Saturday, 16 August 2014 1 On the capacity of mobile ad hoc wireless networks Michele Garetto –...

transcript

Tuesday 11 April 2023 1

On the capacity of mobile ad hoc wireless

networks

Michele Garetto – Università di Torino, Italy

Paolo Giaccone - Politecnico di Torino, Italy

Emilio Leonardi – Politecnico di Torino, Italy

Outline

Introduction and motivation Capacity properties of finite networks Application to experimental traces Asymptotic network capacity Application of asymptotic analysis

Introduction

The sad Gupta-Kumar result: In static ad hoc wireless networks with n nodes, the per-node throughput behaves as

P. Gupta, P.R. Kumar, The capacity of wireless networks, IEEE Trans. on Information Theory, March 2000

Introduction

The happy Grossglauser-Tse result: In mobile ad hoc wireless networks with n nodes, the per-node throughput remains constant

M. Grossglauser and D. Tse, Mobility Increases the Capacity of Ad Hoc Wireless Networks, IEEE/ACM Trans. on Networking, August 2002

Introduction

Node mobility can be exploited to carry data across the network Store-carry-forward communication

scheme

Drawback: large delays (minutes/hours)

Delay-tolerant networking

Mobile Ad Hoc (Delay Tolerant) Networks

Have recently attracted a lot of attention Examples

pocket switched networks (e.g., iMotes)vehicular networks (e.g., buses, taxi)sensor networks (e.g., disaster-relief networks,

wildlife tracking)Internet access to remote villages (e.g., IP over

usb over motorbike)

Key issue: how does network capacity depend on the node mobility pattern ?

The impact of mobility In their original paper, Grossglauser and Tse

assume that the mobility pattern of each node produces a uniform distribution of node presence over the network area

results have later been extended to a restricted mobility model in which each node moves over a random great circle on the sphere

S. Diggavi, M. Grossglauser, and D. Tse, Even One-Dimensional Mobility Increases Ad Hoc Wireless Capacity, IEEE Trans. on Information Theory, November 2005

Per-node throughput is still !

The general (unanswered) problem

What properties in the mobility pattern of nodes allow to avoid the throughput decay of static networks ?

What are the sufficient conditions to obtain per-node throughput ?

Are there intermediate cases in between extremes of static nodes (Gupta-Kumar ’00) and fully mobile nodes (Grossglauser-Tse ’01) ? Under which conditions ?

Our work We take one step forward in addressing the

general problem

We obtain basic results for arbitrary (finite) networks

We provide a general framework to compute the asymptotic transport capacity of mobile networks with anisotropic mobility patterns

We apply the proposed framework to a class of mobile networks comprising heterogeneous nodes and spatial inhomogeneities

Outline

Arbitrary (finite) networksMain result:

Under very general assumptions, the capacity (in networking sense) of a mobile wireless network depends on the mobility process only through the joint stationary distribution of nodes over the area

The details on how nodes move (change of speed, direction, group movements) have no impact on network capacity

Arbitrary (finite) networks Assumptions:

n nodes moving according to a stationary and ergodic mobility process (possibly correlated among the nodes)

A source node s generates traffic for destination d according to a stationary and ergodic process with rate sd

Transmissions between pairs of nodes occur at fixed rate r The set of transmissions that can be scheduled

successfully at time t depends only on the instantaneous node positions

One possible transmission configuration

Another possible transmission configuration

Joint scheduling-routing formulation

Scheduling policy S: selects π(t) among all feasible transmission configurations at time t According to S, between any pair of nodes ( i, j ) there exist a

virtual link of capacity

Routing policy R: described by , denoting the average fraction of the traffic flow from node s to node d, which is routed through link ( i, j ) Quantities satisfy the classic flow-conservation

constraints:

Traffic sustainability

Z(t): network backlog, i.e., the amount of traffic (in bits) already generated by sources that has not yet

been delivered to destinations at time t traffic matrix is sustainable if there

exists a scheduling policy S and a routing strategy R, such that:

Capacity region: the set of all sustainable traffic matrices

Main theorem

Maximum throughput is achieved by the “simple” class of scheduling policies based only on position information (stateless and memoryless policy)

No gain in terms of throughput can be achieved by complex scheduling policies considering:

Speed and direction of nodes History of encounters Queue lengths Age of stored information

Proof’s idea: if a given traffic matrix can be sustained by some arbitrarily complex scheduling, there exist a simple scheduling policy that sustains it

Corollary: the capacity region of a mobile wireless network is convex

Outline

DieselNet-Umass experiment

30 buses running the campus transport service in Spring 2005 (60 days)

traces provide the amount of data transferred through TCP connections using WLAN 802.11 MAC access

ij measured in bytes

Infocom2005-iMotes experiment

iMotes carried by 41 volunteers attending the conference (5 days)

traces provide the radio contact duration between any two iMotes using Bluetooth MAC 802.15 access

ij measured in seconds

Experimental tracesVirtual capacities are directly

measured for each pair of nodes (i,j)

contact graph: a capacitated graph in which each vertex corresponds to a mobile node edge (i,j) is weighted by

The maximum throughput is computed by solving a standard multi-commodity flow problem (for a given flow assignment)

Experimental contact graphs

significant asymmetries and inhomogeneous capacities few edges contribute most of the capacity: class 3-4 contribute for

80% (Umass) and 60% (iMotes) of the overall transport capacity

class 1class 2class 3class 4

x 10x 100x capacity

“minDC”flow assignment

“MaxDC”flow assignment

Theoretical performance of experimental networks

Traffic scenario Maximum aggregate capacity

Average number of hops

Umass mDC 21.131 Gbytes 2.31

Umass MDC 28.578 Gbytes 1.85

iMotes mDC 1.756 Msec 2.60

iMotes MDC 3.008 Msec 1.69

Number of hops

Outline

n nodes moving over unit-area closed connected region independent, stationary and ergodic mobility processes uniform permutation traffic matrix: each node is origin

and destination of a single traffic flow with rate (n) bits/sec

all transmissions employ the same nominal range or power

all transmissions occur at common rate r single-radio, omni-directional antennas interference described by protocol model (next slide)

Assumptions

Protocol Model Let dij denote the distance between node i and

node j, and RT the common transmission range A transmission from i to j at rate r is successful if:

for every other node k simultaneously transmitting

RT (1+Δ)RT

Asymptotic analysis We say that the per-node capacity is Θ( (n) ) if

there exist two constants c and c’ such that

Equivalently, we say that the network capacity in this case is Θ( n (n) )

Uniformly dense networks We define the local asymptotic node density ρ(XO) at

point XO as:

Where is the disk centered in XO , of radius

A network is uniformly dense if:

Properties of uniformly dense networks

Theorem: the maximum network capacity is achieved by scheduling policies forcing the transmission range to be

Corollary: simple scheduling policies leading to link capacities

are asymptotically optimal, i.e., allow to achieve the maximum network capacity (in order sense)

The scheduling policy S*

Theorem: S* is optimal, i.e., link capacities resulting from S* satisfy

(1+Δ)RT(1+Δ)RTnote: it complies with the protocol interference model

Transmission from i to j is enabled when

Outline

A realistic mobility model for DTNs

Realistic mobility processes are characterized by :

Restricted mobility of individual nodes:

Non-uniform density due to concentration points

From: Sarafijanovic-Djukic, M. Piorkowski, and M. Grossglauser, Island Hopping: Efficient Mobility-Assisted Forwarding in Partitioned Networks,, IEEE SECON 2006

From: J.H.Kang, W.Welbourne, B. Stewart, G.Borriello, Extracting Places from Traces of Locations, ACM Mobile Computing andCommunications Review, July 2005.

Heterogeneous nodes with restricted mobility

“home-points” of the nodes

Restricted mobilityThe shape of the spatial distribution of each

node is according to a generic, decreasing function s(d) of the distance from the home-point

Anisotropic node density (clustering)

Achieved through the distribution of home-points

Uniform model: home-points randomly placed over the area according to uniform distribution

n = 10000

Clustered model: nodes randomly assigned to m = nν clusters uniformly placed over the area. Home-points within disk of radius r from the cluster middle point

Scaling the network size

10 nodes……100 nodes…..1000 nodes

We assume that:

Moreover: node mobility process does not depend on network size

Asymptotic capacity results

Recall:

logn [(n)] Uniform Model

Independently of the shape of s(d) !

Asymptotic capacity results

Recall: #clusters

logn [(n)] Clustered Model

“Super-critical regime”: mobility helps

“Sub-critical regime”: mobility does not help

?Lower bound : in case s(d) has finite support

Lower bound : in case s(d) has finite support

Super-critical regime

Let (m = n in the Uniform Model)

When we are in the super-critical regime

Theorem: in super-critical regime a random network realization is uniformely dense w.h.p.Transmission range is

optimalScheduling policy S* is optimal

Mapping over Generalized Random Geometric Graph

(GRGG) Link capacities can be evaluated in terms of contact probabilities:

which depend only on the distance dij between the homepoints of i and j

We can construct a random geometric graph in which Vertices stand for homepoints of the nodesedges are weighted by

Network capacity is obtained by solving the maximum concurrent flow problem over the constructed graph

Upper bound : network cut

Average/random network flows

The “average” flow through the cut is easily computed as

fundamental question:

Proof’s idea:

Consider regular tessellation where squarelets have area γ(n)

Take upper and lower bounds for number of homepoints falling in each squarelets, combined, respectively, with lower and upper bounds of distances between homepoints belonging to different squarelets

Answer: YES !

An optimal routing scheme

The above routing strategy sustains per-node traffic

Routing strategy:

Consider a regular tessellation where squarelets have area

Create a logical route along sequence of horizontal/vertical squarelets, choosing any node whose home-point lie inside traversed squarelet as relay

Sub-critical regime

Restricted mobility does not allow nodes whose home-points belong to different clusters to communicate using

Nodes have to use

System behaves as network of m static node

Model variationsMobility of nodes dependent on network size Spatial distributions not symmetric around

home-point. E.g.: mobility restricted on lines with random orientation

Different classes of nodes (e.g.: fully mobile nodes + nodes with restricted mobility)

Can be studied using the same techniques (e.g. computation of network flow through physical cut)

An interesting case Nodes contrained to move uniformly over

rectangles of area n-β (1/2 < β < 1), with minimum edge n-1/2 and random orientation

In general, network capacity can depend on the geometry of the space visited by the nodes

n1/2-β

Best solution:

network capacity is Θ( n3/2-β)

n-β/2

Worst solution:

network capacity is Θ( n1-β/2)

n-β/2

ConclusionsOne step forward in the capacity

analysis of mobile wireless networks with general node mobility processes

Some results of general validity for finite and infinite number of nodes

Mapping over maximum concurrent flow problem over geometric random graphs

Application to a general class of mobile networks with heterogenous nodes and clustering behavior

Comments ?

Questions ?

Saturday, 16 August 2014 1 On the capacity of mobile ad hoc wireless networks Michele Garetto –...

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