QUORUMS BASED MOBILES LOCATION SCHEME
Nadia Chetta
LSI- Department of Computer Science, Faculty of Electronic Genius & Computer Science, USTHB,
El Alia BP n°32, Bab Ezzouar, Algiers, Algeria
Nadjib Badache
LSI- Department of Computer Science, Faculty of Electronic Genius & Computer Science, USTHB,
El Alia BP n°32, Bab Ezzouar, Algiers, Algeria
Keywords: Mobile networks, Location, Quorums systems, Communication cost.
Abstract: Mobile location management is one of the most important problems in the mobile networks systems.
Indeed, reducing the search cost increases the update cost and vice versa. That's why, a trade off between
the search cost and update cost must be defined. This paper proposes a location management scheme based
on quorums. The communication cost is reduced with our method because the information on a mobile
location is saved in an efficient manner in a subset of location registers that change with the mobile moves.
The proposed algorithm is evaluated in term of total cost of search and update, and is compared to Ihn-Han
Bae algorithm.
1 INTRODUCTION
In the actual distributed systems and applications,
the notion of mobility appears in different forms.
More and more people use mobile computers or
wireless phones. In a mobile environment, the cost
of the communication cost is increased by the
location cost. When a server tries to send a message
to a user that is moving, it must first determine his
current position, i.e. locates it and then transmits it
the message.
To be able to locate mobiles efficiently,
information on their current positions must be saved
somewhere in the network: in a location database.
When a server has to locate a mobile, it queries this
location database. Therefore, every mobile that
moves, must signal its new position in order to
update its address in the location database.
There are two operations in location
management: Search and update. Search is the
operation that permits to locate a mobile node when
there is a need to contact it. The update is the
operation that permits to inform the network (the
location database) about the position of a mobile
when this one moves towards a new position in the
network.
In this paper, we propose a scheme for a location
database, based on quorums.
The present paper is organized as follows: In
section 2, we describe the system model used.
Section 3 is dedicated to previous work related to the
location problem. Section 4 presents the principle of
our solution and its evaluation. The last section is
the conclusion
.
2 SYSTEM MODEL
We consider a system composed of static sites
linked by a classic wireline network (static) and
mobile sites. Some static sites are provided with
wireless communication interface and play the role
of base stations. Every base station covers a
geographical area called a Cell. A mobile site can
only communicate with the base station that covers
the cell in which it is. This base station represents its
current address.
The cells of the network are grouped into
Registration Areas (RA). Every RA has a Location
Register (LR) that maintains the addresses of all
mobile sites that are in this RA.
91
Chetta N. and Badache N. (2005).
QUORUMS BASED MOBILES LOCATION SCHEME.
In Proceedings of the Second International Conference on e-Business and Telecommunication Networks, pages 92-97
DOI: 10.5220/0001410900920097
Copyright
c
 SciTePress

3 PREVIOUS WORK
The simplest solution for location management is the
use of a centralized server. This solution, even if
simple to implement, resents a major inconvenience:
If this server crashes, the location of all mobiles
becomes unreachable. Besides, this solution doesn't
exploit the geographical distribution of the mobiles
in the system and the locality of calls and moves to
reduce the cost of search and update. That’s why it is
necessary to use a distributed location database.
The Standards IS-41 (
EIA/TIA, 1991) and GSM
MAP (
Mouly, 1992) use the two-tier scheme. IS-41
associates a HLR (Home Location Register) to every
mobile. When a mobile moves from a RA to
another, the mobile saves its address in the VLR
(Visitor Location Register) of the LR towards which
it moved. This VLR informs the HLR associated to
this mobile to update its address.
The search and the update in this scheme imply
an important communication cost. Therefore, several
improvements have been proposed to reduce the
search and update costs (Pitoura, 2000) as the use of
cache, Forwarding Pointers (Krishna , 1996), Local
anchoring...
In (Rajagopalan, 1995), authors use the notion of
working sets. A mobile has a tendency to work, in
particular, with a certain number of nodes and that
represents its working set. Thus, when a mobile
moves, its working set is informed. This means that,
its address is updated in each node of its working
set.
In (Awerbuch, 1995), a Regional Directory (RD)
is created to maintain the location information of
mobiles. The RD of the i
th
level allows a node to
search for a mobile in a distance of 2
i
of it. To every
level i, reading and writing sets are associated with
the nodes u and v such as read
i
(u) ∩ write
i
(v) ≠ ∅
∀ u,v where the distance between them doesn't
exceed 2
i
. The reading set of a node is the set of
nodes that has tendency to search for this node. The
writing set of a node is the set of nodes where the
address of this node is saved.
Updating the address of a mobile every time it
moves from a cell to another can be very expensive.
Several alternatives have been proposed to reduce
this cost (Pitoura, 2000). They are based on the time,
the distance, and the number of movements...
In (Prakash, 1996) and (Prakash, 2001), Prakash
and Al. proposed a dynamic location strategy that
permits a load balancing in the system. In this
strategy, the address of a mobile is saved in a subset
of LRs called quorum. This quorum is determined
by a dynamic hashing function that defines the
writing set of a mobile when it moves and its
reading set when it is searched.
Several solutions were inspired from this model
and proposed some improvements.
In (Peleg, 1996) and (Kumar, 2000), authors
propose solutions assuring a trade off between the
load, the fault tolerance and the quorums size. In
(
Ihn-Han, 1999) and (Ihn-Han, 2000), a solution is
proposed to reduce the communication cost with
regard to these last solutions.
4 NEW SOLUTION
4.1 Basic idea
This solution proposes a mobile location database
architecture based on quorums. It is characterized
by:
- The broadcast of messages to update a mobile
address to a set of LRs.
- The broadcast of messages to search for a
mobile to a set of LRs.
The LRs of the network are grouped into
quorums. So, in addition to the information about
the mobiles that are in the base stations, a LR
maintains information related to all mobiles that are
in the other LRs belonging to its quorum.
Let LR
A
be the location register of the
Registration Area of A (RA
A
) that is in the quorum
Q
A
.
- LR
A
contains the information of all mobiles in
RA
A
in terms of base stations. Let x be a mobile that
is in RA
A
, information saved in LR
A
concerning the
address of x is the base station number in which it is.
- LR
A
contains the information of the mobiles of
the other LRs that are in the same quorum that RA
A
in terms of LRs. Let y be a mobile that is in a RA
that belongs to Q
A
, information saved in LR
A
concerning the address of y is the number of the LR
in which it is.
4.2 Updating a mobile address
The update of a mobile address is made when this
one moves from a quorum to another.
When a mobile x moves from one base station A
to another base station B, three cases are possible:
1. A and B are in the same LR y: In this case, the
address of x is updated at y level.
2. A and B are not in the same LR, but remain in
the same quorum: if x moves from the LR of A
(LR
A
) to the LR of B (LR
B
), then LR
B
and LR
A
update the address of x. LR
A
deletes the address of x
in its database associated to LR
A
and adds it to the
one associated to LR
B
. The inverse is done at the
LR
B
level. Then LR
B
broadcasts a message to all
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LRs that are in the same quorum with it (except
LR
A
) to update the address of x. Each of these LRs is
going to delete the address of x in its sub database
associated to LR
A
and to add it to the sub database
associated to LR
B
.
3. A and B are in different quorums: if LR
A
is in
the quorum Q
A
and LR
B
is in the quorum Q
B
, then:
3.1. The LRs that belong to Q
A
-Q
B
delete the
address of x from their databases: LR
A
deletes the
address of x from its database and broadcasts a
delete message to all LRs of Q
A
-Q
B
so that they
delete the address of x from their databases.
3.2. The LRs that belong to Q
B
-Q
A
add the
address of x in their databases: LR
B
adds the address
of x to its database (here the address of x is B) and
broadcasts a message of addition to the LRs of
Q
B
-Q
A
so that they add the address of x in their
databases (here the address of x is LR
B
).
3.3. The LRs that belong to Q
A
∩Q
B
update the
address of x: LR
B
broadcasts an update message to
the LRs of Q
A
∩Q
B
so that they delete the address of
x from the database associated to LR
A
and add it to
the database associated to LR
B
. Here also, the
address of x is the LR to which it belongs (LR
B
).
Update Procedure:
Let Mh_id be the mobile identity of a mobile x,
old_SB the departure base station of x, new_SB the
arrival one, old_LR the departure LR of x, new_LR
the arrival one, old_quorum the departure quorum of
x and New_quorum the arrival one.
If old_LR=New_LR
Then update the address of x in old_LR
Else
if old_quorum = New_quorum
then
- Update the address of x in old_LR and New_LR
- Broadcast an update message in
Old_quorum-{old_LR,New_LR}.
else
- Delete the address of x in old_LR;
- Broadcast a delete message to
Old_quorum-New_quorum-{old_LR}
- Add the address of x in New_LR;
- Broadcast an add message in
New_quorum-old_quorum-{New_LR}
- Broadcast an update message in
New_quorum ∩old_quorum.
4.3 Locating a mobile
When a mobile y that is in a base station A wants to
communicate with a mobile x that is in the base
station B, considering that A belongs to the Location
Register LR
A
and B belongs to LR
B
, A asks LR
A
for
the address of x. Three cases are possible:
1. If x and y are in LR
A
(i.e. LR
A
= LR
B
), then
LR
A
sends the address of x (here B) to A;
2. If LR
A
and LR
B
are in the same quorum, then
LR
A
has the address of x in terms of LR: LR
A
sends
this address (LR
B
) to A. The message that x must
receive, is sent to LR
B
that will send it to B.
3. If LR
A
and LR
B
are not in the same quorum,
three (03) cases are possible:
3.1. LR
A
checks its cache to see if it contains the
address of x. In a LR, the cache is a structure that
saves the address -in termS of LRs - of the last
address of every mobile that have been searched by
the LR.
If x possesses an entry in the cache of LR
A
(Let
LRx be this entry), LR
A
sends a search message to
LRx. If x is still in LRx, LRx sends the address of x
to LR
A
which will send it to A; otherwise, LRx
sends a failure message.
3.2. If LR
A
doesn't find the address of x in its
cache, LR
A
checks its profile. The profile is a
structure that replicates usual mobility models of a
mobile. It is managed on the basis of history, where
each mobile has P LRs (and therefore P entries in
the profile) ordered by their popularity. The
popularity of a LR is the probability that the mobile
is located in the LR for each period of time. The
profile saves for a mobile, the LRs in which it often
resides.
LR
A
broadcasts the search request to the LRs of
the profile of x. When a LR receives the search
message, if x is in this LR, it sends the address of x
to LR
A
that sends it to A; otherwise it sends a failure
message.
3.3. If LR
A
doesn't find the address of x in the
cache and all LRs associated to x in the profile
answer negatively to its search message, then LR
A
doesn't possess the information of the address of x.
LR
A
broadcasts a search message to all LRs that
belong to the intersection of the quorum of LR
A
with
the other quorums of the network. When LR
A
receives the address of x, it sends it to A.
Search Procedure:
Let SB_id1 be the base station that searches for
the mobile x whose identity is MH_id and SB_id2
the base station in which x is.
Let LR_id1 be the LR that contains SB_id1 and
LR_id2 the LR that contains SB_id2.
Let QR_id1 be the quorum that contains LR_id1
and QR_id2 the quorum that contains LR_id2.
QUORUMS BASED MOBILES LOCATION SCHEME
93

Let LR
∩
be the set of LRs that belong to the
intersection of QR_id1 with other quorums of the
network.
If LR_id1=LR_id2
Then
LR_id1 sends MH_id address (SB_id2) to SB_id1
Else
If QR_id1=QR_id2
Then
LR_id1 sends MH_id address (LR_id2) to SB_id1.
Else
LR_id1 searches MH_id address in its cache.
If it exists, let LR_x be this address,
Then
LR_id1 sends a search message to LR_x.
If LR_x=LR_id2
Then
LR_id2 sends MH_id address to LR_id1 that
will send it to SB-id1
Else LR_x sends a failure message.
Goto L1
Else
L1: LR_id1 broadcasts the search message to the
LR of the MH_id profile.
If LR_id2 is in MH_id profile,
Then
LR_id2 sends the address of x to LR_id1 that
will send it to SB_id1 and the other LR send
failure messages.
Else
LR_id1 sends a search message to LR
∩
;
Let LRj є LR
∩
/ LRj є QR_id2 : LRj sends
MH_id address (LR_id2) to LR_id1 ; LR_id1
sends this address to SB_id1
4.4 Algorithm complexity
During a search or an update, the number of
exchanged messages can vary according to the
following cases.
- When a mobile moves from a base station to
another, exchanged messages between the LRs are:
1. If the mobile stays in the same LR, no messages
are sent.
2. If the mobile stays in the same quorum, the new
LR sends
2−q messages to the LRs of the quorum
so that they update the mobile address. q is the
maximum size of the quorum.
3. If the mobile moves to a new quorum:
Let i be the number of LRs that belong to the
intersection of the departure quorum and the arrival
quorum, the number of exchanged messages
is
()
iq −− 1*2 . This number can up to 1*2
−
q
if i=1.
- When there is a search:
1. If the calling mobile and the called mobile are in
the same LR, the number of exchanged messages is
four (04).
2. If the calling mobile and the called mobile are in
the same quorum: the number of exchanged
messages is six (06).
3. If the calling mobile and the called mobile are in
two different quorums:
3.1. If the calling LR finds the searched mobile
address (the address of its LR, let it be LR_MH) in
its cache, it sends the search request to LR_MH. If
the mobile is located, the number of exchanged
messages then is six (06).
3.2. If the search in the cache fails and the called
mobile is in the calling LR profile, the calling LR
queries the LR of the profile of the called mobile. If
P is the size of the profile, the number of exchanged
messages is
(
)
3*2
+
p .
3.3. If the mobile is still not located, the calling
LR broadcasts a search request to all LRs belonging
to the intersection of its quorum with the other
quorums. The number of these LRs is
()
1−q LRs
as maximum. Therefore the number of exchanged
messages in this case is
{
}
2*2 ++ qP .
4.5 Evaluation
To evaluate our work, we have compared it to the
Ihn-Han Bae algorithm (
Ihn-Han, 2000).
The first difference between the Ihn-Han Bae
algorithm and our solution is that Ihn-Han Bae
associates to every LR two quorums: a line quorum
and a column quorum. When a mobile moves, these
quorums are updated according to the state of the
concerned mobile. If this mobile is hot, the two
quorums (line and column) are updated. If it is cold,
one of the two quorums is updated. In our solution,
the notion of reading and writing quorums or line
and column quorums doesn't exist. The LRs of the
network are organized in quorums where each LR
can belong to several quorums and is affected to
only one quorum. When a mobile is searched, a LR
queries the other LRs belonging to its quorum.
Besides, the update in the Ihn-Han Bae solution
is made when a mobile moves from a LR to another.
In our solution, the address of a mobile is updated
when it moves from a quorum to another.
Finally, the quorums construction used is
different. Ihn-Han Bae uses the triangular scheme
(construction in line and in column) where quorums
have the same size that is roughly
N2 . In our
solution, the used construction is the tree based
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scheme where the size of quorums is roughly Log
2
N
with N the number of LRs in the network.
Figure 1: Communication cost according to the number of
cells
In the following, we present a comparison
between the performances of the Ihn-Han Bae
algorithm and our solution in the conditions that
were used by Ihn-Han Bae to compare his algorithm
to the Prakash one. That is: C
fixed
=1, C
wireless
=3, C=7,
P=3, P
cache
=0.3, P
profile
=0.2, P
Hot
=0.5 with C
fixed
is the
wireline communication cost, C
wireless
is the cost of
the wireless communication between a mobile and a
base station, P
cache
is the probability that the address
of the called mobile is in the cache of the calling
mobile, P
profile
is the probability that the address of
the called mobile is in the profile, P
Hot
the
probability that a mobile is hot, C is the number of
base stations (or of cells) in a LR and P the profile
size.
To evaluate our solution, we compare it in terms
of communication cost with Ihn-Han Bae solution in
the case where the scheme used for the construction
of quorums is the triangular scheme and in the case
where it is the tree based scheme.
Figure 1 shows the difference of performances
between the two solutions.
Curve 1: Shows the performance of our solution
with
Cnq 2=
Curve 2: Shows the performance of the solution
of Ihn-Han Bae with
Cnq 2=
Curve 3: Shows the performance of our solution
with
)/(
2
CnLogq =
Curve 4: Shows the performance of the solution
of Ihn-Han Bae with
)/(
2
CnLogq =
First, it is clear that the choice of the quorums
construction is very important. In the two solutions,
the gap of the communication cost is considerable
between the tree based construction and the
triangular construction.
In the case of the triangular construction or the
tree based construction, our solution gives better
results than the Ihn-Han Bae algorithm, even if the
gap is more important in the triangular construction.
If Figure 1 shows globally that our solution is
better than the Ihn-Han Bae one, Figure 2 and Figure
3 show the detail of this curve by comparing search
costs and update costs independently.
Figure 2: Update cost according to the number of cells
Figure 2 compares the update cost between the
two solutions as:
Curve 1: Shows the performance of the solution
of Ihn-Han Bae with
Cnq 2=
Curve 2: Shows the performance of our solution
with
Cnq 2=
Curve 3: Shows the performance of the solution
of Ihn-Han Bae with
)/(
2
CnLogq
=
Curve 4: Shows the performance of our solution
with
)/(
2
CnLogq
=
Our solution reduces the update cost much more
than the Ihn-Han Bae solution. In fact, the update
cost of our solution with a triangular construction is
weaker with regard to the update cost of the of Ihn-
Han Bae solution with a tree based construction,
when we know that the size of a quorum in the
triangular construction is
Cnq 2= and the one
in the tree based construction is
)/(
2
CnLogq = . It is
due to the fact that in the case of the Ihn-Han Bae
solution, when a mobile is hot, four quorums are
updated and two only if it is cold, whereas in our
solution two quorums are updated. Besides, a mobile
has more prone to pass from a LR to another, than to
pass from a quorum to another. So, the number of
updates in our solution is lower than the number of
updates in the Ihn-Han Bae solution.
QUORUMS BASED MOBILES LOCATION SCHEME
95

Figure 3: Search cost according to the number of cells
Figure 3 compares the two solutions in terms of
search cost where:
Curve 1: Shows the performance of the solution
of Ihn-Han Bae with
Cnq 2=
Curve 2: Shows the performance of our solution
with
Cnq 2=
Curve 3: Shows the performance of the solution
of Ihn-Han Bae with
)/(
2
CnLogq =
Curve 4: Shows the performance of our solution
with
)/(
2
CnLogq =
In the case of triangular construction, the Ihn-
Han Bae solution is appreciably better than ours but
in the tree based construction the two curves are
nearly identical with a light advantage for the Ihn-
Han Bae curve.
5 CONCLUSION
In this paper, we proposed a location management
scheme based on quorums. The information of a
mobile location is mobile too. It moves with
displacements of the mobile, the address of a mobile
is updated when it goes from a quorum to another.
The total communication cost induced by our
solution is smaller than the one induced by the Ihn-
Han Bae solution.
The communication cost depends on the chosen
quorums system. Indeed, the tree based scheme
reduces the communication cost with regard to the
triangular scheme whereas the induced load by the
tree based diagram is more important. Besides, to
evaluate the performance of our solution, we
supposed that the mobiles are uniformly distributed
in the LRs. It would be interesting to simulate the
behaviour of our algorithm for real cases that don't
necessarily verify this hypothesis.
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