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Design and Analysis of Optimal Multi-Level Hierarchical Mobile IPv6 Networks. Amrinder Singh Dept. of Computer Science Virginia Tech. Agenda. Introduction OM-HMIPv6 Analytical Modeling Numerical Results Simulation Validation Conclusion. Introduction.

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Design and Analysis of Optimal Multi-Level Hierarchical Mobile IPv6 Networks

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Design and Analysis of Optimal Multi-Level Hierarchical Mobile IPv6 Networks

Amrinder Singh

Dept. of Computer Science

Virginia Tech.


  • Introduction

  • OM-HMIPv6

  • Analytical Modeling

  • Numerical Results

  • Simulation Validation

  • Conclusion


  • Mobility management is essential for keeping track of user’s current location

  • Many schemes proposed for cellular networks

  • Next-generation wireless/mobile network will be unified networks based on IP technology

  • Design of IP-based mobility management schemes has become necessary


  • HMIPv6 is enhanced version of Mobile IPv6

  • Minimizes signaling cost using a local agent called mobility anchor point (MAP)

  • MN entering MAP domain receives Router Advertisement (RA) from one or more local MAPs

  • MN can bind current CoA with an address on MAP’s subnet

Communication of MN

  • MAP receives all packets on behalf of MN

  • Encapsulates and forwards directly to MN’s current address

  • Movement of MN within local MAP domain requires registration of new CoA with MAP reducing location update

  • To reduce location update further, the case of multi-level hierarchical MAPs


  • One of the earlier schemes focused on determination of optimal size of regional network

  • Did not focus on determining optimal hierarchy

  • Other schemes proposed to optimize HMIPv6 did not consider the case of multi-level hierarchical structure

Optimal Multi-Level HMIPv6

  • Multiple MAPs organized in a tree structure

    • Root MAP

    • Intermediate MAP

    • Leaf MAP

  • Better fault tolerance, failure of MAP affects only the sub-tree under the MAP

  • Reduction in location update cost by localization of binding update procedure

  • Increase in packet delivery cost due to encapsulation and decapsulation

Binding Update

  • MN sends Binding Update (BU) message to RMAP

  • At LMAP, check if MN is already registered with it

    • If it is, registration completed

    • Otherwise register and forward the BU

  • At each IMAP, check for registration as with LMAP

  • Process stops at IMAP where MN is already registered

Parameters for determining optimal level

  • The number of MNs

    • Calculate the average number of MNs in network and divide by total area to determine density

  • MN mobility

    • Determine average MN velocity during time interval T

  • MN activity

    • Determine session arrival rate and average session size during T

Configuration of OM-HMIPv6

  • RMAP broadcasts RA with DIST=0

  • IMAP receives RA and re-broadcasts RA after increasing DIST field and compares DIST with optimal depth D*

    • If DIST<D*, MAP appends its IP address to MAP hierarchy list

    • Otherwise, forward RA as it is

  • Can employ some kind of loop elimination

Adaptation Scheme

  • Parameters defined change from time to time

  • Need to redefine optimal hierarchy

  • Recalculate optimal hierarchy and perform reconfiguration

  • Not done very often

Analytical Modeling


  • Access Routers (AR) are uniformly distributed in each LMAP

  • The tree formed is a binary tree

  • Fluid-Flow mobility model with rectangular cell configuration

Rectangular cell configuration

Location update cost

  • Number of cells in network = N, i.e. ARs

  • Number of ARs located in k-level MAP domain

  • Lc is the perimeter if cell

  • Lk is perimeter of k-level MAP domain

Location Update Cost

  • Crossing rate for fluid flow model is given by

  • Total location update cost takes into account all possible crossings in the network

    • MNs moving in from foreign networks

    • MNs moving across k-level MAP domains

    • MNs moving across AR cell boundaries

ρ is the density of MNs

v is the average velocity of MNs

Location Update Cost

Update Cost to HA caused by MN moving to foreign network

Location cost incurred by crossing from one cell to another

Sum of location update incurred by crossing k-level MAP domain area

Unit Location update cost

ω and η are unit update cost over wired and wireless link respectively

where H is distance between RMAP and AR

and di-1,i =1

Packet Delivery Cost

  • Need to consider transmission cost and processing cost at each entity

  • Packet delivery from CN to RMAP is given by

α is the unit transmission cost over a wired link

PHA is processing cost at HA

Packet Delivery Cost

  • Packet delivery cost from RMAP to AR

  • Packet Delivery cost from AR to MN

    • where β is unit transmission cost over wireless link

Calculation of Processing cost

  • PMAP(k) is processing cost at k-level MAP domain

  • Includes lookup cost and packet encapsulation/decapsulation cost

  • PMAP(k) is assumed to be proportional to log(NU(k))

Calculating optimal hierarchy

  • Formulate total cost as a function of hierarchy and SMR

  • SMR is session arrival rate divided by mobility rate

  • Then define the difference function

Calculating optimal hierarchy

  • If is larger than 0, the optimal hierarchy is 0

  • Otherwise optimal hierarchy is given by

  • Optimization can also application based

    • Calculate total costs independently for each application

    • Calculate weighted total cost

Numerical Results

  • System Parameters used

Numerical Results

Session Arrival rate is normalized to 1

As SMR , mobility  and location cost 

As ARs , more levels and location cost 

Optimal Hierarchy increases with number of ARs. More importantly an optimal hierarchy level exists

Numerical Results

Varying the communication costs does change optimal hierarchy by determining which cost dominates.

Higher SMR means that packet delivery cost dominates the total cost and a lower hierarchy will reduce the total cost. Adaptive scheme will be effective

Simulation Validation

  • 5 types of MAP hierarchy evaluated.

  • Use random walk mobility model

    • Routing probability for each direction is the same

Simulation Validation

  • The MN stays in a given cell area for time tR

  • This follows Gamma distribution with b=kλm

  • The session arrival process follows Poisson distribution

  • The session length is modeled by Pareto distribution with mean =ak/(a-1)

Simulation Result

Mean session length is set to 10. Session arrival rate is normalized to 1.

As SMR , mobility , hence frequency of binding updates 

Higher hierarchy implies lower binding cost as more number of LMAPs and IMAPs means binding update does not reach RMAP often

Simulation Result

Mobility rate is fixed at 0.001

We need to count how many MAP processings occur when packets are delivered

As SMR , session arrival rate 

More packets to deliver

Also cost greater for higher hierarchy

Simulation Result

Total cost is the sum of binding update and packet delivery costs

Validates the analytical result that lower SMR means more hierarchical levels while a higher SMR means lower hierarchical levels


  • Authors provide extensive analysis on multi-level HMIPv6 which can support scalable services

  • Showed that optimal hierarchical level exists for the network

  • Investigated the effect of SMR on hierarchy

  • However, did not talk about how often reconfiguration would be needed and did not indicate the cost that would incur.

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