1. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 1 Location Management Based on the Mobility Patterns of Mobile Users Authors: Ignacio Martinez-Arrue Pablo Garcia-Escalle Vicente Casares-Giner GIRBA-ITACA, Universidad Politecnica de Valencia Presented by: Ignacio Martinez-Arrue

2. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 2 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

3. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 3 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)

4. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 4 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

5. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 5 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

6. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 6 3. Proposed mobility model (I) Scenario with hexagonal cells Cell sojourn time featured by a generalized gamma distribution Probability density function (pdf): f c (t) Mean value: 1/λ m ( λ m is the mobility rate) Laplace Transform of the pdf: f c * (s) Call arrivals: Poisson process with rate λ c a = f c * (λ c ) : probability that the MT leaves its current cell before a new incoming call is received Call-to-Mobility Ratio (CMR): θ = λ c /λ m

7. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 7 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

8. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 8 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

9. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 9 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)

10. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 10 4. Location update procedure (II) α(z) : probability that there are z boundary crossings between two call arrivals M s (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 M 0 * (a) : Z-Transform of M 0 (z) evaluated at a LU cost ( C LU ) Unitary LU cost CMR a = f c * (λ c )

11. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 11 5. Terminal paging procedure Shortest-distance-first (SDF) PG The Registration Area (RA) is divided into l PG Areas (PAs) π s,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 π 0,i : probability that the MT is roaming within ring i when a call arrival occurs ρ k : probability that the MT is in the PA A k when a call arrives Computed from π 0,i by adding the terms where the ring i belongs to the PA A k ω k : number of cells polled until the MT is found in the PA A k PG cost ( C PG ) V : Cost of polling a cell

12. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 12 6. Numerical results (I) Total location management cost: C T = C LU + C PG Influence of p, q and r on C T 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)

13. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 13 6. Numerical results (II) Influence of p, q and r on C T 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

14. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 14 6. Numerical results (III) Convex functions: optimum threshold ( D * ) and optimum cost ( C T * ) C LU dominates for D D * Selective PG: C PG decreases and D * increases because C PG 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

15. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 15 6. Numerical results (IV) C T (distance) < C T (reset) < C T (frozen) < C T (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 C T ’s become significative

16. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 16 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

17. 4th Workshop on Wireless and Mobility, Barcelona Grupo de Interconexión de Redes de Banda Ancha, ITACA Universidad Politécnica de Valencia 16th-18th January 2008 17 THE END Thank you very much for your attention Do you have any questions?