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A Theoretical Study of Optimization Techniques Used in Registration Area Based Location Management: Models and Online Algorithms. Sandeep K. S. Gupta Goran Konjevod Georgios Varsamopoulos Arizona State University. Location Management. Part of Mobile Communication System

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A Theoretical Study of Optimization Techniques Used in Registration Area Based Location Management: Models and Online Algorithms

Sandeep K. S. Gupta

Goran KonjevodGeorgios Varsamopoulos

Arizona State University

location management
Location Management
  • Part of Mobile Communication System
    • Location Tracking (update, registration)
    • Call Delivery (search)
  • Components
    • Cells (base stations)
    • Registration Areas, Location Registers
      • Home Location Register (HLR)
      • Visiting Location Register (VLR)
    • Mobile Units (subscribers)
conceptual configuration and related work improvements

HLR

HomeRegistrationArea

Backbone

Network

Cells

VLR 3

VLR1

VLR 2

Registration

Area 1

Registration

Area 2

Registration

Area 3

Conceptual Configuration andrelated work (improvements)
  • Update
    • Subscriber moves to new RA
    • New VLR, HLR updated
  • Search
    • HLR is queried
  • Search cost improvements
    • Location Caching
    • Profile Replication
    • Prediction
  • Update cost improvements
    • Forwarding Pointers
    • Look-ahead Registration
    • Multi-layered Configuration
    • RA Overlapping
previous work
Previous Work
  • Dynamic Overlapping of Registration Areas
    • Find optimal size of a Registration Area by including and excluding cells from RAs
  • Optimal Registration Sequence
    • Minimize the number of registrations (updates) over a given user path in the service area
  • Online Algorithms and Competitiveness in Location Management
overlapping
Overlapping

RA1

RA2

RA1

RA2

  • Overlapping
    • Eliminates updates due to subscriber oscillations at borders
    • Increases coverage of a Registration Area without increasing the number of users
  • Dynamic Overlapping
    • Reduces registration area planning time
    • Adapts to changes of call and mobility
    • Has higher requirements at component logic
optimal registration sequence
Optimal Registration Sequence
  • Registration Areas (statically) overlap
  • Offline version
    • Mobile follows a predetermined path
    • Overlapping gives multiple choices on selection of Registration Area at each part of the mobile’s path
    • Find a sequence of registrations (updates) of minimal count
    • Greedy approach finds optimal solution
offline and online computation
Offline and Online Computation
  • Offline problem
    • All input is given a-priori
    • Complete solution is given in “one time”
  • Online problem
    • Input is given one element at a time
    • Decision/output must be made upon arrival of an element
    • Sequence of output is the partial solution up to that point
  • Competitiveness
    • An online algorithm may not be able to find optimal solution
    • Competitive ratio : the worst possible “performance” or “size” ratio of an algorithm’s solution over the respective optimal solution for any input
online ors problem
Online ORS problem
  • Path is not known – a stochastic mobility model is known.
  • At each intersection decide if the mobile should register with another Registration Area
  • Competitiveness
    • No online ORS algorithm is inherently competitive
this paper
This paper
  • More on competitiveness
  • Modeling of Location Management techniques as Metrical Task Systems (MTS)
    • Known algorithms
    • Known bounds
    • Unified way of comparing LM schemes?
  • MTS lower bounds may not be good enough
    • Bounds depend on number of states
    • Number of states can be very large
    • We can get better bounds under restricted models
metrical task systems cont d
Metrical Task Systems (cont’d)

Tc

Tb

Tc

Tb

  • A Formal Definition
    • Μ=(Σ,Γ,c) metrical task system
    • Σ={S1, S2,…, Sn} set of states
    • Γ={T1, T2,…, Tm} set of tasks
    • c : Σ× (Σ Γ) → R cost function
    • triangular inequality on metric space (cost function)
  • MTS Problem
    • s=(Ti,Tj,…) sequence of tasks
    • Find sequence of states and executions that minimizes total cost for a given sequence of tasks

S2

S1

S4

S3

metrical task systems cont d1
Metrical Task Systems (cont’d)
  • Offline version
    • Has a simple solution
    • Can be mapped to a shortest path problem
  • Online version
    • Best known algorithm achieves polylogarithmic competitiveness ratio to the number of states
    • There is lower bound to competitiveness ratio of (logn) ( n is the number of states)
example of lm problem as mts registration optimization
Example of LM problem as MTS:Registration Optimization
  • System Formulation
    • A state is a pair of a registration and a location
    • Incoming tasks are relocations
  • Problem definition
    • Given a sequence of relocations find a sequence of registrations
  • Performance
    • The number of states is polynomial to number of RAs
  • Example
    • Initial state S1 (location a)
    • Input relocations: b c b c b
    • Result execution: S1 S2 b S4 c S3 b c S2 b

RA1a

RA2b c

1,b

0

1

1,a

2,c

2,b

1

0

bounds under restricted models competitiveness of ors
Bounds under restricted models:Competitiveness of ORS
  • A run is maximal constant subsequence of offline optimal sequence
  • There are as many runs as registrations made by the offline optimal sequence
  • RESTRICTION: Throughout a run there can be up to k different available RAs
  • At each run any algorithm cannot make more than (k-1) bad choices
  • Competitive ratio cannot be worse than k
also in this paper
Also in this paper
  • MTS formulations for
    • Pointer Forwarding
    • Multiple (replicated) registrations
    • Pre-emptive look-ahead registration
  • Bounds under restricted models for
    • Location Caching using sliding window
    • Dynamic Update using stochastic process
conclusions
Conclusions
  • There are many optimization problems in Location Management
  • Many performance enhancements to LM can also be expressed as online decision/optimization problems
  • LM schemes can be modeled as Metrical Task Systems
  • Known bounds to Metrical Task Systems are not good enough
  • Under restricting yet reasonable assumptions, better bounds can be found.