4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha,...

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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia

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Location Management Based on the Mobility Patterns of Mobile Users

Authors:

Ignacio Martinez-ArruePablo Garcia-EscalleVicente Casares-Giner

GIRBA-ITACA, Universidad Politecnica de Valencia

Presented by:

Ignacio Martinez-Arrue

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Contents

1. Introduction

2. Overview on location management

3. Proposed mobility model

4. Location update procedure

5. Terminal paging procedure

6. Numerical results

7. Conclusions

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1. Introduction

Mobility models Location management depends on mobility patterns of Mobile

Terminals (MTs) Random walk mobility model commonly used

We propose A new mobility model that generalizes the random walk model A versatile model that considers mobility patterns through a

directional movement parameter A valid model for

• Macrocellular scenarios (low mobility and random movement)• Microcellular scenarios (high mobility and directional movement)

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2. Overview on location management (I)

There is a trade off between LU and PG procedures

Location Management

Location Update (LU)

Call Delivery (CD)

Registration (RG)

Interrogation (IG)

Terminal Paging (PG)

Location Update (LU)

Location management: set of procedures that allow an MT being locatable at any time

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2. Overview on location management (II)

LU procedures Static schemes: Location Areas (LAs) Dynamic schemes

• Time-based• Movement-based• Distance-based

General framework of the movement-based LU scheme: each time the MT revisits the cell it had contact with the fixed network

Increases the movement-counter with probability p Freezes (stops) the movement-counter with probability q Resets the movement-counter with probability r p + q + r = 1

PG procedure One-step PG Selective PG

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3. Proposed mobility model (I)

Scenario with hexagonal cells

Cell sojourn time featured by a generalized gamma distribution Probability density function (pdf): fc(t)

Mean value: 1/λm (λm is the mobility rate)

Laplace Transform of the pdf: fc*(s)

Call arrivals: Poisson process with rate λc

a = fc*(λc): probability that the MT leaves its current cell before a

new incoming call is received

Call-to-Mobility Ratio (CMR): θ = λc /λm

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3. Proposed mobility model (II)

Directional movement parameter (α) values within [0,∞[ 0 ≤ α < 1 : High probability of moving towards an inner ring or

being roaming within the same ring α = 1 : Random walk mobility model 1 < α < ∞: High probability of moving towards an outer ring

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3. Proposed mobility model (III)

2D Markov chain and 1D Markov chain Each label of the cell layout (x,i) represents a state of the 2D Markov chain

Cells are grouped by rings to obtain a 1D Markov chain that simplifies the model

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4. Location update procedure (I)

Considered movement-based LU mechanism When the MT revisits the cell where it had contact with the fixed

network by last time the movement counter is• Increased with probability p• Stopped (frozen) with probability q• Reset with probability r

(p,q,r) = (1,0,0): Conventional movement-based scheme (LU in A) (p,q,r) = (0,1,0): Frozen scheme (LU in B) (p,q,r) = (0,0,1): Reset scheme (LU in C)

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4. Location update procedure (II)

α(z): probability that there are z boundary crossings between two call arrivals

Ms(z): expected number of LUs triggered by the MT in z movements given that the MT is initially in ring 0 and its movement-counter value is s

It depends on the movement threshold (D), p, q, r and α

M0*(a): Z-Transform of M0(z) evaluated at a

LU cost (CLU)

Unitary LU cost CMR a = fc*(λc)

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5. Terminal paging procedure

Shortest-distance-first (SDF) PG The Registration Area (RA) is divided into l PG Areas (PAs)

πs,i (z): probability that the MT is roaming within ring i after z movements given that the MT is initially in ring 0 and its movement-counter value is s

π0,i: probability that the MT is roaming within ring i when a call arrival occurs

ρk: probability that the MT is in the PA Ak when a call arrives Computed from π0,i by adding the terms where the ring i belongs

to the PA Ak

ωk: number of cells polled until the MT is found in the PA Ak

PG cost (CPG) V: Cost of polling a cell

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6. Numerical results (I)

Total location management cost: CT = CLU + CPG

Influence of p, q and r on CT with random walk model (α = 1) Best performance for the reset strategy (p,q,r) = (0,0,1) Worst performance for the movement strategy (p,q,r) = (1,0,0)

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CMR = 0.10, = 1.0, D = 3, = 2, U = 10, V = 1

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CT

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6. Numerical results (II)

Influence of p, q and r on CT with high and low values of α Best performance for the reset strategy (p,q,r) = (0,0,1) Worst performance for the movement strategy (p,q,r) = (1,0,0)

The cost is less sensitive to the values of p, q and r as α increases

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CMR = 0.10, = 100.0, D = 3, = 2, U = 10, V = 1

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CT

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CMR = 0.10, = 0.1, D = 3, = 2, U = 10, V = 1

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CT

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6. Numerical results (III)

Convex functions: optimum threshold (D*) and optimum cost (CT*)

CLU dominates for D < D* and CPG dominates for D > D*

Selective PG: CPG decreases and D* increases because CPG dominates for greater values of D

Distance-based scheme cost increases quickly as α is greater All strategies perform equally if α tends to infinity

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CT

CMR = 0.10, =2, U = 10, V = 1

Movement ( p, q, r)=(1,0,0), =1.0Movement ( p, q, r)=(1,0,0), =2.0Movement ( p, q, r)=(1,0,0), =100.0Movement ( p, q, r)=(0,1,0), =1.0Movement ( p, q, r)=(0,1,0), =2.0Movement ( p, q, r)=(0,1,0), =100.0Movement ( p, q, r)=(0,0,1), =1.0Movement ( p, q, r)=(0,0,1), =2.0Movement ( p, q, r)=(0,0,1), =100.0Distance, =1.0Distance, =2.0Distance, =100.0

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CT

CMR = 0.10, =1, U = 10, V = 1

Movement ( p, q, r)=(1,0,0), all Movement ( p, q, r)=(0,1,0), =1.0Movement ( p, q, r)=(0,1,0), =2.0Movement ( p, q, r)=(0,1,0), =100.0Movement ( p, q, r)=(0,0,1), =1.0Movement ( p, q, r)=(0,0,1), =2.0Movement ( p, q, r)=(0,0,1), =100.0Distance, =1.0Distance, =2.0Distance, =100.0

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6. Numerical results (IV)

CT (distance) < CT (reset) < CT (frozen) < CT (movement) The distance-based scheme is more sensitive to α than

other schemes As movement is more directional (increasing α), all costs are

approaching among them For α < 10, differences between CT’s become significative

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CT

CMR = 0.10, D = 3, = 1, U = 10, V = 1

Movement ( p, q, r) = (1,0,0)Movement ( p, q, r) = (0,1,0)Movement ( p, q, r) = (0,0,1)Distance

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CT

CMR = 0.10, D = 3, = 2, U = 10, V = 1

Movement ( p, q, r) = (1,0,0)Movement ( p, q, r) = (0,1,0)Movement ( p, q, r) = (0,0,1)Distance

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7. Conclusions

Proposed mobility model Valid for microcellular (directional movement) and macrocellular

(random movement) environments Directional movement modeled through the α parameter

• α = 1 : Random walk mobility model• As α increases from 1 to infinity, a more directional movement is

modeled Studied location management schemes

The distance-based scheme yields the best performance In the movement-based general framework, the lowest cost is

achieved by the reset scheme The cost of all policies is equal as α tends to infinity

The distance-based mechanism is more complex to implement

When movement is directional, a reset scheme may be more suitable for its simplicity

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THE END

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4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha,...

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