mobility model by lewis

7/31/2019 Mobility Model By Lewis

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(1) Brief Survey of Mobility Modelsfor Ad Hoc Networks and WLANs

(2) A Mobility Model for Both Long-term Mobility Characteristics and

Timed Location Prediction in WLANsPresented by Jong-Kwon Lee

November 11, 2005


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Random Walk Model Originally proposed to emulate the unpredictable

movement of particles in physics (referred to asBrownian Motion)

Each node moves from its current location to anew location by randomly choosing a directionand speedin which to travel.

For every interval t, randomly choose

New Speed

[vmin, vmax] New Direction (0, 2]

No pause time


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Random Waypoint Model Widely used in mobile ad hoc network research

Behavior of each node

selects a random point in the simulation area as its destination,and a speedVfrom an input range [vmin, vmax].

Moves to its destination at its chosen speed.

When the node reaches its destination, it rests for some pausetime.

After this pause time, it selectsa new destination and speed,

and repeats the process.


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Reference Point GroupMobility Model

A mobility model with spatial dependency

Represents the random motion of a group of mobilenodes as well as the random motion of each individualnode within the group

Group leader

Movement of a group leader attime t:

Group members

Mobility is assigned with areference point that follows thegroup movement:

t

groupV

t

it

group

t

iRMVV


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Obstacle Mobility Model(MobiCom03)

Nodes move around pre-defined (rectangle) obstacles(e.g. buildings)

Voronoi diagram is used to determine the path of mobilenodes.

Planar graph whose edges are line segments that are equidistantfrom two obstacle corners

A variation of Random Waypoint model

The environment limits the trajectories of

mobile nodes to the Voronoi graph. Obtain the shortest path between a nodes

current location and its destination.


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Empirical Model Weighted Waypoint (WWP) model

Based on surveys from sampled respondents on USC campusduring 4 weeks

Destinations are not randomly picked with the same weight

across the simulation area. The parameters of a mobility model (e.g. pause time) are

location-dependent and time-dependent.

Topology of virtual-campus5-state Markov model for mobile nodetransition between categories


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WLAN Mobility Model(Infocom05)

Uses real-life mobility characteristics extractedfrom WLAN traces to generate mobility scenarios.

load environment description

for every simulated node do

time := 0

while time < t_sim do

call PS{select next destination}call PT{generate timing}

move to next destinationtime := time+current_session

end while

end for

Algorithm used by the WLAN mobilitymodel to generate node trajectories


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Model T (MobiCom05)

Model only for spatial registration patterns

Develop a model as a set of equations thatcharacterize the salient features of the (training)

data set No. and distribution of clusters

No. of popular APs in a cluster size C

Intra-cluster transition probability

Intra-cluster trace length

Inter-cluster transition probability

Inter-cluster trace length


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Motivation

Recent studies on characterization of usermobility and network usage in WLANs

Few studies on how the user mobility is

correlated in time (daily, weekly, monthly timescales).

Existing prediction models for user

locations in WLANs Predict only the next location w/o time

information


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Semi-Markov Mobility Model Continuous-time Markov chain (CTMC)

can characterize users state transitions as well as thesojourn times spent in each state.

However, the sojourn time characteristics ofusers in campus-like WLAN do not follow anexponential distribution.

Semi-Markov Processes Generalization of Markov processes with arbitrary

distributed sojourn times.

Can be used for obtaining both steady-statedistribution and transient distribution

characterize long-term usage of network resource +

timed location prediction with one model!


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Semi-Markov Mobility Model

Discrete state space S={1, , m}

Markov renewal process {(Xn, Tn): n0}

(Time homogeneous) semi-Markov process

Transition prob. from i to j

Sojourn time distribution instate i when the next state is j

Transition prob. matrix of the embedded Markov chain

Sojourn time distribution instate i regardless of the next state


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Steady-state User Distributionover APs

~D

noOFF

During 11/1/2003~2/29/2004

786 active users


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Similarity of Mobility Patternsbetween Different Periods

Use ofsimilarity measuresto check thecorrelation of the mobility behavior Cosine distance(= correlation coefficient)

: a pattern similarity measure

* 0 sim(p,q) 1sim(p,q) = 1 Identical Pattern

qpqp

qp

qpqpsim

m

i i

m

i i

m

i ii

1

2

1

2

1),(


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Monthly Correlation 1 month = 4 weeks 8 months (11/2/2003 ~ 6/12/2004)

More similar between consecutive periods

3/21/2004~4/17/2004


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Weekly Correlation 14 weeks (2/1/2004~5/8/2004)

3/21/2004~4/17/2004


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Daily Correlation For each day of week (Sunday, Monday, , Saturday)

8 weeks (11/2/2003~12/27/2003)


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Different User Groups


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Ping-Pong Phenomena Ping-pong transition: for APs i, j, and k,

(ijij) or (ijki)

For each user, Ping-pong ratio = [# of ping-pong transitions] / [# of all transitions]

For 786 users, Average ping-pong ratio = 0.40

Median = 0.38

Ping-pong happens quite oftenand should not be ignored !

=> The transition probability and residence time characteristics at each APwith the original association patterns can distortthe actual mobilitybehavior.

CDF

(cumul

ativefractionofusers)

Ping-pong ratio

M bili Ch D Pi


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Mobility Change Due to Ping-Pong Phenomena

Elimination of ping-pong transitions from theoriginal association history of each user Identify a sequence of ping-pong transitions

Cluster the states (i.e. APs) in the sequence of the

ping-pong transitions into an Aggregate State (AS) Replace the sequence of the ping-pong transitions

with just one transition to the dominant AP with whichthe user has mostly associated among the APs in the

same ASex) a->1->4->1->4->b=> a->1->b if 1 is dominant in AS={1,4}

a->4->b if 4 is dominant in AS={1,4}


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Mobility from Corrected Data(after Elimination of Ping-Pong)

~D

noOFF


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Mobility from Original Data

~D

noOFF


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Change in Residence Time

Ti d P di ti f U


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Timed Prediction of UserLocation

Transient behavior of semi-Markov model

Numerical solution: discretize by t = kh

Ti d P di ti f U


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Timed Prediction of UserLocation

Predict users location at every k time steps k

ij

nk(n-1)k (n+1)k

Ti d P di ti f U


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Timed Prediction of UserLocation: Results

h = 600, K = 12, Tp = 1800

A li ti M bilit


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Application: Mobility-awareLoad Balancing in WLAN

Lets take advantage of ping-pong phenomena. Rationale: APs in the same AS has served in turn the user with

the acceptably high SNR.

Basic idea of load balancing over APs Assume the load at each AP is the number of users at the AP.

(We may later extend this to the case of traffic amount at eachAP.)

Move users at overloaded APs to a lightly loaded AP in the sameAS.

Balance Index:

where m: # of APs, Li: load at AP i

= 1 : All Lis have the same value. 1/n : Heavily unbalance.

22

iiLmL


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Overview of the Mobility-awareLoad Balancing Algorithm

Incorporating timed location prediction Can predict future load distribution.

Can avoid load unbalance in advance.

Use a 1xm bit vector AC to control the association of users to APs(m: # of APs)

Initially, AC(i) = 1 for all AP i If the load at AP i is predicted to be greater than a thresholdL, AC(i)

0.

AC(i) is reset to 1 if the load at AP i is underL (either expectedly oractually).

When a user moves to a new location, First checks the AC bit corresponding to the AP having highest signal

strength.

If it is 0 (i.e. it is overloaded), the user tries to associate to alternativeAPs in the same AS as that AP.

If the overloaded AP belongs to no AS, or there are no alternative APshaving sufficient signal strength, the user is allowed to associate to theoverloaded AP.


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Simulation Results Total users = 786, OFF users = 509, Active users = 277

Original distribution : Balance Index = 0.180823 with max load = 9 at AP 361

After load balancing : Balance Index = 0.327917 with max load = 3 at AP 373

Sim lation Res lts Mo e


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Simulation Results: MoreActive Users

Total users = 786, OFF users = 201, Active users = 585 (OFF users artificially reduced)

Original distribution : Balance Index = 0.284616 with max load = 12 at AP 361

After load balancing : Balance Index = 0.506377 with max load = 4 at AP 275

mobility model by lewis

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