L = f (n) ∼ nα
α ∈ [0, 1/2]
↑ constant size, increasing density ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Scaling the Network Size Network size grows as more nodes are joining.
Assume that L = f (n) ∼ nα
α ∈ [0, 1/2]
↑ increasing size, constant density ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Basic Assumptions Mobility Model
Scaling the Network Size Network size grows as more nodes are joining.
Assume that L = f (n) ∼ nα
α ∈ [0, 1/2]
Node mobility does not depend on network size. ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Outline 1
Introduction Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
2
Model and Assumptions Basic Assumptions Mobility Model
3
Uniformly Dense Networks Our Results Basic Ideas of Proof
4
Non-uniformly Dense Networks Weak Mobility Trivial Mobility ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Main Results If the network is uniformly dense, then per-node capacity is Θ(1/f (n)) + Θ(min(k2 c/n, k/n)). ϕ ≥0
1 4 Infrastructure
1 − 4
Infrastructure Dominant
1
Dominant
3 − 8 1 − 2
g lo
]
1 − 2 y] it ac ap [c
g lo
ity ac ap [c
n
Mobility
Dominant
3 4
3 − 8
Mobility Dominant
n
1 2
ϕ =−
K
1 − 4
0
3 4
1 − 8
1
1 − 8
K
0
1 4
1 2
α
1 2
Recall that f = nα , k = nK and kc = nϕ ICDCS 2010
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0
1 4
1 2
α
Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Uniformly Dense Networks Definition Local density of nodes at point X is defined as: n+k X ρ(X) = E[1Zi ∈B(X,1/√n) |Fn+k ] i=1 √ √ where B(X, 1/ n) is the disk centered at X with radius 1/ n, and Fn+k are the locations of all wireless nodes and BSs. Definition A network is said to be uniformly dense if for any X ∈ O, there exist two positive constants h and H, such that h < ρn (X) < H w.h.p.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Uniformly Dense Networks Even though the home-points may be clustering, the local node density is possible to be (almost) uniformly dense. Non-uniformly dense (clustered)
Uniform dense
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Uniformly Dense Networks
Theorem p If f (n) γ(n) = o(1), where γ(n) = network is uniformly dense.
ICDCS 2010
log m m ,
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and k = O(n), then the
Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Property of Uniformly Dense Networks
Lemma
√ The optimal transmission range is R∗T = Θ(1/ n). Lemma Based on a simple scheduling policy with optimal range R∗T , for any pair of nodes (i, j), the link capacity between them is 1 µ(i, j) = Θ Pr dij ≤ √ n
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Mapping over Random Geometric Graph
Link capacities can be evaluated in terms n o of contact 1 probabilities: µ(i, j) = Θ Pr dij ≤ √n We can construct a random geometric graph: vertices stand for home-points of the nodes edges are weighted by link capacity µij
Network capacity is obtained by solving the maximum concurrent flow problem over the constructed graph
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Upper Bound of Capacity Upper bound of capacity: network cut
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Upper Bound of Capacity
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Upper Bound of Capacity We need to compute the total link capacity crossing the cut Red edge: wireless node to wireless node Yellow edge: wireless node to BS Black edge: BS to BS
Proof’s Idea: Tessellate the network into squares. Upper and lower bound the number of BSs within each square. Upper and lower bound the distance from a particular node’s home-point to this square. Sum over all squares and turn it into integral.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Lower (Achievable) Bound of Capacity Mobility dominant state: capacity λ = Θ(1/f (n)).
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Our Results Basic Ideas of Proof
Lower (Achievable) Bound of Capacity n 2 o k Infrastructure dominant state: capacity λ = Θ min k c(n) , . n n
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Weak Mobility Trivial Mobility
Outline 1
Introduction Capacity of Ad Hoc Network Methods to Increase Capacity The General (Unanswered) Problem
2
Model and Assumptions Basic Assumptions Mobility Model
3
Uniformly Dense Networks Our Results Basic Ideas of Proof
4
Non-uniformly Dense Networks Weak Mobility Trivial Mobility ICDCS 2010
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Weak Mobility Trivial Mobility
Weak Mobility
Occurs when node mobility is not strong enough to offset clustering. But within a cluster, mobility still plays a significant role to improve capacity. Therefore we use infrastructure to deliver inter-cluster traffic, and use mobility to deliver intra-cluster traffic.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Weak Mobility Trivial Mobility
Weak Mobility
Definition q p p p Let γ˜ (n) = r log(n/m) ˜ (n) = o(1), f (n) γ(n) = ω(1), n/m . If f (n) γ then the network falls into weak mobility regime. Theorem 2 Under weak mobility, per-node capacity is λ = Θ min knc , nk . q The optimal transmission range is RT = r(n) m(n) n .
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Weak Mobility Trivial Mobility
Trivial Mobility
Node mobility is so weak that even within a cluster the node density is not uniformly dense. Mobility will not have any effect on capacity, either inter-network traffic or intra-network traffic. Communication schemes of static networks can be readily applied.
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Introduction Model and Assumptions Uniformly Dense Networks Non-uniformly Dense Networks
Weak Mobility Trivial Mobility
Trivial Mobility
Definition p If f (n) γ˜ (n) = ω(log mn ), then the network falls under trivial mobility regime. Theorem 2 Under trivial mobility, per-node capacity is λ = Θ min knc , nk . q The optimal transmission range is RT = r(n) m(n) k .
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Summary
Summary
Mobile ad hoc network with infrastructure support Node mobility divided into strong, weak and trivial cases Network capacity is determined for each case, and optimal communication schemes are proposed.
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Summary
Questions?
Thanks for listening.
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