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Intelligent Paging Strategy based on Location

Probability of Mobile Station and Paging Load

Distribution in Mobile Communication Networks

Dong-Jun Lee

Mobile Development Team,

Telecommunication Systems Division,

Information & Communication Business,

Samsung Electronics Co., Ltd.,

Republic of Korea

HyeJeong Lee and Dong-Ho Cho

Div. of Electrical Engineering,

Dept. of Electrical Engineering and Computer Science,

Korea Advanced Institute of Science and Technology,

Republic of Korea

Abstract—When the cells in a location area are paged sequen-

tially based on the specific information such as last registered

area or mobile speed, paging load may be non-uniformly dis-

tributed among the cells. This non-uniform paging traffic causes

additional paging delay due to the increase of waiting time in

the cell with high paging load. In this paper, we introduce a

new paging strategy in which the paging sequence in a location

area is optimized based on both the location probability of a

mobile terminal and paging load distribution among the cells.

From numerical results, we show that the paging cost of our

proposed scheme is very close to the optimal one. In addition,

we observe the effects of the paging load distribution and the

location probability distribution on the paging cost.

I. INTRODUCTION

Third generation mobile communication systems such as

UMTS and cdma2000 are characterized as offering worldwide

communication and various multimedia services. In the mobile

networks, it is very critical to keep track of the location of a

mobile terminal when it moves between cells or even between

different systems. In addition, increasing demands on universal

access and global roaming make efficient location (mobility)

management play a very important role.

In general, location management consists of two basic

procedures: location registration (location update) and paging.

Location registration is the process in which a mobile user

informs the networks of the current location information. To

facilitate this, the entire service area of the communication

system is divided into several location areas and a location

update is performed when a mobile user crosses a boundary

of the location area. When a call request arrives to the user,

paging is performed within the last registered location area to

search for the mobile user by sending polling messages to the

cells.

In particular, several paging schemes such as blanket paging,

sequential paging, and intelligent paging, have been proposed

for call delivery. Blanket paging scheme, in which all cells in a

location area are paged simultaneously to deliver an incoming

call, causes low paging delay. However, blanket paging wastes

excessive wireless resources. In sequential paging, a location

area is divided into smaller areas called a paging area and the

group of cells in a paging area is searched in one polling cycle.

A polling cycle in a sequential paging scheme is defined by

the round trip time from the time when a paging message

is transmitted to the time when the response is received.

Sequential paging scheme is efficient to reduce paging load,

but it may increase paging delay exponentially.

During the last decade, much research has been done on

an intelligent paging scheme, which determines an efficient

paging sequence in a multi-step paging [1]∼[4]. To improve

the performance of paging strategy in intelligent paging, cells

are paged sequentially based on specific user information such

as last interaction area, mobile speed and etc. Because cells

with higher probability in which the target user may be found

should be paged first to reduce paging traffic and paging delay,

previous research mainly has focused on the calculation of

the user location probability. User location probability can be

determined based on most recent location of registration, user

mobility and elapsed time since the last location update.

A multi-step paging based on user location probability is

useful for finding the target user. However, in contrast to

a blanket paging in which all cells in a location area have

the same paging load, a multi-step paging searches cells

selectively and so paging traffic is not distributed uniformly

among the cells of the location area. Non-uniform paging

load distribution among cells makes paging response times in

cells different each other. Moreover, if paging in a particular

paging area fails, the paging delay of the paging area is

determined by the longest response time, which is derived

from that cell in the paging area that has the greatest paging

load. Therefore, to optimize the paging sequence with respect

to the paging load and the paging delay, the non-uniform

paging load distribution should be considered in addition to the

location probability distribution. While the location probability

distribution is related to the individual mobility behavior of a

mobile terminal, the paging load distribution is determined by

the global distribution of traffic in the system.

In this paper, we propose an enhanced paging scheme

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m

m

m

m

m

m

n

n

m

m

m

m

m

m

n

n

m

m

m

m

m

m

n

n

Fig. 1.Partitioning Nc cells into Np paging areas

considering both the location probability distribution of a

mobile terminal and the non-uniform paging load distribution.

The rest of this paper is organized as follows. In Section II, we

provide an analytic model and formulate the paging cost. In

Section III, proposed strategy based on both the paging load

and the user location probability is explained in detail. We

show numerical results in Section IV and conclude this paper

in Section V.

II. PAGING COST FORMULATION

In this section, we define modified paging cost formula

similar to the approach adopted in [5]. In our model, we

additionally consider the effect of paging load distribution on

the paging cost.

We assume that there are Nc cells in a location area. Let

λibe the probability that a user exists in the ithcell and ρi

be the paging load, which is the number of paging requests

waiting in the ithcell (i = 1,2,···Nc), respectively. Then,

?Nc

or long-term average of paging load in a system. As shown

in Fig. 1, it is assumed that a location area is divided as Np

paging areas (1 ≤ Np≤ Nc) for a multi-step paging, and the

size of the jthpaging area (i.e., the number of cells in the jth

paging area) is nj(j = 1,2,···Np).

We define the paging success probability of a paging area as

the probability that the target user for an incoming call will be

found in the corresponding paging area. Then, paging success

i=1λi= 1 (0 ≤ λi≤ 1) and ρimay be given as an instant

value when a paging process is initiated or as a short-term

probability of the jthpaging area, pj, can be calculated as

pj=

mj+nj

?

i=mj+1

λi,

(1)

where mj=?j−1

late the paging delay that is the time taken until paging is

successful, we assume that paging request is queued and not

blocked although paging load in a cell is high. Let¯Djbe the

normalized paging delay when the paging in the jthpaging

area succeeds andˆDjbe the normalized delay when the paging

in the jthpaging area fails. Then, average paging delay (D) of

a mobile user until paging succeeds is calculated in sequential

way as follows.

?

j=1

??

i=1ni, m1= 0 and?Np

j=1pj= 1.

Now, we derive the paging delay cost. In order to calcu-

D

=

p1¯D1+ (1 − p1)

ˆD1+p2¯D2

1 − p1

ˆDNp−1+

?

+···

1 −

pj¯Dj+

Np−1

?

Np−1

?

pj

?

pNp¯DNp

1 −?Np−1

·ˆDj

j=1

pj

?

=

Np

?

j=1j=1

1 −

j

?

i=1

pi

??

(2)

In (2), we can obtain the average delays¯D andˆD which are

caused by successful paging and failed paging respectively, as

follows.

¯D

=

Np

?

Np−1

?

j=1

pj¯Dj

(3)

ˆD

=

j=1

??

1 −

j

?

i=1

pi

?

·ˆDj

?

(4)

Given that the transmission time for a paging message over

a wireless link, 1/τ, is assumed to be constant throughout

cells, the normalized paging delay of successful paging in jth

paging area,¯Dj, is represented by

¯Dj

=

1

pj

mj+nj

?

i=mj+1

λi·

?ρi

τ

?

,

(5)

where ρi/τ is the normalized paging load in each cell.

Meanwhile, the normalized paging delay of failed paging in

jthpaging are,ˆDj, is expressed as

max(ρmj+1,ρmj+2,...,ρmj+nj)

ˆDj

=

τ

.

(6)

Note that from (3) and (5),¯D is determined by the given

location probability distribution (λi) and paging load dis-

tribution (ρi) regardless of the particular paging sequence.

Therefore, hereafter, we consider onlyˆD as the paging delay

cost. Because?Np

ˆD =

1−

i=1

j=1pj= 1,ˆD in (4) can be rewritten as

?

j=1

Np−1

?

j=1

? ?

j

?

pi

·ˆDj

?

=

Np

?

? ?

1−

j

?

i=1

pi

?

·ˆDj

?

.

(7)

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Similarly to (2), the paging load cost, which is the average

number of cells searched until paging succeeds, is defined by

?

L

=

Np

?

j=1

pj·

j

?

i=1

ni

?

.

(8)

Accordingly, the total paging cost, C, can be given by the

weighted sum of the paging delay cost (ˆD) and the paging

load cost (L) as follows.

C

=

L + ω ·ˆD

Np

?

Np

?

=

j=1

?

?

pj

j

?

j

?

i=1

ni

?

+ ω

Np

?

j=1

??

1 −

j

?

·ˆDj

i=1

pi

?

·ˆDj

?

=

j=1

pj

i=1

ni+ ω

?

1 −

j

?

i=1

pi

??

(9)

where ω is a weighting factor which is called delay factor.

According to the constraints of the amount of paging traffic

and the delay bound, the delay factor ω can be appropriately

assigned.

III. PROPOSED INTELLIGENT PAGING SCHEME

In [4], a paging scheme that optimally partitions a location

area into several paging areas has been proposed, but the

optimal partitioning scheme is based only on the user location

probability, without consideration of the paging load distribu-

tion. In this paper, we propose an enhanced paging scheme that

divides a location area into paging area by considering both

paging load distribution and location probability distribution.

First, we sort all Nccells in the increasing order of ρi/λi

(i = 1,2,···Nc) and choose the sorted sequence for the initial

paging sequence of our paging strategy. To increase paging

success probability, a cell with a high location probability

should be searched first. In addition, searching a cell with low

paging load results in the reduction of paging response time. If

paging process fails in a particular cells, it takes time to report

its paging failure, thus, the overall paging delay will increase.

Accordingly, proposed initial paging sequence according to

increasing order of ρi/λiis feasible and very reasonable.

Following the determination of the initial paging sequence,

we find optimal sizes of paging areas and allocate cells to

given sets of paging areas. Given that there are Nc cells in

a location area, the location area can be divided into paging

areas with various sizes. Fig. 2 shows an example to partition

Nc cells into paging areas by the typical branch-and-bound

method and our proposed scheme. In Fig. 2, the number within

a circle represents a size of the paging area (nj) (i.e., the

number of cells allocated in the paging area) and the leftmost

paging area will be searched first in the paging process.

Let state n be all possible cases that partition n cells. If

the size of the paging area that will be paged first is k, there

are 2n−k−1possible partitions of the remaining (n−k) cells.

These 2n−k−1possible sets of paging area sizes correspond

to state n − k. Note that in Fig. 2 (b), state 2 includes state

0 and 1, and state 3 includes state 0, 1 and 2, respectively.

Fig. 2. An example of partitioning Nc cells into paging areas

Accordingly, a location area with n cells is divided into a first

paging area with size k (k = 1,2,···,n) and state n − k. In

addition, state n can be divided into combinations of the first

paging area with the size k and the remaining state n−k, and

can be generally represented by state 1 through state n − 1,

as shown in Fig. 2 (b).

If the size of each paging area is determined, all cells in a

location area can be partitioned into each paging area in the

sorted order for the initial paging sequence. Moreover, in Fig.

2 (b), if we calculate the optimal cell partitioning of state i

(i = 1,···,n−1), the optimal cell partitioning for state n can

be obtained recursively. If the size of the first paging area in

state n is k, the paging cost for state n, Cn, can be expressed

as

??

i=1

for k = 1,···,n − 1

whereˆD(k) is the maximum normalized load among k cells

in the first paging area. In (10), the value of k that gives the

minimum Cnis the optimal size of the first paging area for

state n. If the size of the first paging area is determined, the

remaining cells in state n − k can be partitioned in a similar

way to minimize the paging cost.

In the case of the conventional branch-and-bound method, to

find an optimal partition for n cells into paging areas, 2n−1(=

1+1+2+4+···+2n−1) paging sequences should be compared

as shown in Fig. 2 (a). In contrast, we can reduce the total

number of sets for paging areas to (n2−n+2)/2 (= 1+1+2+

3 + ··· + (n − 1)) using the proposed partitioning algorithm,

as shown in Fig. 2 (b). Moreover, our proposed algorithm

requires time complexity O(n2), which is far simpler than the

exponential time complexity of the branch-and-bound method.

Cn =

k

?

λi

?

· k + ω ·

?

1 −

k

?

i=1

λi

?

·ˆD(k)

?

+ Cn−k,

(10)

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TABLE I

RATIO OF PAGING COST FOR THE PROPOSED METHOD TO THE PAGING

COST OF THE OPTIMAL SEQUENCE

( a) when ρdevvaries (Nc= 10, ω = 1, ρmean= 10, λdev= 0.5)

ρdev

02

RC

1.00001.00231.0043

468 10

1.0109 1.0054 1.0135

( b) when λdevvaries (Nc= 10, ω = 1, ρmean= 10.0, ρdev= 5.0)

λdev

0.00.2 0.4

RC

1.00001.00001.0057

0.60.8 1.0

1.01041.0061 1.0147

( c) when Nc varies (ω = 1, ρmean= 10.0, ρdev= 5.0, λdev= 0.5)

Nc

567

RC

1.00141.00171.0063

8910

1.00611.00691.0064

( d) when ω varies (Nc= 10, ρmean= 10.0, ρdev= 5.0, λdev= 0.5)

ω

124

RC

1.00641.00091.0005

6810

1.00041.0000 1.0000

IV. NUMERICAL RESULTS AND DISCUSSION

In this section, we provide numerical results for our paging

strategy, on the basis of the analysis in Section II.

Suppose that the location probability (λi) of a user in ithcell

is obtained from a Gaussian distribution with a mean (λmean)

of 1.0 and a standard deviation of λdev. We normalize λnwith

λdev so that the sum of location probabilities of all cells in

a location area is equal to 1. If the standard deviation (λdev)

is 0, all cells have the same location probability. We assume

that each cell has a normalized paging load (ρi/τ), and ρi/τ

is given by a Gaussian distribution with mean (ρmean) 10.0

and standard deviation ρdev. When ρdevis 0, all cells have the

same paging load. If a random number below zero is generated

from the Gaussian distribution, we assign an arbitrary small

positive value instead.

In Table I, numerical results of our proposed partitioning

algorithm and the conventional branch-and-bound method are

compared. Here, RC denotes the ratio of the paging cost

for our proposed scheme to the optimal paging cost obtained

by using the branch-and-bound method. We can see that the

paging costs of our proposed strategy using the heuristic

approach based on (ρi/λi) are very close to the optimal results

for the cases when ρdev, λdev, Nc and ω vary. In all cases,

the differences between the paging cost of our partitioning

method and that of the optimal paging sequence are within

2%. Therefore, the proposed partitioning algorithm performs

very accurately, and with far lower complexity than the branch-

and-bound method.

Now, we investigate the characteristics of our intelligent

paging scheme when there are 100 cells per location area.

In Fig. 3(a), the average number of paging areas decreases

when the delay factor (ω) increases because a large number of

paging areas causes long paging delays. When paging delay

is not critical, the paging load in the cells can be reduced

by partitioning a location area into a large number of paging

areas. Fig. 3(b) shows the paging delay cost (ˆD) obtained

in (7), when the delay factor (ω) varies. When ω increases,

the number of paging areas decreases because large number

of paging areas causes long paging delay. Thus, paging delay

cost, which is the elapsed time until paging success, decreases

according as ω increases. Paging load cost (L) in (8) is shown

in Fig. 3(c). Paging load cost is given by the number of

cells which is actually paged until the target user is found.

Therefore, as the number of paging area decreases due to

increasing value of ω, paging load cost increases as shown

in Fig. 3(c).

Consider the effect of ρdev in Figs. 3(b) and 3(c). As

ρdev increases, the paging response time of some paging

areas becomes shorter than the average paging response time.

Because the cells with low paging load are paged first in our

paging strategy, paging delay cost (ˆD) can be lower at high

ρdev, as shown in Fig. 3(b). Meanwhile, the overall response

time of failed paging is determined by the response time

of the cell with the highest paging load in the paging area.

Therefore, when the deviation of paging load increases, it

is more beneficial to divide the location area into a larger

number of paging areas. Thus, increasing ρdev results in an

increase in paging load cost, as shown in Fig. 3(c). In addition,

because the effect of the paging load distribution on the paging

sequence increases for high ρdev, it is possible that the cells

with low paging load are paged early, despite their having a

low location probability. Consequently, high ρdevincreases the

paging load cost.

Figs. 4(a), 4(b) and 4(c) show the effect of deviation of

location probability (λdev) on the average number of paging

areas, paging delay cost and the paging load cost, respectively.

For high λdev, the probability, with which the target mobile

terminal is found earlier, increases. Therefore, the number of

paging areas becomes larger as λdev increases, as shown in

Fig. 4(a). Accordingly, the paging delay cost increases when

λdevbecomes high, as shown in Fig. 4(b). For the same reason,

the paging load cost decreases as λdevincreases, as shown in

Fig. 4(c).

V. CONCLUSIONS

In this paper, we have proposed a modified paging cost

formula that considers the effect of non-uniform paging load

distribution on paging delay as well as the effect of typical

location probability distribution. In addition, we have intro-

duced a simple polynomial time algorithm to determine the

sub-optimal paging sequence. Numerical results show that

the paging sequence obtained by our proposed scheme is

almost equivalent to the optimal paging sequence. Moreover,

because our proposed scheme requires very low computation

complexity, it can be efficiently used in real-time paging

applications.

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0 .0

0 .5

1 .0

1 .5

2 .0

0 .0

2 0 .0

4 0 .0

6 0 .0

8 0 .0

1 0 0 .0

Delay factor ( )

?

Average number of paging areas

dev = 0 .05

?

dev = 0 .25

?d

?

ev = 0 .45

0 .00 .5

1 .01 .5

2 .0

Delay factor ( )

(b) Average paging delay cost

?

0 .0

5 .0

1 0 .0

1 5 .0

2 0 .0

Average delay cost (sec)

dev = 0 .05

?

dev = 0 .25

?d

?

ev = 0 .45

0 .00 .5

1 .0

1 .5

2 .0

3 5 .0

3 7 .0

3 9 .0

4 1 .0

4 3 .0

4 5 .0

4 7 .0

4 9 .0

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?

dev = 0 .25

?d

?

ev = 0 .45

Delay factor ( )

?

Average load cost (cells)

(a) Average number of paging areas

(c) Average paging load cost

Fig. 3.Effects of the deviation of the paging load (ρdev)

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0 .0

0 .5

1 .0

1 .5

2 .0

0 0

2 0 .0

4 0 .0

6 0 .0

8 0 .0

1 0 0 .0

Delay factor ( )

?

Average number of paging areas

dev = 0.1

?

dev = 0.5

?

dev = 0.9

0 .0

0 .51 .0

1 .5

2 .0

0 .0

5 .0

1 0 .0

1 5 .0

2 0 .0

dev = 0.1

?

?

?

dev = 0.5

dev = 0.9

Delay factor ( )

?

Average delay cost (sec)

0 .0

0 .5

1 .0

1 .5

2 .0

3 0 .0

4 0 .0

5 0 .0

6 0 .0

Delay factor ( )

?

Average load cost (cells)

dev = 0.1

dev = 0.5

dev = 0.9

(a) Average number of paging areas

(b) Average paging delay cost

(c) Average paging load cost

?

?

?

?

Fig. 4.Effects of the deviation of the location probability (λdev)

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