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Design and Analysis of Optimal
Multi-Level Hierarchical Mobile
IPv6 Networks
Amrinder Singh
Dept. of Computer Science
Virginia Tech.
Agenda
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Introduction
OM-HMIPv6
Analytical Modeling
Numerical Results
Simulation Validation
Conclusion
Introduction
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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
Introduction
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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
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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 multilevel hierarchical MAPs
Background
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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
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Multiple MAPs organized in a tree structure
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Root MAP
Intermediate MAP
Leaf MAP
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Better fault tolerance, failure of MAP affects only the subtree under the MAP
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Reduction in location update cost by localization of binding
update procedure
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Increase in packet delivery cost due to encapsulation and
decapsulation
Binding Update
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MN sends Binding Update (BU) message to RMAP
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At LMAP, check if MN is already registered with it
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If it is, registration completed
Otherwise register and forward the BU
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At each IMAP, check for registration as with LMAP
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Process stops at IMAP where MN is already registered
Parameters for determining
optimal level
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The number of MNs
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MN mobility
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Calculate the average number of MNs in network and divide
by total area to determine density
Determine average MN velocity during time interval T
MN activity
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Determine session arrival rate and average session size
during T
Configuration of OM-HMIPv6
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RMAP broadcasts RA with DIST=0
IMAP receives RA and re-broadcasts RA after
increasing DIST field and compares DIST with
optimal depth D*
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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
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Parameters defined change from time to time
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Need to redefine optimal hierarchy
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Recalculate optimal hierarchy and perform
reconfiguration
Not done very often
Analytical Modeling
Assumptions
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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
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Number of cells in network = N, i.e. ARs
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Number of ARs located in k-level MAP domain
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Lc is the perimeter if cell
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Lk is perimeter of k-level MAP domain
Location Update Cost
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Crossing rate for fluid flow model is given by
ρ is the density of MNs
v is the average velocity of MNs
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Total location update cost takes into account all possible
crossings in the network
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MNs moving in from foreign networks
MNs moving across k-level MAP domains
MNs moving across AR cell boundaries
Location Update Cost
Update Cost to HA caused
by MN moving to foreign
network
Sum of location update incurred by
crossing k-level MAP domain area
Location cost incurred by crossing
from one cell to another
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
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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
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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
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PMAP(k) is processing cost at k-level MAP domain
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Includes lookup cost and packet encapsulation/decapsulation cost
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PMAP(k) is assumed to be proportional to log(NU(k))
Calculating optimal hierarchy
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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
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If is larger than 0, the optimal hierarchy is 0
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Otherwise optimal hierarchy is given by
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Optimization can also application based
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Calculate total costs independently for each application
Calculate weighted total cost
Numerical Results
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System Parameters used
Numerical Results
Optimal Hierarchy increases with
number of ARs. More importantly
an optimal hierarchy level exists
Session Arrival rate is normalized to 1
As SMR , mobility  and location cost 
As ARs , more levels and location cost 
Numerical Results
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
Varying the communication costs does
change optimal hierarchy by determining
which cost dominates.
Simulation Validation
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5 types of MAP hierarchy evaluated.
Use random walk mobility model
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Routing probability for each direction is the same
Simulation Validation
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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
Conclusions
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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.