a comparative cost analysis of degradable location management algorithms in wireless networks

A Comparative Cost Analysis of A Comparative Cost Analysis of Degradable Location Management Degradable Location Management Algorithms in Wireless NetworksAlgorithms in Wireless Networks

Ing-Ray Chen and Baoshan Gu

Presented by: Hongqiang Yang , Jianghui Ying

Northern Virginia Center, Virginia Tech

Agenda Agenda

Architecture of Paper:– Introduction– Notion of Degradable Location Management Algorithm – Examples of Degradable Location Management

Algorithm– Two-tier Hierarchical Framework– Comparison– Application in the analysis of service handoffs– Summary

IntroductionIntroduction

ProblemA class of degradable location management

algorithms in Personal Communication Service network for tracking mobile user in two-tier HLR-VLR structure

IS-41, FRA, PLA, LAAWhich is better?


Objective– Develop a uniform framework to provide a cost analysis of

location update and search operations for a class of degradable location management algorithms in personal communication service (PCS) networks


Method--Two level hierarchical modeling framework High-level model Calculate the costs incurred to the PCS network:

Location-update operations Call-delivery operations

Low-level model A stochastic model to estimate the values of high-level model

parameters


Location Management Scheme– Aimed to minimize the total cost Location Update

Occurs when a mobile user moves to a new location

Call delivery Occurs when there is a call for mobile user and the network must

deliver the call.


Workload condition is indicated by Call-to-Mobility ratio (CMR) – CMR is high: Location Cache Scheme is

effective

– CMR is low: FRA, PLA, LAA are effective

Degradable Location ManagementDegradable Location Management

No assumption regarding the structure of the PCS network

Conceptually, HLR is in high level and VLR is in low level.

Maybe some network switches connecting the HLR to VLRs in the mobile network


IS41:– Service area divided into registration areas each

corresponding to a VLR

User moves to a new registration area

Send the registration information to the new VLR

Update information

A hierarchical PCS network

HLR

PSTN

RSTP

LSTP LSTP LSTP

VLR VLR VLR VLR VLR VLR

… … …

Home Location Register

Public Switched Telephone Network

Regional Signaling Transfer Point

Local Signaling Transfer Point

Visitor Location Register


The state of a location management algorithm: depends on the extent to which the location information has been degraded since the last location update operation was performed to the HLR– Strong– Weak


Strong State:– means the HLR store the current information of the

mobile user in its own database– HLR can find the mobile user directly

Weak State:– means the current information of the mobile user is

not in the HLR– HLR must consult location database stored

elsewhere to find the mobile user


The spectrum of degradable location algorithms– encompasses all existing location management

algorithm– differ on how fast and in what way the system’s

state degrades over time as the user moves across VLR boundaries


The spectrum of degradable location algorithmIS-41

LAA(2)

FRA(2)

PLA(2)

LAA(3)

FRA(4)

PLA(3)

Paging

Degradable Location ManagementDegradable Location ManagementIS-41

User moves across VLR boundary

Send information to new VLR

Update information in HLR

Degradable Location ManagementDegradable Location ManagementFRA(K)

User moves across VLR boundary– Length of link of pointers < K:

Set up a pointer to the two involved VLRs

– Length of link of pointers = K:Update information in HLR

Degrades over time as more and more moves


PLA(n)– HLR records a VLR as the agent– The agent covers all VLRs within a distance n from the

agent( local region)– No update at all with local moving– Update when across local region boundary– Paging starts from the agent

Degrades over time since the location of the mobile user becomes fuzzier to the HLR as more and more time has elapsed since the last update performed


LAA(n)– HLR records a VLR as the local anchor(LA)– The LA covers all VLRs within a distance n from the

LA– Update in LA with local moving– Update in HLR when across a regional switch boundary

Three steps researching:– HLR -> LA -> VLR


Performance metric:– The network cost due to location update

between two successive calls to a mobile user

Paper contribution: – Provides method to quantifying the location

update cost for a given location management algorithm with respect to the basic scheme

– Classify the algorithm

0

0.2

0.4

0.6

0.8

1

Location Update Cost:CMR=0.1

IS-41

LAA(2)

FRA(2)

PLA(2)

LAA(3)

FRA(4)

PLA(3)

Paging

The ratio of the average communication cost between two VLRs to the average communication cost between the HLR and a VLR is 0.3


Classify mobile users into priority classes based on their quality of service(QoS) requirements

Separate QoS classes are being served by separate location management schemes

Simplify the per-user-based location management to the per-class-based location management

Modeling Degradable Location Modeling Degradable Location Management AlgorithmManagement Algorithm

Description of two-level modelExamples of Degradable location

management algorithm– Description of algorithm– Low-level model

Modeling Degradable Location Modeling Degradable Location Management AlgorithmManagement Algorithm

Two-level model– High-level model: cost model

Update cost Xupdate

Query cost Xsearch

Xcost = Xupdate * / + Xsearch

– Low-level model Aimed to provide the parameters for high-level model

– Low-level model Parameterize equation in high-level model Define parameters in our model

Per-mobile-user parameters

The rate at which the mobile user moves across VLR boundaries

The rate at which the mobile user is being called

CMR / , the call-to-mobility ratio of the mobile user

Mobile network parameters

T The average VLR-HLR round-trip communication cost

The average VLR-VLR round-trip communication cost

Basic HLR/VLRBasic HLR/VLR

A mobile user is permanently registered under a location register(HLR)

Mobile user enters a new VLR areaReports to VLRVLR inform HLRHLR update location information

Location Update Cost = 1

Paging and Location Algorithm(PLA)Paging and Location Algorithm(PLA)

Agent: the VLR performs the last update operation to the HLR

HLR update location information only when the distance between the agent and the current VLR is great than or equal to a predefined distance value n

R0R1

R1R1

R1

R1R2

R2R2

R2R2

R1

R2

R2

R2R2

R2R2

R2

SDF partitioning under the hexagonal model

PSTN

HLR

F

A

Local Movement: within the 2-Distance region

Update Action: None

Regional Movement: Outside of 2-Distance Region

Action: Update the HLR

PLA Algorithm

ED

CB

Paging and Location Algorithm(PLA)Paging and Location Algorithm(PLA) Modeling parameters

– n: specify the (n-1)-distance region within a user causes no update cost

i : the mobility rate of the mobile user moving from ring i to ring i + 1

i : the mobility rate of the mobile user moving from ring i + 1 to ring i

r : the execution rate to perform a location update to the HLR

I : the execution rate to locate the mobile user currently located in ring I

– P(i,j):The probability that the system is in a particular state in equilibrium


Assuming random move The probability of the mobile user moving from

ring i to i + 1, i >= 0(2i + 1) / 6i , if i >= 1,

1, if i = 0. The probability of the mobile user moving from

ring i + 1 to i, i >= 0(2 (i + 1) - 1 )/ (6(i +1)), if i >= 0,


The mobility rate of the mobile user moving from ring i to ring i + 1

(2i + 1) / 6i , if i >= 1,

i = , if i = 0.

The mobility rate of the mobile user moving from ring i + 1 to ring i i = (2i +1) /( 6* (i + 1)) , i >= 0


The execution rate to perform a location update from a new VLR agent to the HLRr = 1 / T


The time to locate the mobile user in ring i– From HLR to agent– From the agent to the current VLR(in ring i)– From the current VLR back to the HLR

The execution rate to locate the mobile user in ring ii = 1/(T + 0.5*(3i2 + 3i) * )

Query one-half of the VLRs in the i-distance region


Low-level Makov model – State represented by (a, b)

a: 0, IDLE 1, CALLED

b: the current distance between the mobile user and the local agent

Markov Model for PLAMarkov Model for PLA

0,0 0,1 0,2 0,n-1 0,n-1*

1,0 1,1 1,2 1,n-1 1,n-1*

r

0 1

n-1

0 1 2 0

2

01 2 n-1

0 1 21 2 n-1 r

Average cost for location update operation

Average cost for location search operation

Average total cost:


))(1/ ) P (P( pla1

0

*1)-n(i,1)-n(i, i

update

) (1/)P(P

) ) (1/ P(pla

01)*-n(1,*1)-n(0,

j

1

0i

1-n

0j

j)(i, search

searchupdate plaplapla /cost

Forwarding and Resetting Algorithm(FRA)Forwarding and Resetting Algorithm(FRA)

HLR only points to the VLR at the beginning of the forwarding chain

User moves across VLR boundary– Length of link of pointers < K:

Set up a pointer to the two involved VLRs

– Length of link of pointers = K:Update information in HLR

PSTN

HLR

F

A

Local Movement: length of the forwarding chain is less than 5

Update Action: update the Forwarding Pointer between Two involved VLRs

Regional Movement: Chain Length = 5


FRA Algorithm: K=5

ED

CB


Two additional behaviors in modified Markov Model under FRA– The forwarding chain will be reset after a

location query operation is performed– When the mobile user moves back to the

previously visited VLR in the chain, the length of the forwarding chain is reduced by 1 and no pointer deletion operation is required between

Obsolete pointers will be purged automatically after a period of time much greater than the average reset period


Looping behavior is accounted in Markov model

Assume : when the mobile user moves across a VLR, the forwarding pointer information will be updated before it crosses another VLR– Imply that the dwell time of mobile user in a

VLR is much greater than the forwarding pointer update operation time


Model Parameters – k : the length of the forwarding chain at which a reset

operation is performed n : the mobility rate of the mobile user moving to a new

VLR. b : the mobility rate of the mobile user moving to the

previous VLR r : the execution rate to reset a forwarding chain, i.e. to

update the HLR f : the execution rate to set-up or travel a pointer

between two VLRs i : 0<= i <=k-1, the execution rate to locate the mobile

when the length of forwarding pointer is i.


The mobility rate of the mobile user moving to a new VLRn= (5/6) *

The mobility rate of the mobile user moving to the previous VLRb= (1/6) *


The execution rate to reset a forwarding chain, i.e. to update the HLRr = 1/T

The execution rate to set-up a forwarding chain, i.e. to update the HLR

f = 1/ The execution rate to locate the mobile when the

length of forwarding pointer is i( 0<= i <= k-1)

i = 1/(T + i *)


Low-level Markov Model– States represented by (s1, s2)

s1= 0 , standing for IDLE

1 , standing for Called s2 indicates the current length of the forwarding chain

– States followed by symbol ‘*’ means the mobile user just enters a new VLR but the forwarding pointer operation is not yet performed

Markov model for the PCS network under FRAMarkov model for the PCS network under FRA

0,0 0,1* 0,1 0,2* 0,k-1 0,k-1*

1,0 1,1* 1,1 1,2* 1,k-1 1,k-1*

0

1 k-1

b b

b b

f n f

f n f

n

r

n

r


P(i , j) : represent the probability that the system is in state (i , j)

fraupdate: average cost to perform a location update operation

)/1(

))()((

)/1(

)(

1

1

)*,1(*),0(),1(

2

0

),0(

)*,1(*),0()1,1()1,0(

f

k

i

iii

k

i

i

r

kkkkupdate

PPPP

PPPPfra


frasearch: average cost to perform a location search operation

fracost: the average total cost

))/1()((1

0

)*,1(*),0(),1(),0( i

k

i

iiiisearch PPPPfra

searchupdate frafrafra /cost

Local Anchor Algorithm(LAA)Local Anchor Algorithm(LAA)

Basic idea Location Registration operations should be as localized

as possible so as to reduce the number of registration messages to the HLR.

Local Anchor (LA)The VLR which performs the last registration operation

with the HLR is called the LA of the mobile user.


LA’s Coverage

N M

(VLR in ring)

Coverage

1 1 1

2 6 7

3 12 19

… … …

n 6(n-1) 3n2 – 3n + 1


AlgorithmMovement: Cross a VLR boundary but within the local

region

Operation: New VLR informs the LA without informing the HLR

Movement: regional move

Operation: New VLR informs the HLR and also becomes the new LA of the mobile

user.

PSTN

HLR

F

Local Movement: within the 3-Layer Area

Update Action: Only Update the LA(VLR A)

Regional Movement: Outside of a 3-Layer Area


LAA Algorithm

E

DCBA

Modeling a PCS network Modeling a PCS network operating under LAAoperating under LAA

Parameters

n: specify the n-layer VLR region which covers 3n2 – 3n + 1 VLRs

P1: the probability of the mobile user moving under the same network switch

P1 = 6*(3n2 – 3n + 2) – (12n - 6)/6*(3n2 – 3n + 1)

= (3n2 – 5n + 2) /(3n2 – 3n + 1)


Parameters

σ1: the mobility rate of the mobile user moving under the same network switch

i.e. σ1 = P1σ

= (3n2 – 5n + 2) /(3n2 – 3n + 1)σ

σr: the mobility rate of the mobile user crossing a network switch boundary

i.e. σr = (1- P1)σ

= (2n - 1) /(3n2 – 3n + 1)σ


Parameters

μq: the search execution rate when the mobile user is located in the agent’s area

μq = 1/T

μa: the search execution rate when the mobile user is not located in the agent’s area

μq = 1/(T + τ)


Parameters

δ1: the execution rate to update the agent, i.e. to set up a pointer between the new VLP and the agent

δ1 = 1/ τ

δ: the execution rate to update the HLR

δ = 1/ T


Markov model state representation (a, b, c)

a: whether the mobile user is in the state of being called

0 ---- idle 1---- busy

b: whether the mobile user makes a move

0 ---- not move 1---- local move

2 ---- regional move

c: whether the agent currently covers the mobile user

0 ---- yes 1 ---- no

0,0,0 0,1,10,0,10,1,0

1,0,0 1,1,11,0,11,1,0

0,2,1 1,2,1

λ λ λ λμg

μa

σr

σr

σr

σr

δ δσ1

σ1

σ1σ1

δ1

δ1

δ1

δ1

λ

(0, i, j) (1, i, j) when a call comes, the transition rate is λ

(1, 0, 0) (0, 0, 0) with the transition rate of μq

(1, 0, 1) (0, 0, 0) with the transition rate of μa

Regional move(i, 0, j) (i, 2, 1) with the transition rate of σr

(i, 2, 1) (i, 0, 0) with the transition rate δ

Local move(i, 0, j) (i, 1, j) with the transition rate of σl

(i, 1, j) (i, 0, 1) with the transition rate δl


Markov model Laaupdate

)/1()(

)/1(

)]/1()1()/1([

)1,2,()0,0,(

1

1

0

1

0

111

1

0

1

0

),1,(

),0,(

ii

i j

i j

update

PP

P

PPP

laa

ji

ji


Markov model Laasearch

Laacost

)/1()(

)/1(

1

0

)1,1,()1,0,()0,1,(

1

0

)1,2,()0,0,(

a

i

iii

g

i

ii

search

PPP

PP

laa

searchupdatet laalaalaa /cos

Analysis and ComparisonAnalysis and Comparison

Using two two-level hierarchical modeling Compare PLA, FRA, LAA with basic HLR/VLR IS-41 algorithm

VLR-to-VLR/VLR-to-HLR = 0.3

T = 1 τ = 0.3

IS-41

where IS-41update = T

IS-41search = T

searchupdatet ISISIS 41/4141cos

Comparison of PLA under different n-distance values

Performance n=3 is better than n=2 when CMR is small

Larger n means local agent can cover larger area, thus a smaller probability to cross a regional boundary. Consequently the number of update operations to HLR is reduced as n increase.

After CMR exceed a threshold, n=2 is better than n=3

As CMR increase, the larger location query cost attributed by the larger cover area starts to dominate the reduced location update cost.

searchupdatet plaplapla /cos

threshold

Comparison of FRA under different k values

Performance k=4 is better than k=2 when CMR is small

Location update cost dominates the location query cost, so a longer chain is favored since it reduces the location update cost .

After CMR exceed a threshold, k=2 is better than k=3

As CMR increase, higher cost associated with location update operations which happen frequently starts to offset the benefit of lower update operation cost.

threshold

searchupdatet frafrafra /cos

Comparison of LAA under different distance values

Performance n=3 is better than n=2 when CMR is small

Larger n means local agent can cover larger area, thus a smaller probability to cross a regional boundary. Consequently the number of update operations to HLR is reduced as n increase.

After CMR exceed a threshold, n=2 is better than n=3

As CMR increase, the larger location query cost attributed by the larger cover area starts to dominate the reduced location update cost.

threshold

searchupdatet laalaalaa /cos

Comparison of PLA, FRA and LAA head to head Comparison of location

update cost only Provide the basis for classifying

existing degradable location management algorithms based on the update cost per move relative to IS-41 for a wide range of CMR.

IS-41 keeps the system in Strong State all the time, LAA(2) is next to it in terms of maintaining the location information in a good state.

PLA(3) incurs the least amount of update overhead, since under PLA(3) the possibility of local movement is high.

PLA(3) least

LAA(2) highest

Comparison of PLA, FRA and LAA head to headComparison of the search

cost only PLA(3) incurs the most

overhead to deliver a call

Comparison of the search cost onlyComparison of location update cost only

LAA 2FRA 2PLA 2LAA 3FRA 4PLA 3

PLA 3PLA 2FRA 4LAA 3FRA 2LAA 2

Comparison of total communication cost

PLA(3) is the best when CMR is 0.1

FRA(4) is the best when CMR>0.3

PLA(2) is the worst when CMR is small

PLA(3) is the worst when CMR is large

Comparison of total communication cost for multiple users

All users are served under a single algorithm against the case when individual users are served by their respective per-user best algorithms.

As the number of users increases, the total cost difference increases because of cumulative effect.

Under single algorithm, FRA(4) is the best.

Per-user selective strategy outperform all single-algorithm cases.

Service HandoffService Handoff

What is Service HandoffThe process of transferring or migrating the service of a client from one server to another in client-server applications

Difference between location handoff and service handoff transfer of context information

Static: user profile, authentication data Dynamic: files opened, locks, stamps


Analysis of Service Handoff Using LAA scheme Assumptions

A service area corresponds to a network switch area, when a user moves across a switch boundary a service handoff will be triggered.

Context transfer communication cost Cs

Mobile user communicates with the serer by means of operations

The location and service networks are integrated


Cost factors The communication cost between the server and the LA,

the cost is τ The communication cost between the LA and the VLR in

which the mobile user currently resides if the LA is not the current VLR, which is also τ

The communication cost of migrating the service context from the old server to the new server if during the time of access, the mobile user happens to cross a service boundary, the cost of which is Cs


Recall Markov model of LAAstate representation (a, b, c)

a: whether the mobile user is in the state of being called

0 ---- idle 1---- busyb: whether the mobile user

makes a move 0 ---- not move 1---- local move 2 ---- regional movec: whether the agent

currently covers the mobile user 0 ---- yes 1 ---- no


Average cost per service operation Reward of Cs+τ to states in

which component b is 2, i.e. (0, 2, 1) and (1, 2, 1)

Reward of τ to states in which c is 0, i.e. (0,0,0) (1,0,0) (0,1,0) and (1,1,0)

Reward of 2τ to states in which c is 1 but b is not equal to 2, i.e. (0,0,1) (1,0,1) (0,1,1) and (1,1,1)

Crossover Point

Cost per service operation in LAA under different CMR and Cs values

τ =1 When Cs is relatively low, LAA(2)

is better especially at low CMR value.

Since when CMR when CMR is low and the probability of crossing switch boundary is low, so the call ratio must be low, therefore the contribution of context transfer cost is low for both schemes. There are more VLRs covered when n=3, the contribution of the 2rd cost factor is higher in LAA with n=3.

Cross point shift left as CMR increases.

As Cs increases, LAA(3) will be favored over LAA(2) for smaller probability of crossing boundary

As CMR increases, the advantage become manifest even in small Cs.

SummarySummary

Discussed the notion of degradable location management algorithm used in PCS for locating users

Classified existing location management algorithmsDeveloped methods to obtain the location update cost

for location management algorithmsTested the method by modeling PLA, FRA and LAA

and demonstrated the applicability of the modeling method

Showed how the modeling methodology can be applied to support service handoff

Conclusion and Future WorkConclusion and Future Work

Future WorkIntroducing a real-time component into the design

and deriving conditions under which user location queries can be satisfied in real-time while minimizing the location update cost

Considering users with different priority classes and discovering an optimal way to design location management algorithms so that a global design objective can be best satisfied

Investigating the applicability of the uniform framework developed in this paper to the analysis of tree-based location management algorithms.

Thank You!Thank You!

a comparative cost analysis of degradable location management algorithms in wireless networks

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