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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

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A theoretical study of optimization techniques used in registration area based location management models and online al

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










Area 1


Area 2


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

    • 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)





  • 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





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


RA2b c









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



  • 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.

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