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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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)
00.2
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q
CMR = 0.10, = 1.0, D = 3, = 2, U = 10, V = 1
r
CT
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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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q
CMR = 0.10, = 100.0, D = 3, = 2, U = 10, V = 1
r
CT
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q
CMR = 0.10, = 0.1, D = 3, = 2, U = 10, V = 1
r
CT
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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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D
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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D
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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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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Grupo de Interconexión de Redes de Banda Ancha, ITACAUniversidad Politécnica de Valencia
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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