48 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 1, JANUARY 2001
A Contention-Free Mobility Management Scheme
Based on Probabilistic Paging
Wing Ho A. Yuen and Wing Shing Wong, Senior Member, IEEE
Abstract—In forthcoming personal communication systems
(PCSs), small cells are deployed to achieve high spectral efficiency.
This has significant impacts on location tracking of mobile
users. The increase in location update (LU) load leads to more
contention on the reverse control channel. Thus, many algorithms
are designed to distribute the LU load to a larger number of
cells. This avoids the inefficiency of random accessing due to high
offered load. In an alternative approach [3], a contention-free LU
algorithm is proposed. Two or more mobile units are permitted
to register with a base station simultaneously without contention.
A probabilistic paging mechanism called Bloom filtering is used
to select cells to be paged. Since there is no contention in LU,
inefficiencies due to random accessing are bypassed. In this
paper, we present another contention-free LU algorithm. It is
hybrid in the sense that LUs are temporally or geographically
triggered. The use of hybrid LU alleviates inefficiencies inherent
to temporal triggered LU in [3]. Three selective paging schemes
are considered in this paper. Tradeoff between paging delay and
paging bandwidthis addressed.The performance of this algorithm
is compared to [3] and other conventional strategies. Numerical
results shows that the new algorithm compares favorably with
previous proposed strategies.
I. INTRODUCTION
I
N personal communication systems (PCSs), microcells and
picocells are extensively deployed. This allows power sav-
ings in base-station transceivers and mobile handsets. More im-
portant, spectral efficiency is enhanced through denser spatial
reuse of frequency. However, the use of small cells poses a se-
vere burden on the common air interface and the signalling net-
work. On the reverse control channel, higher contention of loca-
tion update (LU) messages is expected. Retransmission of LU
messages is needed. This leads to a large increase in signalling
traffic on the radio link.
The geographic-based strategy is currently adopted by the
wireless standards [GSM mobile application part (MAP) and
IS-54 [4]]. The whole network is partitioned into nonoverlap-
ping location areas. Each mobile unit (MU) monitors the for-
ward control channel of the local cell for its cell identifier, which
is broadcasted periodically. When it detects that the local cell
has fallen out of the original location area, an LU is triggered.
Thus, when a call is terminated to an MU, the network determin-
istically retrieves the location of the called MU at a resolution
of a single location area.
Manuscript received May 5, 1999; revised April 25, 2000. This work was
supported by the Hong Kong Research Grants Council under a Grant.
W. H. A. Yuen was with the Chinese University of Hong Kong. He is now
with Wireless Information Network Laboratory (WINLAB), Rutgers—The
State University of New Jersey, Piscataway, NJ 08854-8060 USA (e-mail:
andyyuen@winlab.rutgers.edu).
W. S. Wong is with the Department of Information Engineering, The Chinese
University of Hong Kong, Hong Kong (e-mail: wswong@ie.cuhk.edu.hk).
Publisher Item Identifier S 0018-9545(01)01222-1.
The geographic-based strategy performs well in second-gen-
eration cellular networks. However, the efficiency of geographic
LU deteriorates dramatically when small cells are deployed.
This is because the LU load is shared by the boundary cells of a
location area only. The high offered load in each cell adversely
affects the probability of a successful transmission. Thus the
geographic-based strategy is not an ideal candidate for forth-
coming systems.
Many strategies have been proposed in literature to tackle the
problem. A convenient way of classifying these strategies is out-
lined below.
1) Forsystems employing a static strategy, the location areas
are globally defined for all MUs. Each MU has the same
set of location areas irrespective of its mobility and call
arrival behavior. The geographic-based strategy is an ex-
ample of a static strategy.
2) In semistatic strategies [10], [12], location areas are also
predefined. The system consists of overlapping layers of
location areas. When an MU exits a location area of the
present layer, it switches to another layer that matches to
its mobility profile. Note that the strategy proposed in [8]
is classified as a static strategy under this definition, for
the reason that overlapping layers of location areas are
used to provide hysteresis against frequent switching be-
tween location areas, rather than match to specific mo-
bility profiles of MUs.
3) In dynamic strategies, each MU has a location area tai-
lored for its mobility profile. No permanent location area
boundaries are defined for any MU. The well-known dis-
tance-basedstrategy[5]anditsvariants[11],[14]belongto
this category. Since location area sizes for dynamic strate-
gies are tailored for individual users, these algorithms in
general outperform static strategies. However, as noted in
[15],thesestrategiesareamenable to implementation only
when the size of the location area is small.
In literature, location tracking algorithms are engineered
such that the combined LU and paging bandwidth is minimal.
This is often accomplished through personalized assignment of
location areas. Nevertheless, these algorithms still experience
the same problem as the geographic-based strategy. The inef-
ficiency associated with random access is only partially solved
by distributing the LU load to a larger number of cells. An
alternative approach to the problem is proposed in [3]. Instead
of adopting random accessing on the reverse control channel, a
contention-free algorithm for LU is proposed. Each cell main-
tains cell vectors, which summarize the location information
of local mobile users. When a call is terminated to a mobile
user, relevant location information in each cell is retrieved. A
0018–9545/01$10.00 © 2001 IEEE
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YUEN AND WONG: A CONTENTION-FREE MOBILITY MANAGEMENT SCHEME 49
probabilistic paging mechanism called Bloom filtering is used
to select cells to be paged. Since there is no contention in LU,
inefficiencies due to random accessing are bypassed.
In this paper, we propose another contention-free LU algo-
rithm. It is hybrid in the sense that LUs are temporally or ge-
ographically triggered. The use of hybrid LU alleviates ineffi-
ciencies inherent to temporal triggered LU in [3]. With our LU
scheme, paging (Bloom filtering)is more accurate. Performance
of our algorithm compares favorably with [3] and conventional
strategies.
The rest of this paper is organized as follows.In Section II, the
system model is described. A contention-free LU scheme and
the probabilistic paging mechanism are outlined in Section III.
We refer to the algorithm as the time-based Bloom filter (TBBF)
algorithm. Section IV describes our hybrid Bloom filter algo-
rithm (HBF), which is analyzed in Section V. A numerical study
is given in Section VI to compare the HBF with [3] and other
conventional strategies. This is followed by a discussion in Sec-
tion VII. For completeness, a simulation study is reported in the
Appendix to verify the numerical results we obtained.
II. S
YSTEM MODEL
We consider a cellular system consisting of cells and
MUs. The number of users in a cell is denoted by . In steady
state, the average value of
is assumed to be . We assume
that each cell is identically shaped. The actual shape could be
arbitrary as long as the cells are packed regularly. The dwell
time in a cell of each MU is assumed to be exponentially dis-
tributed with mean 1
. Individual call interarrival time is also
exponentially distributed with mean 1
. Since the interarrival
time of calls is generally much larger than the period
between
two LUs, we assume that there can be at most one incoming call
during one update cycle. By the memoryless property of expo-
nentially distributed random variable,the call arrival time is uni-
formly distributed in the update cycle.
Every MU has a unique mobile unit identity vector (MUID)
for unique identification during paging. It is also assigned an
-bit Bloom filter identity vector (BFID), which is used for LU
and will be described in detail in Section III. Each bit of an
arbitrary BFID is independent and is a “1” with probability
.
Note that we do not require the BFIDs to be unique. We also
assume that the maximum propagation delay of pulses from the
MUs to a base station is much smaller than the bit time of an LU
message. That is, there is no bit synchronization problem when
LU is performed.
III. C
ONTENTION-FREE LOCATION UPDATE ALGORITHM
In [3], the time-based Bloom filter algorithm is presented. It
belongs to a category of LU algorithms characterized by con-
tention-free access of the reverse control channel during LU.
Collision of LU messages is prevented.
Periodically, each MU performs an LU by sending its
-bit
BFID to the local cell. When the corresponding bit in the BFID
is a “1,” a pulse is sent. Otherwise, the MU sends nothing. A
base station receives the superimposition of pulses from all MUs
in the local cell and store it as a cell vector. If the base station
Fig. 1. Illustration of contention-free LU and Bloom filtering.
detects one or more pulses in the th bit interval, it infers that
at least one MU in the cell contains a “1” in the
th bit. On the
other hand, if the base station detects no pulse in the
th bit, it
concludes that all MUs inside the cell have BFIDs that are zeros
at the
th bit. The zero in the th bit in the cell vector conveys
significant information. One could infer that a MU with an ID
of “1” in the
th bit is not in the cell.
Consider a system consisting of three cells and six MUs as
depicted in Fig. 1. During the most recent LU cycle, the cell
vectors of cell 1 to cell 3 are 10011, 11101, and 01 100, respec-
tively. Suppose a call is terminated to MU 6. We compare the
BFID of MU 6 with the cell vectors. Since the third and the last
bit of MU 6 are one, we should send a paging message to the cell
only if the corresponding bits of the cell vectors are also “1.” It
turns out that only cell 2 should receive the paging message.
Mathematically, we denote
, as the cell vector
obtained in the most recent LU cycle in cell
from a system of
cells. When a call arrives for the MU with ID BFID, cell
is paged if
BFID
BFID
where
denotes bit by bit multiplication. This operation is
called Bloom filtering [6]. Only the cells whose cell vectors
match to the targeted MU will be paged. After the network
“filter” out cells to be paged, the MUID of the called MU is
then broadcasted on the paging channel of the matched cells.
Suppose there are
MUs in a cell. The probability that an
arbitrary bit in the cell vector is “0” is
. The cell
is not paged if the corresponding bit in the BFID is a “1.” This
occurs with probability
. Thus, on average, a cell is paged
with probability
(1)
It is possible that the targeted MU is not located in the paged
cells. This happens when the targeted MU leaves a cell between
the call arrival time and the most recent LU cycle. Denote the
probability of successful and unsuccessful paging as
and
, respectively. Denote the period of an LU cycle by . As-
sume that the dwell time of an MU and the call interarrival time
are exponentially distributed with mean 1
and 1 , respec-
tively. Since
in general, we further assume that at
most one call arrives between two update cycles. By the memo-
ryless property of an exponentially distributed random variable,
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50 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 1, JANUARY 2001
Fig. 2. Illustration of LU on uplink control channel for an arbitrary MU.
the call arrival time is uniformly distributed in the time interval
of
. It is straightforward to show that
(2)
(3)
In the TBBF algorithm, each MU periodically reports its
BFID to the local cell. The large number of superimposed LUs
a cell receives increases the probability that this cell will be
paged when a call arrives. This in turn increases the system
paging cost. It is desirable to reduce the LU rate of each MU
promote more accurate paging. With this insight, we propose
a hybrid LU strategy in which LU could be temporally or
geographically triggered. We limit the rate of updates when an
MU is less mobile. This promotes efficient paging and leads to
lower control overhead ultimately in an optimized system.
IV. H
YBRID BLOOM FILTER ALGORITHM
In this section, we present a new, hybrid location update pro-
tocol for MUs and a choice of algorithms that can be used by
the fixed network in tracking the MUs.
A. Location Update Protocol
Under the new protocol, the reverse control channel periodi-
cally allocates registration slots with period
. Only LU mes-
sages are allowed in these slots. All other control messages such
as call setup negotiations can contend for the channel in other
unreserved time slots. When an MU crosses a cell boundary at
time
, it attempts to register to the new cell. However, it can do
so only at the next registration slot. In the meantime, the system
loses track of the MU temporarily, as shown by the shaded area
in Fig. 2. At time
, the MU sends its BFID to the reverse con-
trol channel. If more than one MU enters the given cell since the
last registration slot, the received cell vector is a superimposi-
tion of several BFIDs.
The registration information is held at the base station for a
period of
. If an MU remains in the same cell at the end of
this period, it is preprogrammed to perform a temporally trig-
gered LU reregister with the cell. If the cell does not receive any
reregistration from an MU that registered at a time
before,
the system infers that the MU has left the cell and deregisters
it. Viewed from the base station, a bit in the cell vector will be
reset if no pulse is received in the corresponding bit time for the
most recent registration slots.
We need to fix some notation to help our subsequent discus-
sion. At any time
, label the beginning of the most recent reg-
istration slot by
, label the end of the immediately preceding
registration slot by
, and so on. The cell vector at time
is denoted by . We label the time interval as the reg-
istration memory window at time
.
B. Paging Protocol
When an MU is called, the system retrieves the most recent
cell vectors from each cell. These cell vectors are used to locate
an MU via Bloom filtering. There is a finite probability
that the targeted MU has just left the cell when the call arrives.
In this casen the MU is lost and flooding is needed to locate it.
With probability
n the targeted MU is still in
the registered cell when the call arrives. This MU is registered in
one of the
most recent cell vectors stored at the corresponding
base station.
By the nature of the LU algorithm, any one of the
cell vec-
tors provides usable information for the Bloom filtering oper-
ation. However, based on our mobility assumption, the prob-
ability of successfully locating the targeted MU is higher for
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YUEN AND WONG: A CONTENTION-FREE MOBILITY MANAGEMENT SCHEME 51
more recent cell vectors (see Lemma 1). To exploit this prop-
erty, we institute up to
matching cycles in paging. In each
matching cycle, a group of consecutive cell vectors are used to
decide whether the targeted MU is in the cell under consider-
ation. The first matching cycle uses the most recently received
group of cell vectors. The second matching cycle uses the next
most recently received group, and so on. If the targeted MU is
found, the matching cycle stops immediately. If the targeted MU
cannot be identified with this process, the system will flood all
yet unpaged cells in the system to locate it.
Three types of matching cycle groupings are considered here
for comparison. In paging scheme 1, there is only one matching
cycle. That is, all
cell vectors in each cell are used to match the
BFID of the incoming MU. In paging scheme 2, there are two
matching cycles. In the first pass, the
most recent cell vectors
from each cell are used. In the second pass, the remaining
vectors are used. In paging scheme 3, there are matching
cyclesconsisting of a single cell vectorfrom each cell. The cycle
starts with the most recent cell vector. In all three cases, if the
targeted MU cannot be located after all the matching cycles, the
remaining cells will be flooded.
V. P
ERFORMANCE EVALUATION
In order to compare different location update schemes, a
common cost function needs to be identified. Since the radio
bandwidth is a more critical resource than the bandwidth of
a fixed network, we define the cost function to be a weighted
sum of location update and paging data rate per MU per hour
on the radio link. The expected value of the cost function for
the proposed algorithm is derived in Theorem 1.
Assume a call arrives at time
and the targeted MU is located
atcell0. Consider the registration memory window attime
.As-
sumethetargetedMUhasnotchangedcellduringthetimeinterval
.Define .Itfollowsfromthebasicassumptionof
thesystemmodelthat
isuniformlydistributed between .
ThetargetedMU mustregisteratleastoncewithcell0duringthe
registration memory window at time
. Let be the most recent
registration slot in the window when the targeted MU updates at
cell 0. Denote the probability
by .
Let
be the time instants at which the targeted MU changes
cells. Let
fall in the interval defined by and .By
renewal theory, the age of the arrival defined by
is
known to be exponential distributed with mean
[1]. With this
assumption,
is derived in the following lemma.
Lemma 1:
(4)
where
(5)
Proof: The event
is equivalent to havingageograph-
ically or temporally triggered registration at
. This in turn is
equivalent to the age
fallingin the intervals
for some (refer to Fig. 3). Note that if ,
Fig. 3. When an MU is registered in slot
i
, the dwell time up to the call arrival
may take the value in the interval
[(
lr
0
i
)
+
Z;
(
lr
0
i
+1)
+
Z
] for
l
=1
;
2
;
...
.
the registration is geographically triggered. It is temporally trig-
gered if
. Since is exponential distributed with
mean
,wehave
(6)
(7)
(8)
(9)
(10)
For any cell, define as the probability that the th cell
vectormatches to theBFID of the targeted MU. Define
page
to be the probability that a cell is paged when the paging scheme
is used.
Theorem 1: The combined paging and update radio band-
width usage per MU per hour is given by the following equa-
tion:
page
(11)
where
page for the paging schemes are given by
page (12)
page
(13)
page (14)
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52 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 50, NO. 1, JANUARY 2001
and
(15)
Proof: Define
tobe the number of MUssending updates
in registration slot
in cell 0. Since the BFID bits are generated
independently, the probability that there is a match in a given bit
between the BFID and the
th cell vectoris .Therefore,
the probability that a match is identified using the
th cell vector
is given by
.
In paging scheme 1, for any cell, all
cell vectors,
, are used. The cell will be paged if there is a match with
any one of the
cell vectors. Therefore
page at least one cell vector match
(16)
In paging scheme 2, cell vectors from slot
are used for matching in the first pass. With probability
, the MU is not located in first matching cycle. There-
fore,
is given by
no match
(17)
(18)
In paging scheme 3, a cell vector is used only if no match has
been found with succeeding cell vectors. Therefore
page
(19)
(20)
It is obvious that page page page by our
paging construction. Thus, paging bandwidth is conserved by
trading off paging delay.
Since
are intricately interdependent random
variables, it is intractable to compute cost
exactly. For the
purpose of comparison with other algorithms in our numerical
study section, we have chosen to use average values of
for the
computation of
.
In steady state, all
s are identical. We denote the average as
. is equal to sum of the mean number of temporally triggered
TABLE I
S
YSTEM PARAMETERS ADOPTED IN THE NUMERICAL STUDY
registrations and the mean number of geographically triggered
registrations. By symmetry, the mean number of incoming MUs
in a cell during an update cycle is equal to the mean number of
departures of MUs in the same cycle. Thus, the mean number
of geographically triggered registrations is equal to
Pr (21)
The mean number of temporally triggered updates is given by
Pr (22)
Hence
or
(23)
Substitute all
for . It follows that for all .
The average probability of paging a cell for the proposed paging
schemes are, respectively
page (24)
page
(25)
page (26)
Suppose the length of a BFID is
, the period of a registration
slot is
, and is the same for both hybrid (HBF) and time-
based Bloom filter (TBBF) schemes. Note that when
,
the hybrid algorithm degenerates to the time-based Bloom filter
algorithm. This is obvious since every MU must register in every
registration slot. The number of update messages expected in
each registration slot
equals the number of MUs in each cell
. The probability of paging a cell page when is thus
given by
(27)
which agrees to (1).
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