IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO.

6, JUNE 2016 4117

Efficient Tracking Area Management Framework

for 5G Networks
Miloud Bagaa, Tarik Taleb, Senior Member, IEEE, and Adlen Ksentini, Senior Member, IEEE

Abstract—One important objective of 5G mobile networks is to that covers several geographical areas. UEs in a specific area
accommodate a diverse and ever-increasing number of user equip- are attached to a base station (eNodeB), which manages their
ment (UEs). Coping with the massive signaling overhead expected access to the mobile core network. UEs are usually in idle mode
from UEs is an important hurdle to tackle so as to achieve this
objective. In this paper, we devise an efficient tracking area list and have no call activity for some duration. When a connection
management (ETAM) framework that aims to find optimal distri- request comes for a UE in idle mode, the Mobility Management
butions of tracking areas (TAs) in the form of TA lists (TALs) and Entity (MME) sends a signaling message, namely paging, to all
assigning them to UEs, with the objective of minimizing two con- eNodeBs to find the UE’s location (i.e., cell) in the network.
flicting metrics, namely paging overhead and tracking area update Accordingly, in case a high number of UEs need to be paged,
(TAU) overhead. ETAM incorporates two parts (online and offline)
to achieve its design goal. In the online part, two strategies are a massive number of downlink signaling messages have to be
proposed to assign in real time, TALs to different UEs, while in the transmitted, resulting in high signaling overhead and wasting
offline part, three solutions are proposed to optimally organize TAs scarce resources of the mobile network. To overcome this issue,
into TALs. The performance of ETAM is evaluated via analysis the Tracking Area (TA) concept has been introduced in Release
and simulations, and the obtained results demonstrate its feasibil- 8 of the 3GPP mobile network specifications (i.e., replacing
ity and ability in achieving its design goals, improving the network
performance by minimizing the cost associated with paging and the Routing Area concept in previous releases). The key idea
TAU. beneath the TA principle consists in grouping several cells or
Index Terms—5G, LTE, convex optimization, game theory.
sites into one TA. MME keeps record of the location of UEs
in idle mode at the TA granularity. Thus, when a connection
I. I NTRODUCTION setup request comes for a UE in idle mode, the UE in question
is paged only within its current TA, which would mitigate the
O NE OF the main challenges of the upcoming 5G net-
works is to accommodate the high demand of data raised
from the increasing number of devices. In this vein, deploying
overhead of paging in the network.
Each time a UE moves to a new location and connects to a
new cell not belonging to its current TA, the UE sends an uplink
small cells should be considered with high interest to overcome message, namely Tracking Area Update (TAU), to MME, which
this issue. 5G networks would deploy densely self-organizing subsequently updates the TA of the UE. In this vein, it is worth
low-cost and low power small base-stations. However, deploy- noting that a TA is also defined as an area where the UE can
ing high number of small cells would increase the signaling move without transmitting TAU messages to MME. Despite the
overhead caused by the tracking and paging of User Equipment advantages of the TA concept in minimizing the paging over-
(UE). Combined with the high number of UEs and Machine head, it has the following limitations on the TAU signaling: (i)
Type Communication (MTC) devices [1], [2], the use of small many TAU signaling messages might be generated due to ping-
cells will introduce a major challenge in term of signaling over- pong effect, i.e, a UE keeps hopping between two adjacent cells
head for 5G networks. In order to tackle the increased data belonging to different TAs, which could be exacerbated in case
rate expected from the usage of the envisioned 5G network, the of densely deployed small cells; (ii) the mobility signaling con-
signaling overhead should be minimized as much as possible. gestion due to a large number of UEs having a similar behavior,
Usually, the Radio Access Network (RAN) of a mobile oper- e.g. massive number of UEs simultaneously moving from one
ator is organized into a set of cells (including small cells) TA to another TA (train scenario); (iii) the use of TA strategy
Manuscript received May 23, 2015; revised October 3 and December 28, has the symmetry limitation: If two cells are in the same TA,
2015; accepted February 13, 2016. Date of publication February 26, 2016; then neither of them can be in any other TA. To overcome this
date of current version June 7, 2016. This work was supported by the TAKE 5
limitation, Release 12 introduces the Tracking Area List (TAL)
project funded by the Finnish Funding Agency for Technology and Innovation
(TEKES), a part of the Finnish Ministry of Employment and the Economy. concept in order to simplify the TA configuration. The TAL con-
The associate editor coordinating the review of this paper and approving it for cept aims for reducing the TAU signaling messages by grouping
publication was W. Saad. several TAs in one TAL and allowing the overlapping of TAs.
M. Bagaa is with Aalto University, Espoo, Finland (e-mail:
miloud.bagaa@aalto.no).
Each time a UE visits a new TA that does not belong to its TAL,
T. Taleb is with Sejong University and Aalto University, Espoo, Finland a TAU message is sent to the MME. Upon receiving the TAU
(e-mail: taleb-tarik@ieee.org). message, MME assigns a new TAL to the UE. The new TAL
A. Ksentini is with EURECOM, Sophia-Antipolis, France (e-mail: should include the visited TA. Furthermore, Release 12 allows
adlen.ksentini@eurecom.fr).
Color versions of one or more of the figures in this paper are available online
network operators to include up to 15 TAs in each TAL and the
at http://ieeexplore.ieee.org. MME always adds the last visited TA to the list to overcome the
Digital Object Identifier 10.1109/TWC.2016.2535217 problem of frequent updates due to ping-pong situations. Given
1536-1276 © 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
4118 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

Fig. 1. The tradeoff between TAU and paging overhead in 4G and beyond mobile networks.

that TALs are overlapped, the above-mentioned limitations of into account only the priority between TALs. As for the sec-
conventional TAs, defined in Release 8, can be accordingly mit- ond one, in addition to the priority between TALs, it takes into
igated. However, the current LTE specifications do not provide account the UEs activities (i.e., in terms of incoming communi-
any details on how to define TALs and allocate them to UEs. cation frequency and mobility patterns) to enhance further the
Each time a UE moves to a new location and connects to network performance.
a new TA not belonging to its current TAL, the UE sends a The remainder of this paper is organized as follows.
TAU message to MME. On the other had, when a connection Section II introduces some related research work. Section III
request comes for a UE, the MME sends a paging message to presents the envisioned network model and formulates the
all TAs (i.e., TAL) where the UE is registered. An increase in target problem. It also presents an overview of the ETAM
TALs size leads to a rise in paging signaling messages and a framework. Section IV presents the online part of the ETAM
decrease in TAU signaling messages. Fig. 1 shows the trade- framework for assigning TALs to UEs. The three solutions pro-
off between TAU and paging overheads when forming TALs. In posed for the offline part of the ETAM framework are described
the figure, we assume that the network contains four TAs along in Section V. Section VI details a Markov-based analytical
a railway path, in which each TA has two other neighboring model for the three offline solutions. Besides the numerical
TAs on the left and the right sides. From Fig. 1(a), we observe results obtained by solving the Markov model, Section VII
that the organization of each TA in a separate TAL causes many presents the simulation setup to evaluate the performance of
TAU signaling messages in the network, which are generated ETAM and discusses the obtained results. Finally, the paper is
and forwarded from the RAN to the evolved packet core (EPC). concluded in Section VIII.
Whereas Fig. 1(b) and Fig. 1(c) show that increasing TAL size
reduces TAU overhead and increases paging overhead. Fig. 1(c)
II. R ELATED W ORK
shows that the TAU overhead can be ignored if all TAs are
organized in the same TAL. Mitigating signaling overhead, due to UE mobility in cellu-
Several research works have been conducted to solve the lar mobile networks, has attracted high attention during the last
TAL problem, whereby the aim is to capture the tradeoff that years. As stated earlier, in the Evolved Packet System (EPS),
mitigates the overhead of TAU and paging messages when con- MMEs keep records of UEs’ positions in order to adequately
structing and assigning TALs to UEs. Most of these solutions forward their relevant incoming connections. For this purpose,
formulate the problem using a multi-objectives optimization 3GPP introduced two types of signaling messages to support
technique to achieve a fair tradeoff between signaling mes- UE mobility: (i) paging messages from the network, namely
sages overhead of TAL and paging, i.e. minimize both signaling MME, in order to find the locations of UEs in idle mode; (ii)
messages due to TAU and paging. In this paper, we devise TAU messages from UEs to MME to update their positions. A
an efficient tracking area list management (ETAM) framework TAU message is sent each time a UE enters into a new loca-
for 5G cloud-based mobile networks [3], [4]. The proposed tion (cell) that does not belong to its current TA. Conventional
framework consists of two independent parts. The first part is TA assignment procedures whereby the network assigns only
executed offline and is responsible of assigning TAs to TALs, one TA for different UEs is not sufficient when UEs are highly
whereas the second one is executed online and is responsible of mobile. Indeed, high number of TAU messages could be sent by
the distribution of TALs on UEs during their movements across UEs as they frequently cross their corresponding TA borders.
TAs. For the first part, we propose three solutions, which are: An enhancement to the conventional procedure was envisioned
(a) F-PAGING favoring the paging overhead over TAU, (b) F- to reduce TAU overhead by i) grouping several cells (i.e.,
TAU favoring TAU over paging, and (c) FOTA (i.e., Fair and eNodeBs) in one TA or ii) introducing delays between TAU
Optimal Assignment of TALs to TAs) for a solution that uses messages sent by UEs. Another solution to reduce the impact
bargaining game to ensure a fair tradeoff between TAU and pag- of TAU messages on the network was proposed in [5] whereby
ing overhead. For the second part, two solutions are proposed to queuing models and buffer information at eNodeBs are used to
assign TALs to UEs. The computation load is kept lightweight delay the TAU frequency.
in both solutions not to downgrade the network performance. To further alleviate the effect of TAU messages on the
Furthermore, both solutions do not require any additional new network performance, 3GPP has introduced the concept of
messages when assigning TALs to UEs. The first solution takes TAL in Long Term Evolution (LTE), wherein each cell
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4119

Fig. 2. The proposed framework for tackling TAU and paging overhead in 4G and beyond mobile networks.

(eNodeB) assigns different TALs to UEs [6], [7]. Since TALs are In contrast to the existing works, in this paper, we propose a
overlapped, the number of UEs performing TAU when crossing framework optimizing the management of TALs and consist-
TA border drastically decreases. Besides reducing the num- ing in: (i) an offline part that assigns TAs to TALs; (ii) an
ber of TAU messages, TAL prevents the ping-pong effect, i.e., online part that assigns TALs to UEs. Two solutions are pro-
frequent TAU messages when a UE keeps hopping between posed to achieve the aim of the online part. The first one takes
adjacent TAs. Nevertheless, the current LTE specifications do into account only the priority between TALs, whereas the sec-
not provide any details on how to define TALs and allocate them ond one, in addition to the priority between TALs, takes into
to UEs. To address this open issue, several solutions have been account the UE behavior in terms of mobility and connection
proposed. In [8], Chung et. al. proposed a solution that orga- frequency. Regarding the offline part, we have devised three
nizes cells into rings, where UEs in each ring use the same TAL. solutions, which differ from the existing ones on their way to
Solutions, proposed in [9] and [10], use the same concept as in cope with the problem. Indeed, most existing solutions assign
[8] by assigning the same TAL to different UEs when visiting a the same TAL: i) to the same TAs in a static manner [8]–[10]; or
cell in the network. However, all these solutions [8]–[10] have ii) with the same probability [7], [11]. In contrast, the devised
not fully explored the advantage of TAL against the conven- solutions dynamically assign the same TAL to different TAs
tional TA approach. In [7] and [11], Razavi et. al. overcome this with different probabilities. The first one, dubbed F-PAGING,
limitation by allowing UEs residing in the same cell to regis- is proposed for a network known with a high rate of paging
ter with different TALs. Indeed, in [7] they proposed a solution (i.e., for voice call as well as for IP-based web applications) in
for congestion mitigation along a railway path. On the other comparing to the mobility rate. This solution maybe designated
hand, in [11] an extension of the former work is proposed with for small cities with high-density populations. The second one,
two new aspects: i) the solution is generalized for any arbitrary dubbed F-TAU, is proposed for a network which is known with
network instead of only train scenario; ii) a new solution that a high mobility rate compared to the paging rate. Such kind
handles the extenuation of paging signaling messages via TAL of solution maybe useful for a network known with low-density
management is proposed. populations and/or high mobility. The last one, dubbed FOTA, is
Generally speaking, assigning TALs to UEs shall depend on proposed to be generic for any kind of networks. It takes advan-
the mobility patterns of UEs as well as on their geographi- tage of both previous solutions, jointly addressing the overhead
cal distribution and density. MME may group, under the same due to both TAU and paging messages. FOTA uses Nash bar-
TAL, a large number of TAs in an area that has low density gaining game to ensure a fair tradeoff between both conflicting
to reduce the impact of TAU overhead on the network perfor- overhead, i.e., TAU and paging signaling messages.
mance. Similarly, MME may group under the same TAL a small
number of TAs serving a highly densed area. Indeed, to alleviate III. E NVISIONED N ETWORK M ODEL AND F RAMEWORK
the impact of paging messages on the network performance, it is OVERVIEW
worth assigning more than one TAL to the same TA. To the best
knowledge of the authors, most existing solutions focus only on A. ETAM Framework Overview
the offline part for assigning the TAs to TALs. Moreover, they Fig. 2 depicts a general overview of the ETAM framework.
consider only the TAU overhead and ignore the paging over- We assume that the network is subdivided into N TAs, N =
head. The only research work that addressed both constraints is {1, 2, · · · N }. Each TA consists of a set of cells, whereby a cell
presented in [11], wherein Razavi et al. proposed two separate is managed by an eNodeB (i.e., base station). As depicted in the
solutions, addressing the impact of TAU and paging overhead, figure, the geographically close eNodeBs can be grouped in the
respectively. Both solutions are based on multi-objectives opti- same TA, using any existing algorithm [12], [13], to optimize
mization techniques for assigning the TAs to TALs. The first the network performance in terms of paging overhead. Initially,
one tries to minimize the TAU overhead while setting paging as the ETAM framework starts by an inefficient solution and then
a constraint, and the second one minimizes the paging overhead converges, through iterations, to the optimal one. As depicted
while fixing the TAU overhead as a constraint. in Fig. 2, ETAM framework starts by considering each TA as
4120 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

a separated TAL. Then it executes, repetitively, two steps to

converge to the optimal solution. The first step is the offline-
assignment of TAs-to-TALs, whereas the second one is the
online-assignment of TALs-to-UEs. To efficiently map between
TAs and TALs, the information about TAU and paging signal-
ing messages are transferred from the online step to the offline
one. The latter enhances the mapping between TALs and TAs
and then provides the former with the new mapping to optimize Fig. 3. An example illustrating how to construct neighboring graphs G from an
LTE network.
further the network performance. The online step is executed
during a specified period D, where all the information about
the TAU and paging overhead are gathered from the network to TAs, named A, B, C, D and E. The blue arrows between
be transferred to the offline step. The duration D may be fixed TAs denote the movement of different UEs in the network.
by the network operator, but it can be changed when there is a The movement of UEs can be deduced from the handover
noticeable update in the network. statistics of different eNodeBs or from the handover command
Since there is no exact indication on the trajectory of UEs, messages sent by MME. To form , we begin by forming
during the online-assignment of TALs-to-UEs, we use a proba- the neighboring graphs G from the network as depicted in
bility strategy to assign TALs to UEs. In each visited TA, TALs Fig. 3(b). An edge between two vertices (i.e., TA) A and B
are assigned to visiting UEs with different probabilities. Indeed, exists, if there is a TAU possibility between them. In Fig. 3(b),
the TAL that reduces more the TAU and paging signaling mes- an edge is generated between the vertices A and B, if there
sages would have more priority to be assigned to a UE. There is a blue arrow between TAs A and B in Fig. 3(a), which
is a tradeoff between TAU and paging signaling messages. means the possibility of UEs movement between these TAs. In
Clearly, the smaller the size of TALs is, the higher the TAU Fig. 3(b), we do not construct an edge between vertices A and
overhead is, but the smaller the paging overhead becomes. For E since a direct blue arrow does not exist between them; UEs
the online-assignment of TALs-to-UEs, we consider two solu- cannot move from A to E without passing by another TA (i.e.,
tions. The first one takes into account only the priority between B or D). Finally,  A is formed from the neighboring graph
TALs that was learned from the offline step. Whereas, the sec- G. Indeed, the different elements of  A are those having all
ond one, in addition to the priority between TALs, takes into vertices of all sub-graphs of G that contain the vertex A and
account the UEs behavior, in terms of incoming communica- their length do not exceed 15. Thus, the vertices of a sub-graph
tion frequency and mobility patterns. For the offline-assignment of G that contain the vertex A are considered as one element
of TAs-to-TALs, we consider three different solutions, which in  A . From Fig. 3,  A = {{A}, {A, B}, {A, D}, {A, B, C},
define the core of our ETAM framework. It is worth recalling {A, B, D}, {A, B, E}, {A, D, E}, {A, B, C, D}, {A, B, C, E},
that (i) the first solution favors the paging overhead when form- {A, B, D, E}, {A, B, C, D, E}}.  Finally,  is formed from
ing TALs; (ii) the second one favors the TAU overhead; and different i as follows:  = i . An element of i is a
i∈N
(iii) the third solution uses the bargaining game theory to dis- set, i.e. {A, B} and {B, A} are considered as the same ele-
tribute TALs among TAs by capturing a fair tradeoff between ment in . From Fig. 3,  = {{A}, {B}, {C}, {D}, {E}, {A, B},
TAU and paging overhead. The TAL that exhibits the high- {A, D}, {B, C}, {B, D}, {B, E}, {C, E}, {D, E},{A, B, C},{A,
est fairness in the TAU and paging overhead has the highest B, D}, {A, B, E}, {A, D, E}, {B, C, D}, {B, C, E},{C, D, E},
probability to be assigned to a UE. {A, B, C, D} , {A, B, C, E}, {A, B, D, E}, {A, B, C, D, E}}.
We assume that each UE has a specific probability to be
B. Network Model and Notations called/paged (i.e., for voice call as well as for IP-based web
applications). Further, each UE follows a different mobility pat-
Let  denote the set of all possible TALs in a mobile net- tern, hence the number of sites (cells) visited by each UE is
work, and let  A denote the set of possible TALs that can be different. In the online-assignment of TALs-to-UEs step, the
assigned to UEs in TA A. As mentioned earlier, each time a UE network is monitored in order to track the number of signaling
visits a new TA that does not belong to its TAL, a TAU message messages (i.e., TAU and paging) sent and received by different
is sent to the MME. Upon receiving the TAU message, MME UEs. We denote by α = {α1 , α2 · · · } and β = {β1 , β2 · · · } the
computes and sends a new TAL to the UE. The new TAL should probability of paging and TAU of UEs in the network, respec-
include the visited TA. From Release 12 of the 3GPP specifi- tively. In other words, in the offline-assignment step, we have
cations, the operator can specify for each TAL a list of up to the information about different existing UEs in the network. We
15 TAs and the MME always adds the last visited TA to the list denote by ϒ the different UEs. For each UEu ∈ ϒ, we have its
to prevent the risk of ping-pong updates. For this reason,  is probability αu to send a TAU message and its probability βu to
formed by considering the different possible combinations of be called (i.e., cause a paging). We denote by γ = {γ1 , γ2 , · · · }
TAs, such that the length of each element in  should be higher the overhead of mobility and paging ratio of different UEs. γu
or equal to one and less than 16, i.e. each TAL i ∈  should denotes the overhead of mobility and paging ratio of UEu , i.e.
contain at least 1 TA and at most 15 TAs to allow the MME to the ratio between the paging and the TAU of a UEu . Formally,
add the last visited TA. ραu
γu is computed as follows: γu = , where τ and ρ
Throughout the paper, we will refer to the example depicted ραu + τβu
in Fig. 3 in order to show how  should be constructed. In are the amount of overhead of one TAU operation and one
this example, we assume that the network consists of five paging message, respectively. Intuitively, the values of τ and
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4121

TABLE I
N OTATIONS U SED IN THE PAPER .

Fig. 4. TALs  A and their probabilities PA at TA A: an example.

then in the online step. Indeed, offline step generates Matrix S

in a way that the TAL that optimizes more the network perfor-
mance has a higher probability to be assigned to different UEs.
From above, i , for ∀i ∈ N, can be also defined as follows:

i = { , Si, = 0 for ∀ ∈  ∧ i ∈ }

accordingly, when a UE visits a TA i, MME will assign to

this UE a TAL from i . We denote by i the sorted element
of i . TALs in i are sorted according to the number of TAs
in each TAL, such that TALs having the smallest number of
TAs are placed in the tail. i ( ) represents the th TAL of i .
We denote by Pi ( ) the probability to assign TAL i ( ) by
TA i to different UEs. Pi ( ) can be deduced from the matrix
S. Fig. 4 shows an example of  A and PA . In this example,
 A (1) = {A, B, C, D, E} and  A (2) = {A, B, C, D}.
ρ depend on the “radio system” [14]. Knowing that γu ∈ [0, 1], The assignment of TALs to UEs should be lightweight in
the higher the value of γu is, the higher the number of paging of terms of computational cost and communication overhead. In
UEu becomes in comparison to TAU messages. Accordingly, γu this vein, the proposed solutions for this part are designed to be
represents an important parameter to consider when designing simple and easy to deploy. When a UE u visits a new TA A, the
TALs to assign to UEs. Indeed, when a UE has a high value of MME selects a new TAL  A ( ) from  A according to the set of
γu , meaning that it generates more paging messages than TAU probability PA . The TAL that has the highest probability would
messages, it is better to assign a TAL with a few number of have more chance to be elected than the others. Then, the MME
TAs to reduce the paging overhead. However, if a UE has a low adds the last visited TA to  A ( ), to prevent the risk of ping-
value of γu , meaning that it generates more TAU messages than pong updates, before assigning it to UE u. It is worth noting
paging, it is more appropriate to assign to it TALs with more that  A ( ) should be also assigned to each UE according to its
TAs to reduce the TAU overhead. mobility and paging features. Indeed, some UEs exhibit high
Moreover, in the online-assignment of TALs-to-UEs step, we mobility, while others are called more often. For this reason,
can deduce the number of UEs h i, j that moved from each TA i unlike all existing works, in this paper we consider both the
to another TA j. We define by H the matrix that represents the probability of each TAL PA ( ) and the features of UEs when
number of UEs that moved from different TAs. Each entry in assigning TALs to different UEs. In this paper, two strategies
the matrix H at row i and column j, denoted by h i, j , indicates are considered as explained below.
the number of UEs that moved from TA i to TA j. The value
of h i, j can be deduced from the handover statistics of differ- A. Assigning TALs to UEs Without Prioritization
ent eNodeBs or from the handover command messages sent by In this strategy, we use only the probability of each TAL
MME. Furthermore, each UEi spends different times in differ- PA ( ); i.e. no prioritization among UEs is considered. All UEs
ent TAs. Let M denote the matrix that represents the duration have the same priority to obtain any TAL from the visited TAs.
spent by different UEs in different TAs. The rows in M repre- This strategy could be used to reduce the involvement of UEs
sent the UEs, whereas the columns represent the different TAs (and hence associated overhead and battery consumption) in the
in the network. The element Mi, j denotes the duration spent by TAL assignment process. In this case, when a UE u visits a new
N TA A, the MME generates a random variable V1 ∈ [0, 1] using
UEi in TA j. Note that, ∀i ∈ ϒ, Mi, j = D. a uniform distribution. Then, TAL is assigned to UE u as the
j=1
For the sake of readability, the notations used throughout the one that satisfies the following condition:
paper are summarized in Table I. −1
 
PA (k) < V1 ≤ PA (k)
IV. O NLINE -A SSIGNMENT OF TALs-to-UEs k=1 k=1

The mapping between TAs and TALs is represented through a Using the example depicted in Fig. 4, if V1 = 0.38, then TAL
matrix S, where the rows are the different TAs and the columns 3 would be assigned to UE u. By using this strategy, we
are the different TALs. An element Si , in the matrix S, repre- ensure that TALs having higher probabilities will be more likely
sents the probability to assign TAL in TA i to different UEs. assigned to UEs. From above, we observe that the assignment
Matrix S is first generated during the offline step and is used of TALs to UEs without prioritization is light weighted. In fact,
4122 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

it is in the order of the generation of a random value V1 that

follows a uniform distribution.

B. Assigning TALs to UEs With Prioritization

In this strategy, UEs exhibiting higher mobility rate than pag-
ing rate, should get TALs that have large number of TAs to
mitigate the effect of TAU signaling. Employing the example
depicted in Fig. 3, TAL {A, B, C, D, E} is assigned to UEs
that exhibit higher mobility features than paging, and that is to
reduce the overhead of TAUs. Whereas, TAL {A} is assigned to
UEs having more paging than being highly mobile, and that is Fig. 5. The impact of ν values on the cumulative distribution function of
Poisson.
to reduce the impact of paging on the network performance. As
discussed earlier, when a UE u visits a new TA T Au , the MME
in charge of T Au , has the following information: (i) the matrix value of PA ( ), for both cases it is more likely that V1 (resp.,
S and (ii) the overhead of mobility and paging ratio γu . We 
−1 
F(ν = νu , V2 )) is in [ PA (k), PA (k)]. Therefore, in both
recall that the higher the value of γu is, the higher the number k=1 k=1
of paging is, i.e., in comparison to TAU (mobility). cases TAL that has the highest value of PA ( ) is more likely
To prioritize among UEs without impacting the probabilities to be selected by UEs. 
of TALs, we define F(ν = x, k) as the cumulative distribu- Theorem 2: When assigning TALs to UEs via prioritization
tion function of Poisson distribution until k, where ν is the strategy, a UE u having higher speed (i.e., highly mobile) than
mean value. Fig. 5 depicts F(ν = x, k) according to ν and paging ratio γu , is more likely to be assigned a TAL with large
k. When UE u visits TA A, MME computes for this UE its size to mitigate the effect of TAU.
1
νu as νu =  . Since γu ∈ [0, 1], then νu ≥ 1. Afterwards, Proof: Based on the above, the UE which has higher
γu
a random variable V2 ∈ [0, 100] is generated using a uniform speed than paging ratio, has the smallest value of γu , and then,
distribution. Now, TAL is assigned to UE u as the one that the highest value of νu . From Fig. 5, it is more likely to get
satisfies the following condition: F(ν = νu , V2 ) in the vicinity of zero, and consequently select
a TAL from the head of  A that has a large size. 
−1
 
PA (k) < F(ν = νu , V2 ) ≤ PA (k)
k=1 k=1 V. O FFLINE -A SSIGNMENT OF TAs-to-TALs

From above, high values of γu mean that UEu receives more As discussed in Section III, this step is executed offline to
paging messages than it issues TAU messages (due to mobility). allow the mapping between different TAs and TALs. At the end
For this UE, it is preferable to assign a TAL with small number of this step, a matrix S is generated, whereby the rows repre-
of TAs. Note that large values of γu means small values of νu . sent the different TAs N and the columns represent the TALs
From Fig. 5, UE u will have high probability to get a value in . An element Si j in the matrix S refers to the probability that
the vicinity of 1 and will be hence assigned TALs from the tail TA i assigns TAL j to different UEs. The sites (cells) belonging
of  A (i.e., TAL with small size). Whereas, when γu is small to the same TA i use the same row i in the matrix S to assign
(i.e., UE u has high mobility features than paging), its νu will TALs to different UEs. As mentioned in Section III, the result of
be large. Then, UE u has high probability to be assigned a TAL this step is used by the online step of our framework to assign
from the head of  A (i.e., TAL with large size). The assign- different TALs to different UEs. In what follows, we present
ment of TALs to UEs with prioritization is also in the order of three problem formulations for optimizing TALs distribution in
the generation of a random value V2 that follows a uniform LTE and beyond networks. The two first optimizations are lin-
distribution. ear programs, whereas the last one is a convex optimization.
Theorem 1: TAL having the highest value of PA ( ), has As it is well known in the literature [15], the linear program
higher probability to be selected for different UEs. and convex optimization have polynomial time complexity. It
shall be noted that the result of the three solutions is the same
Proof: Let T AL denote the TAL that has the high-
matrix S, however, with different elements Si j . The latter are

est value of PA ( ) at TA A. Formally, PA ( ) = PA (k) − considered as the variables for the problem optimizations. In
k=1 the first optimization problem, we assume that the TAU over-

−1
head is dominator and we then propose a solution to optimize
PA (k). We have two cases: (i) Assigning TALs from T AL A
k=1 the network performance that favors TAU on paging. In the
to UEs without prioritization and (ii) Assigning TALs from second solution, we propose an optimization problem whereby
T AL A to UEs with prioritization. In the first case, a random the paging overhead is dominator. Finally, we introduce FOTA,
probability V1 ∈ [0, 1] is generated to select TALs. Whereas, in which aims at capturing the tradeoff between the TAU and pag-
the second case, a random number V2 ∈ [0, 100] is generated ing overhead when assigning TALs to TAs (Fair and Optimal
and then F(ν = νu , V2 ) is computed. As TAL has the highest Assignment of TALs to TAs - FOTA), and ultimately to UEs.
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4123

In FOTA, a bargaining game is used to capture the tradeoff B. Optimizing the Network Performance via the Reduction of
between TAU and paging. Paging Overhead
In this subsection, we introduce F-PAGING, which favors the
A. Optimizing the Network Performance via the Reduction of paging overhead when assigning TAs to TALs. As in F-TAU,
TAU Overhead we use the min-max approach as depicted in the linear program
((7). . .(8)). In this linear program, the goal (7) is to optimize the
In this subsection, we propose the solution, named F-TAU,
network performance seeking the optimal distribution of TALs
that favors TAU when assigning TAs to TALs. In F-TAU, we
that minimizes the paging overhead. In this solution, we set the
seek the optimal distribution of TALs by applying the min-
maximum amount of TAU overhead tolerated by the network to
max approach. The aim is to minimize the maximum number
T AUmax . Its value could be defined according to the capacity of
of TAU messages. Formally, we aim to minimize the maxi-
MMEs in the network. Otherwise, T AUmax can be fixed to ∞.
mum aggregate number of TAU messages sent by UEs between
In this case, the optimal solution would converge to putting each
any two TAs in the network. In this solution, we denote by
TA in a separate TAL in order to reduce the paging overhead.
P AG I N G max the maximum number of paging messages tol-
The linear program is formulated as follows:
erated by the network. Its value could be fixed according to the ⎛ ⎞
capacity of MMEs in the network. Otherwise, P AG I N G max   
can be fixed to ∞. In this case, the optimal solution would con- min ρ ⎝Si αk Mki ηj⎠ (7)
verge to putting all TAs into the same TAL in order to reduce ∈ i∈ k∈ϒ j∈ ∧ j=i
the TAU overhead. At this point, the optimization model which S.t,
aims at reducing the TAU overhead can be formulated according
(2)−(5) and
to the following linear program ((1). . .(6)):
⎛ ⎞ ∀i, j ∈ N ∧ i = j :
  ⎛ ⎞
min max τ ⎝ h i j Si + h ji S j ⎠ (1)  
∀i, j∈N∧i= j
∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i τ⎝ h i j Si + h ji S j ⎠ ≤ T AUmax
∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i
S.t,
(8)
∀ ∈ , ∀i ∈ N ∩ , Si ≥ 0 (2)
∀ ∈ , ∀i ∈ N ∩ , Si ≤ 1 (3) The first fourth constraints ((2). . .(5)) are similar to the first
 linear program presented in the precedent section. The last con-
∀i ∈ N, Si = 1 (4) straint ensures that the total number of TAU messages sent by
∈ UEs when transiting between any two adjacent TAs i ∈ N and
∀ ∈ , ∀i ∈
/ N ∩ , Si = 0 (5) j ∈ N should not exceed the threshold T AUmax .
⎛ ⎞
  
ρ Si αk Mki ⎝ η j ⎠ ≤ PAGINGmax C. Trading off TAU Against Paging Using Nash Bargaining
∈ i∈ k∈ϒ j∈ ∧ j=i
(6) In contrast to the conventional techniques (eg., weighted-sum
method) used to solve the multi-objectives problems, which
In the objective function (1), the number of UEs that transited may not ensure a fair tradeoff between the conflicting objec-
from TA i (resp., j) is scaled by the variable Si (resp., S j ), tives, FOTA uses a Nash bargaining game to achieve this
which represents the proportional use of TAL by TA i (resp, tradeoff. As we have mentioned in Fig. 1, an increase in the size
j). It shall be also noted that the condition,“ ∈ i ∧ ∈ / j ⇔ of TALs reduces the TAU signaling messages, however it has a
∀i, j ∈ N, i = j, ∀ ∈  : i ∈ ∧ j ∈ / ”, aims at reducing the negative impact on the paging signaling messages. Meanwhile,
number of UEs moving between different TAs that do not reducing TALs size has a negative impact on TAU signaling
belong to the same TALs. The first three constraints ((2)–(4)) messages and positive impact on the paging signaling mes-
are used to ensure that each TA i ∈ N can select its TAL from sages. The UE’s mobility and call ratio have a great impact
Si with a fixed probability. The fourth constraint (5) ensures on the total number (i.e., TAU and paging) of signaling mes-
that a TA delivers TALs to UEs only if it belongs to this TALs. sages in the network. For a network characterized by a high
The last constraint (6) ensures that the sum of all paging over- mobility, we have to favor the reduction of TAU overheads in
head in the network should not exceed a predefined threshold order to reduce the number of total signaling messages in the
P AG I N G max . For any TAL , the overhead caused by pag- network. Whereas, for a network characterized by a high call
ing UEs residing in TA i ∈ (by sending paging messages to ratio, the reduction of paging signaling messages significantly
all TAs j ∈ ∧ j = i) is the number of sites η j in these
 TAs, reduces the total signaling messages. In FOTA, TAU and paging
scaled by αk Mki and a variable Si . Note that αk Mki overhead represent the conflicting objectives and are considered
k∈ϒ k∈ϒ as two players in the bargaining game. The two players (i.e.,
is a constant that represents the paging overhead at TA i and
TAU and paging signaling messages) would like to barter goods
Si represents the proportional use of i. Formally, αk Mki is
k∈ϒ (i.e., total signaling messages). It was theoretically proven in
defined as the sum of the probabilities of paging of each UE k [16] that the use of Nash bargaining game ensures a fair trade-
scaled by its residence time in TA i. off between the players according to the network characteristics
4124 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

in terms of UE’s mobility and call ratio. FOTA will favor the
reduction of TAU overhead for a network characterized by a
high mobility, whereas it will favor the reduction of paging
overhead for a network characterized by a high call ratio. In
what follows, some background on the Nash bargaining game
is introduced and then FOTA solution is presented.
1) Nash Bargaining Model and Threat Value Game: Nash
bargaining model can be viewed as a game between two players
who would like to barter goods. This model is a cooperative
game with non-transferable utility. This means that the utility
Fig. 6. The geometric interpretation of the Nash bargaining game.
scales of the players are measured in non-comparable units.
This model is adopted in our proposed FOTA scheme to find overhead players, respectively. The tradeoff problem between
a Pareto efficiency between the paging and TAU overhead. In TAU and paging overhead can be modeled as a convex opti-
our case, the players are the paging and TAU overhead which mization problem ((9). . .(13)).
do not use the same unit. This model is based on two elements,
assumed to be given and known to the players. First, the set of max (T AUwor st − f (S))(PAGINGwor st − g(S)) (9)
vector payoffs P achieved by the players if they agree to coop- S.t,
erate. P should be a convex and compact set. Formally, P can be (2)−(5) and
defined as P = {(u(x), v(x)), x = (x1 , x2 ) ∈ X }, whereby X is
∀i, j ∈ N ∧ i = j :
the set of strategies of two players, and u() and v() are the util- ⎛ ⎞
ity functions of the first and second users, respectively. Second,  
the threat point, d = (u ∗ , v∗ ) = (u((t1 , t2 )), v(t1 , t2 )) ∈ P, τ⎝ h i j Si + h ji S j ⎠ ≤ f (S)
which represents the pair of utility whereby the two players ∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i
fail to achieve an agreement. In Nash bargaining game, we aim (10)
to find a fair and reasonable point, (u, v) = f (P, u ∗ , v∗ ) ∈ P ⎛ ⎞
  
for an arbitrary compact convex set P and point (u ∗ , v∗ ) ∈ P. ρ Si αk Mki ⎝ η j ⎠ ≤ g(S) (11)
Based on Nash theory, a set of axioms are defined that lead ∈ i∈ k∈ϒ j∈ ∧ j=i
to f (P, u ∗ , v∗ ) in order to achieve a unique optimal solution
(u, v): f (S) ≤ T AUwor st (12)
1) Feasibility: (u, v) ∈ P. g(S) ≤ P AG I N G wor st (13)
2) Pareto Optimality: There is no point (u(x), v(x)) ∈ P
In the optimization problem, in addition to matrix S, we added
such that u(x) ≥ u and v(x) ≥ v except (u, v). In other
two variables f (S) and g(S) that represent the maximum
words, if P is symmetric about the line u(x) = v(x), and
values of TAU and paging overheads in the network, respec-
u ∗ = v∗ , then u = v.
tively. The use of Nash bargaining game in FOTA ensures
3) Independence of irrelevant alternatives: If T is a closed
fairness among the players (TAU and paging overheads) and
convex subset of P, and if (u ∗ , v∗ ) ∈ T and (u, v) ∈ T ,
produces a Pareto optimal solution. From the second and the
then f (P, u ∗ , v∗ ) = (u, v).
third axioms of the bargaining game, we can deduce that
4) Invariance under change of location and scale:
FOTA yields a fair Pareto optimal solution according to the
If T = {(u  (x), v (x)), u  (x) = α1 u(x) + β1 , v (x) =
threat point (T AUwor st , P AG I N G wor st ), which represents the
α2 v(x) + β2 f or (u(x), v(x)) ∈ P}, where α1 > 0,
performance thresholds of TAU and paging overheads, respec-
α2 > 0, and B1 and B2 are given numbers, then
tively. Let ST AU and S P AG I N G be the optimal solutions of the
f (T, α1 u ∗ + β1 , α2 v∗ + β2 ) = (α1 u + β1 , α2 v + β2 ).
linear programs ((1). . .(6)) and ((7). . .(8)), respectively. Then,
Moreover, the unique solution (u, v), satisfying the
we can define P AG I N G wor st , P AG I N G best , T AUwor st and
above axioms, is proven to be the solution of the following
T AUbest as follows:  
optimization problem:  
⎧ 1) P AG I N G wor st = ρ αk Mki
⎪
⎪ max(u(x) − u ∗ )(v(x) − v∗ ) ∈ i∈ k∈ϒ
⎨
s.t. 
⎪ (u(x), v(x)) ∈ S η j SiT AU
⎪
⎩ j∈ ∧ j=i
(u(x), v(x)) ≥ (u ∗ , v∗ )  
 
2) P AG I N G best = ρ αk Mki
A general geometric interpretation of the Nash bargaining ∈ i∈ k∈ϒ
game is shown in Fig. 6. 
2) Fair and Optimal TALs Assignment: We denote by d = η j SiP AG I N G
(T AUwor st , P AG I N G wor st ) the threat point of our bargaining j∈ ∧ j=i
game that solves FOTA. In contrast to conventional bargaining 
game, the utility function of each player, (i.e., TAU and pag- 3) T AUwor st = max τ h i j Si
∀i, j∈N,i= j ∈i ∧ ∈
/ j
ing overhead) in our model, is the opposite of its cost. In other
words, (T AUwor st , P AG I N G wor st ) ≥ ( f (S), g(S)), ∀S ∈ X , 
+ h ji S jP AG I N G
where f () and g() are the utility functions of TAU and paging ∈ j ∧ ∈
/ i
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4125

 Therefore, the optimization problem is reformulated as follows:

4) T AUbest = max τ h i j Si
∀i, j∈N,i= j ∈i ∧ ∈
/ j max log((T AUwor st − f (S)))+log((P AG I N G wor st −g(S)))
 (24)
+ h ji S Tj AU S.t,
∈ j ∧ ∈
/ i (2)–(5) and
It is easily noticeable that P AG I N G best ≤ P AG I N G wor st
and T AUbest ≤ T AUwor st . Fig. 7 illustrates the physical inter- ∀i, j ∈ N ∧ i = j :
⎛ ⎞
pretation of the trade-off between TAU and paging overheads.  
From this figure, we can observe that a reduction in TAU τ⎝ h i j Si + h ji S j ⎠ ≤ f (S)
signaling messages increases the number of paging signaling ∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i
messages, and vise versa. FOTA aims at finding the Pareto opti- (25)
mal point ( f (S), g(S)) between TAU and paging overhead. The ⎛ ⎞
slope of P would vary according to the network characteris-   
ρ Si αk Mki ⎝ η j ⎠ ≤ g(S) (26)
tics, in terms of UE’s mobility and paging ratio, which have an
∈ i∈ k∈ϒ j∈ ∧ j=i
impact on the Pareto optimal point ( f (S), g(S)).
The values of P AG I N G best , P AG I N G wor st , T AUbest f (S)) ≤ TAUworst (27)
and T AUwor st are obtained by updating the linear programs g(S)) ≤ PAGINGworst (28)
((1). . .(6)) and ((8). . .(8)) as follows:
Theorem 3: The optimization problem ((24). . .(28)) is con-
min f (S) (14) vex and admits a unique solution.
S.t, Proof: To prove the unicity of the solution, we have to
show that the optimization problem in ((24). . .(28)) is convex.
(2)−(5) and It shall be stated that for an optimization problem to be convex,
∀i, j ∈ N ∧ i = j : the objective function should be convex, the equality con-
⎛ ⎞
straints should be linear, and the inequality constraints should
 
τ⎝ h i j Si + h ji S j ⎠ ≤ T AUbest be convex [15]. For our optimization problem ((24). . .(28)),
∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i the equality and the inequality constraints are linear. This also
(15) means that the inequality constraints are convex. Thus, to show
⎛ ⎞ that the optimization problem in ((24). . .(28)) is convex, it is
   sufficient to prove that the objective function is convex. In the
ρ Si αk Mki ⎝ η j ⎠ ≤ P AG I N G wor st optimization problem ((24). . .(28)), we have T AUwor st and
∈ i∈ k∈ϒ j∈ ∧ j=i P AG I N G wor st as constant values, whereas f (S) and g(S)
(16) are variables. For the sake of simplicity, we denote T AUwor st ,
P AG I N G wor st ≤ P AG I N G max (17) P AG I N G wor st , f (S) and g(S) by A, B, x and y, respec-
T AUbest ≤ f (S) (18) tively. Thus, the objective function becomes max log(A − x) +
log(B − y). Based on [15], the convex optimization problem
min g(S) (19) should be minimized. For this reason, the objective func-
S.t, tion is transformed, without changing the solution as follows:
min P = −(log(A − x) + log(B − y)). To prove that the opti-
(2)−(5) and
mization problem ((24). . .(28)) is convex, it is sufficient to
∀i, j ∈ N ∧ i = j : show that the Hessian matrix H of P is positive definite.
⎛ ⎞
  ∂2 P ∂2 P
∂ 2 x ∂ x∂ y
τ⎝ h i j Si + h ji S j ⎠ ≤ TAUworst ∂2 P ∂2 P
∈i ∧ ∈
/ j ∈ j ∧ ∈
/ i ∂ y∂ x ∂ 2 y
(20) Computing the different components of the Hessian matrix, we
⎛ ⎞
obtain
  
ρ Si αk Mki ⎝ η j ⎠ ≤ PAGINGbest ∂2 P ∂2 P
= =0
∈ i∈ k∈ϒ j∈ ∧ j=i ∂ x∂ y ∂ y∂ x
(21) ∂2 P 1
PAGINGbest ≤ g(S) (22) = >0
∂ x
2 (A − x)2
TAUwor st ≤ TAUmax (23) ∂2 P 1
= >0
∂2 y (B − y)2
The optimization problem shown in the linear program
((9). . .(13)) is non-convex. Using the approach proposed in It follows that the Hessian matrix is diagonal with positive
[17], the problem can be transformed to convex-optimization eigenvalues. Therefore, the Hessian matrix is positive definite,
problem without changing the solution. The key idea is to the optimization problem is thus convex and admits a unique
introduce the log function which is an increasing function. solution. 
4126 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

Fig. 8. An illustrative example network used in the analysis.

Fig. 7. The geometric interpretation of the tradeoff between TAU and paging
overhead using Nash bargaining game.

VI. A NALYTICAL M ODEL

In this section, we introduce a Markov-based model for
analyzing the three offline solutions, F-TAU, F-PAGING and
FOTA. We use the same intuition to model the three solu-
tions, since the main difference between these solutions is
the output matrix S. To ease the explanation of the pro-
posed analytical model, let us consider the network topology
depicted in Fig. 8. The possible TALs for Fig. 8 is  =
{{η1 }, {η2 }, {η3 }, {η1 , η2 }, {η1 , η3 }, {η2 , η3 }, {η1 , η2 , η3 }}. We
numerate the elements in  from 1 to 7, respectively. Now,
Fig. 9. The way to construct the embedded Markov chain used in the analysis.
we consider the following matrix S, which can be produced via
F-TAU, F-PAGING or FOTA:
⎡ ⎤ These assumptions lead us to model the system using a
0.3 0 0 0.2 0.5 0 0 Markov Chain X = {X t , t ≥ 0} on the state space  defined by
S = ⎣ 0 0.3 0 0.3 0 0 0.4 ⎦  = {(i, k), ∀k ∈  ∧ ∀i ∈ k ∧ Sik = 0}. In this model, X t =
0 0 0 0 0.1 0.4 0.5 (i, k) indicates that at instant t, TAL k is assigned to UEs when
visiting TA i. According to this description, it is obvious that we
We denote by H the expected probability of movement of a UE
are dealing with a Continuous-Time Markov Chain (CTMC).
in the network. H can be deduced from H. Each element h̄ i, j
In what follows, rather than the CTMC, we will use the corre-
in H can be computed as follows:
sponding Embedded Markov Chain (EMC), which is depicted
h i, j in Fig. 9(a). From this figure, we notice two events that lead to
∀i ∈ N, h̄ i, j = 
h i, j leave a state (i, k) in EMC. The first one is when an incoming
∀ j∈N call arrives for a UE before it leaves its current TA i, whereas
the second event is when the UE moves from its TA to another
Considering the example of Fig. 8, H is: one before the incoming call arrives. As Mi ∼ E x p(μi ) and
⎡ ⎤
0 0.1 0.9 T ∼ E x p(λ), the probability for the first and the second events
H = ⎣0.5 0 0.5⎦ to be occurred can be defined as follows:
0 1 0 • For an incoming call to arrive before the UE leaves its
λ
state i, the probability is Ci = P(T < Mi ) = .
Let M denote the expected duration of a UE in each TA. λ + μi
Formally, M is a vector with a size L. Each element Mi in M • For the UE to leave its TA i before the incoming
represents the time that the UE can spend in TA i. Mi can be call arrives, the probability is 1 − Ci = P(Mi ≤ T) =
μi
computed as follow: .
 λ + μi
Mi, j Let j1 , · · · , j N be the neighboring TAs of TA i. As depicted
∀ j∈ϒ in Fig 9(a), when a UE exists its TA i, it has to move to
∀i ∈ N, Mi =
|ϒ| its neighboring TA j according to the matrix H . Furthermore,
when it moves to TA j, it has to select its TAL k according to
In our analysis, we assume that Mi , for ∀i ∈ ϒ, are indepen-
the matrix S. The EMC depicted in Fig. 9(a) can be reduced by
and each Mi follows an exponential distribution of rate μi .
dent 
grouping its states to a new EMC as shown in Fig. 9(b). Indeed,
1
|N| αi denotes the average arrival traffic of UEs in the net-
i∈N when a UE, assigned TAL l, moves from TA i to another TA j,
work. Assuming that this traffic follows a Poisson process of two types of events can happen: (i) the first one corresponds to
rate λ, the inter arrival time between two consecutive calls is the case where TA j belongs to TAL k; (ii) the second one is
a random variable T that follows an exponential distribution of when TA j does not belong to TAL k, in this case a TA update
rate λ. process should be accomplished to assign a new TAL k to the
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4127

⎧
⎪
⎪ π1,1 = C1 π1,1 + B2,1,1 (π2,2 + π2,4 + π2,7 )
⎪
⎪
⎪
⎪ π1,4 = C1 π1,4 + B2,1,4 (π2,2 + π2,7 ) + A2,1,4 π2,4
⎪
⎪
⎪
⎪ π1,5 = C1 π1,5 + B2,1,1 (π2,2 + π2,4 + π2,7 )
⎪
⎪
⎪
⎪ π2,2 = C2 π2,2 + B1,2,2 (π1,1 + π1,4 + π1,5 )
⎪
⎪
⎪
⎪ +B3,2,2 (π3,5 + π3,6 + π3,7 )
⎪
⎪
⎪
⎪ π2,4 = C2 π2,4 + B1,2,4 (π1,1 + π1,5 ) + A1,2,4 π1,4
⎪
⎪
⎨ ×B3,2,4 (π3,5 + π3,6 + π3,7 )
π2,7 = C2 π2,7 + B1,2,7 (π1,1 + π1,4 + π1,5 )
⎪
⎪
⎪
⎪ ×B3,2,7 (π3,5 + π3,6 ) + A3,2,7 π3,7
⎪
⎪
⎪ π3,5
⎪
⎪
= C3 π3,5 + B1,3,5 (π1,1 + π1,4 ) + A1,3,5 π1,5
⎪
⎪ +B2,3,5 (π2,2 + π2,4 + π2,7 )
⎪
⎪
⎪
⎪ π3,6
⎪
⎪
= C3 π3,6 + B1,3,6 (π1,1 + π1,4 + π1,5 )
⎪
⎪ +B2,3,6 (π2,2 + π2,4 + π2,7 )
⎪
⎪
⎪
⎪ π3,7 = C3 π3,7 + B1,3,7 (π1,1 + π1,4 + π1,5 )
⎪
⎩
+B2,3,7 (π2,2 + π2,4 ) + A2,3,7 π2,7

Let N T AU and N paging denote the expected numbers of TAU

and paging generated in the network, respectively. Their values
are obtained as follows:
⎧
⎪
⎪  
Fig. 10. An illustrative example of Embedded Markov Chain. ⎪
⎨ NTAU =
⎪ πi,k Bi, j,
i-k∈ j- ∈∧ =k∧i= j
⎪
⎪  
⎪
UE. Let denote by Ai, j,k and Bi, j,k the probability of the first ⎩ Npaging =
⎪ πi,k Ci ηj
i-k∈ j∈k∧i= j
and the second events, respectively. In fact, Ai, j,k and Bi, j,k
represent the probabilities of moving from TA i to another TA j
and then selecting TAL k. VII. P ERFORMANCE E VALUATION

⎧ In this section, we evaluate the performance of the three

⎪
⎪ Ai, j,k = Pr (T > Mi )h̄ i, j S jk . offline solutions FOTA, F-TAU and F-PAGING, by solving the
⎪
⎪
⎨ ∀i, j ∈ N, ∀k ∈ , i = j and i, j ∈ k analytical model. Then, we evaluate ETAM framework through
Bi, j,k = Pr (T > Mi )h̄ i, j S jk . simulation. Throughout this section, we fix the overhead of a
⎪
⎪
⎪
⎪ ∀i, j ∈ N, ∀k ∈ , i = j, j ∈ k and i ∈
/k single TAU, τ , to be ten times the value of ρ [14]. All solutions
⎩
Ci = Pr (T < Mi ). ∀i ∈ N (i.e. FOTA, F-TAU and F-PAGING) are evaluated in terms of
the following metrics:
1) TAU overhead: the overhead of TAU messages (UP-Link)
Hence, generated by UEs when visiting new TALs.
2) Paging overhead: the overhead of paging packets sent
⎧ μi from MME to locate UEs during the call establishment.
⎪
⎪ Ai, j,k = h̄ i, j S jk .
⎪
⎪ λ + μi 3) Total overhead: the generated overhead due to both pag-
⎪
⎪
⎪
⎪ ∀i, j ∈ N, ∀k ∈ , i = j and i, j ∈ k ing and TAU. The aim of this metric is to show the
⎨ μi
Bi, j,k = h̄ i, j S jk . Pareto-efficiency between the TAU and paging overhead.
⎪
⎪ λ + μi To evaluate ETAM, we divided the deployed area into a
⎪
⎪ ∀i, j ∈ N, ∀k ∈ , i = j, j ∈ k and i ∈
/k
⎪
⎪ set of TAs, where each TA has a rectangular shape with a
⎪
⎪ λ
⎩ Ci = .∀i ∈ N specific length and width. Note that TAs may have different
λ + μi surfaces according to their length and width. The mobility of
UEs is modeled according to the Random Waypoint Mobility
Model [18] with the pause-time sets to zero. Initially, we start
Fig. 10 shows the corresponding Embedded Markov
the evaluation by placing each UE in a given TA. During the
Chain of the network topology depicted in Fig. 8.
evaluation, each UE chooses a random destination (TA) in
The balance equations of EMC can be written accord-
the deployed area and a speed that is uniformly distributed
ing to the following  formulas:  ∀( j, k) ∈  : π j,k =
between [avgSpeed − , avgSpeed + ], where avgSpeed
C j π j,k + (Bi, j,k πi, ) +
i∈N∧i= j∧Sik =0∧h̄ i, j =0 ∈∧Si =0 is the average speed of different UEs and  is the variation in
 the speed between UEs. In the evaluation, we set  to 5 km/ h.
Ai, j,k πi,k Where π j,k denotes the
i∈N∧i= j∧Sik =0∧h̄ i, j =0 The UE then travels toward the newly chosen at the selected
probability at steady state to assigning TAL k to UEs in TA i. speed. This process is repeated until the evaluation time fin-
The following equations show the balance equations of the ishes. In the evaluation, we executed the online and the offline
illustrative example shown in Fig 10: steps 10 times. The numerical results were obtained by solving
4128 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

Fig. 11. Performance of the proposed solutions as a function of λ.

Fig. 12. Performance of the proposed solutions as a function of μ.

the Markov model corresponding to network model of Fig. 10, The TAU, paging and total overhead for each solution are
while the simulation were obtained through Matlab. Indeed, the evaluated using the following formulas:
simulator tool was implemented on top of Matlab and CVX (a ⎧
package for disciplined convex optimization and geometric pro- ⎨ OverheadTAU = τ NTAU
gramming) [19]. In our evaluation, the sites (i.e., eNodeBs) are Overheadpaging = ρ Npaging
⎩
randomly deployed over the network. Without any loss of gen- TotalOverhead = τ NTAU + ρ Npaging
erality, we assume that the sites are already organized into TAs
through any solution in the literature. The grouping of different Fig. 11 and Fig. 12 show the performance of the proposed
sites into TAs is outside the scope of this paper. 1
solutions against increasing values of λ and , respectively.
μ
As shown in Eq. 6, the increase of transitions probability of
type “B” in EMC, reduces the sojourn time at each state in
A. Numerical Results
EMC. This results in a negative impact on TAU overhead and
In this subsection, we present the numerical results, focusing a positive impact on paging overhead, respectively. Whereas,
on the impact of TAU and paging overhead on each solution by the increase of transitions probability of type “C” in EMC,
varying μi and λ. μi is the exponential distribution rate of the increases the sojourn time at each state in EMC. The latter has a
sojourn times of UEs in TA i, whereas λ is the average ratio of positive impact on TAU overhead and a negative impact on pag-
calls for a UE in the network. λ can be also defined as the expo- ing overhead, respectively. The rise on λ values increases (resp.,
nential distribution rate of the inter arrival time between two decreases) the transition probability of type “C” (resp., “B”),
consecutive calls for a UE. The latter refers to the percentage whereas the rise on μ values increases the transition probabil-
of time that a UE is called. Here, the term “call” refers not only ity of type “B” and decreases the transition probability of type
to the classical voice call but also to data connection, such as “C”.
VoIP and web applications. This parameter allows us to model For this reason, as depicted in Fig. 11(a) and Fig. 11(b), the
1 increase of average arrival traffics (λ) has a negative impact on
the user activity in terms of active connections. Whereas,
μi the paging overhead and a positive impact on the TAU over-
refers to the average time spent by a UE (i.e., sojourn time) in head. Fig. 12(a) and Fig. 12(b) show that the increase of the
each TA. Increasing the values of μi corresponds to an increase 1
sojourn time ( ) in each TA has also a negative impact on
in UEs’ speeds and/or a decrease in the size of cells (micro-cell μ
for 5G network) in the real world. Two scenarios are consid- the paging overhead and a positive impact on TAU overhead.
ered: (i) we vary λ from 1 to 10 while μi is fixed to 5; (ii) we Fig. 11(a) and Fig. 12(a) show that F-PAGING exhibits better
vary μi from 1 to 10 while we fix λ to 5. performance than FOTA and F-TAU in terms of TAU overhead
BAGAA et al.: EFFICIENT TRACKING AREA MANAGEMENT FRAMEWORK FOR 5G NETWORKS 4129

1 call ratio, respectively. We clearly observe that assigning

regardless the values of λ and . This is attributable to the fact
μ TALs to UEs with prioritization (e.g., per UE’s activities -
that the key objective of F-PAGING is to minimize paging over- mobility and call ratio) has a positive impact on the per-
head without tacking into account the TAU overhead. Whereas, formance of the three solutions. From Fig. 13(c), for the
Fig. 11(b) and Fig. 12(b) show that F-TAU exhibits better per- speed of UEs equals to 70 km/ h, we observe that the selec-
formance than FOTA and F-PAGING in terms of TAU overhead tion of TALs with prioritization reduces the total overhead
1 from 13060 to 12340 (an enhancement with more than
regardless the values of λ and . This is obvious as F-TAU
μ 5.51%) for F-TAU, and for FOTA the total overhead is
is designed to optimize the TAU overhead without tacking into reduced from 14460 to 13321, which means an enhancement
account the paging overhead. exceeding 7.87%. Meanwhile from Fig. 14(c), we observe
Fig. 11(c) and Fig. 12(c) show the total overhead due to that when the call ratio equals to 90 call/ h, the selection
1
both paging and TAU for different values of λ and , respec- of TALs with prioritization reduces the total overhead of
μ FOTA from 18556 to 16336, which means an enhancement
tively. FOTA achieves a tradeoff between the two conflicting
exceeding 11.96%.
objectives, i.e; reduction of both TAU and paging overhead.
Fig. 13(b) and Fig. 13(c) show that the speed of UEs has a
We observe from these figures that: (i) F-TAU has better per-
negative impact on TAU and total overhead, respectively. This
formance in terms of total (i.e., paging and TAU) overhead
behavior is expected as highly mobile users perform frequently
when the values of λ and μ are below 5; (ii) F-PAGING
handoff between TAs and ultimately generate high TAU mes-
has better performance when the values of λ and μ exceed 5.
sages. Thus, the higher the speed of UEs is, the higher the TAU
Indeed, the performance of FOTA is always between F-TAU
1 overhead becomes. Further, we remark from Fig. 13(b) that F-
and F-PAGING, whatever the values of λ and . FOTA has TAU exhibits better performance than FOTA and F-PAGING in
μ
performance similar to that of F-TAU when values of λ and μ terms of TAU overhead regardless the speed of UEs. This is
are below 5 and similar to that of F-PAGING when values of λ attributable to the fact that the key objective of F-TAU is to
and μ exceed 5. Thus, FOTA always finds an optimal tradeoff minimize TAU overhead without tacking into account the pag-
between TAU and paging overhead by maintaing the total over- ing overhead. Whereas, Fig. 14(a) and Fig. 14(c) demonstrate
head near to the optimal value regardless the UEs’ behavior. that the call ratio has a negative impact on paging and total over-
This demonstrates that it successfully achieves the key objective head, respectively. This is also predictable as highly active UEs
of its design. (i.e., with high call ratios) cause high number of paging mes-
sages when they go in the idle mode and their locations are
searched the network. Moreover, from Fig. 14(a), we observe
B. Simulation Results that F-PAGING exhibits better performance than FOTA and F-
In this subsection, the proposed schemes are evalu- TAU in terms of paging overhead regardless the call ratio. This
ated through simulations. We used the proposed framework is intuitively due to the fact that F-PAGING is designed to opti-
(ETAM) to evaluate through simulation the three solutions mize the paging overhead without tacking into account the TAU
(F-PAGING, F-TAU and FOTA) of offline step and the two overhead.
solutions of online step. Formally, we have six possible combi- Fig. 13(c) and Fig. 14(c) illustrate the tradeoff achieved by
nations of protocols. The same trajectory logs of UEs are used FOTA between the two conflicting objectives, i.e; reduction of
to evaluate the different combinations of protocols. The infor- both TAU and paging overhead. They show the total overhead
mation of handover between different TAs is forwarded from incurred in the three solutions and that is for different values of
the online to the offline step. During the movement of a UE, a the UE speed and call ratio, respectively. We observe from these
TAU message is generated and sent to MME every-time a UE figures that: (i) F-PAGING exhibits better performance in terms
crosses a TA that does not belong to its TAL in the online step. of total (i.e., paging and TAU) overhead when the speed of UEs
The optimization problems are solved considering different val- is below 50 km/ h or when the call ratio exceeds 50 calls/ h;
ues of the average speed avgSpeed of UEs and the average ratio (ii) F-TAU exhibits better performance when the average speed
of calls of each UE in the network. The average speed of UEs of UEs exceeds 50 km/ h or when the call ratio does not exceed
shows the impact of TAUs signaling on the different optimiza- 50 calls/ h; and (iii) FOTA has performance similar to that
tion problems. In the simulation evaluation, we evaluate two of F-PAGING when the speed of UEs is below 50 km/ h or
scenarios: (i) we vary the average speed avgSpeed of UEs and when the call ratio exceeds 50 calls/ h. It is also observed that
fix the average call ratio to 50 calls/ h for each UE in the net- FOTA performs similarly to F-TAU when the call ratio does
work; (ii) we vary the average call ratio of UEs and fix the not exceed 50 calls/ h or the speed of UEs exceeds 50 km/ h.
average speed avgSpeed of UEs to 50 km/ h. In contrast to the Indeed, the performance of FOTA is always between F-TAU
analysis part, the two solutions of online part are considered and F-PAGING, depending on the UEs’ speed and their activity
in the simulation evaluation: (i) UEs pick their TAL without levels (i.e., call rate). For highly mobile UEs, FOTA performs
any prioritization; (ii) each UE picks a TAL with prioritization, similar to F-TAU (optimal) and better than F-PAGING, whilst
according to its behavior, to reduce the overhead of TAU and for highly active UEs, FOTA performs similar to F-PAGING
paging signaling. (optimal) and better than F-TAU. FOTA always finds an opti-
Fig. 13 and Fig. 14 show the resilience of FOTA, F- mal tradeoff between TAU and paging overhead by maintaing
TAU and F-PAGING against increase in UEs’ speed and the total overhead near to the optimal value regardless the UEs’
4130 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 6, JUNE 2016

Fig. 13. Performance of the proposed solutions as a function of speed of UEs.

Fig. 14. Performance of the proposed solutions as a function of the call ratio.

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[15] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: He is an IEEE Communications Society (ComSoc) Distinguished Lecturer. He
Cambridge Univ. Press, 2004. is a Member of the IEEE Communications Society Standardization Program
[16] J. Nash, “The bargaining problem,” Econometrica, vol. 18, no. 2, pp. 155– Development Board. In an attempt to bridge the gap between academia and
162, Apr. 1950. industry, he founded the IEEE Workshop on Telecommunications Standards:
[17] Y. Zhao, S. Wang, S. Xu, X. Wang, X. Gao, and C. Qiao, “Load balance vs From Research to Standards, a successful event that was recognized with
energy efficiency in traffic engineering: A game theoretical perspective,” the Best Workshop Award by the IEEE Communication Society (ComSoC).
in Proc. IEEE INFOCOM, Apr. 2013, pp. 530–534. Based on the success of this workshop, he has also founded and has been
[18] T. Camp, J. Boleng, and V. Davies, “A survey of mobility models for ad the Steering Committee Chair of the IEEE Conference on Standards for
hoc network research,” Wireless Commun. Mobile Comput., vol. 2, no. 5, Communications and Networking. He is the General Chair of the 2019
pp. 483–502, 2002. edition of the IEEE Wireless Communications and Networking Conference
[19] M. Grant and S. Boyd, “Graph implementations for nonsmooth convex (WCNC’19) to be held in Marrakech, Morocco. He is/was on the Editorial
programs,” in Recent Advances in Learning and Control, V. Blondel, Board of the IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, the
S. Boyd, and H. Kimura, Eds. Berlin, Germany: Springer-Verlag, 2008, IEEE Wireless Communications Magazine, the IEEE JOURNAL ON INTERNET
pp. 95–110. OF T HINGS , the IEEE T RANSACTIONS ON V EHICULAR T ECHNOLOGY , the
IEEE COMMUNICATIONS SURVEYS & TUTORIALS, and a number of Wiley
journals. He is serving as the Chair of the Wireless Communications Technical
Miloud Bagaa received the Engineer’s, Master’s, and Committee, the largest in IEEE ComSoC. He also served as the Vice Chair
Ph.D. degrees from the University of Science and of the Satellite and Space Communications Technical Committee of the IEEE
Technology Houari Boumediene (USTHB), Algiers, ComSoc (2006–2010). He has been on the technical program committee of dif-
Algeria, in 2005, 2008, and 2014, respectively. ferent IEEE conferences, including Globecom, ICC, and WCNC, and chaired
From 2009 to 2015, he was a Researcher with some of their symposia. He was the recipient of the 2009 IEEE ComSoc
the Research Center on Scientific and Technical Asia-Pacific Best Young Researcher Award (June 2009), the 2008 TELECOM
Information (CERIST), Algiers, where he was a System Technology Award from the Telecommunications Advancement
Member of the Wireless Sensor Networks Team, Foundation (March 2008), the 2007 Funai Foundation Science Promotion
DTISI Division. From 2015 to 2016, he was granted a Award (April 2007), the 2006 IEEE Computer Society Japan Chapter Young
postdoctoral fellowship from the European Research Author Award (December 2006), the Niwa Yasujirou Memorial Award
Consortium for Informatics and Mathematics, and (February 2005), and the Young Researcher’s Encouragement Award from
worked with the Norwegian University of Science and Technology, Trondheim, the Japan chapter of the IEEE Vehicular Technology Society (VTS) (October
Norway. Currently, he is Senior Researcher with the Communications and 2003). Some of his research works have been also awarded Best Paper Awards
Networking Department, Aalto University, Espoo, Finland. His research inter- at prestigious conferences.
ests include wireless sensor network, Internet of Things, 5G wireless commu-
nication, security, and networking modeling. Adlen Ksentini (SM’14) received the M.Sc. degree
in telecommunication and multimedia networking
Tarik Taleb (S’05–M’05–SM’10) received the B.E. from the University of Versailles Saint-Quentin-en-
degree in information engineering (with distinction), Yvelines, Versailles, France, and the Ph.D. degree
the M.Sc. and Ph.D. degrees in information sciences in computer science from the University of Cergy-
from GSIS, Tohoku University, Sendai, Japan, in Pontoise, Cergy-Pontoise, France, in 2005. From
2001, 2003, and 2005, respectively. He is currently a 2006 to 2015, he worked with the University of
Professor with the School of Electrical Engineering, Rennes 1, Rennes, France, as an Associate Professor.
Aalto University, Espoo, Finland. Prior to his cur- During this period, he was a Member of the Dionysos
rent academic position, he was a Senior Researcher Team with INRIA, Rennes, France. Recently,
and 3GPP Standards Expert with NEC Europe Ltd., he joined the Mobile and Wireless Networking
Heidelberg, Germany. He was then leading the NEC Department, EURECOM Institute, as an Associate Professor. He has been
Europe Labs Team working on R&D projects on car- involved in several national and European projects on QoS and QoE support in
rier cloud platforms, an important vision of 5G systems. He was also serving future wireless, network virtualization, cloud networking, and mobile networks.
as Technical Leader of the main work package, Mobile Core Network Cloud, He has coauthored over 100 technical journal and international conference
in EU FP7 Mobile Cloud Networking project, coordinating among 9 part- papers. He has been acting as the TPC Symposium Chair for the IEEE ICC
ners including NEC, France Telecom, British Telecom, Telecom Italia, and 2016 and 2017. He was a Guest Editor of the IEEE Wireless Communications
Portugal Telecom. Before joining NEC and until March 2009, he worked as Magazine the IEEE Communications Magazine, and two ComSoc MMTC let-
an Assistant Professor with the Graduate School of Information Sciences, ters. He has been on the Technical Program Committee of major IEEE ComSoc,
Tohoku University, in a laboratory fully funded by KDDI, the second largest ICC/Globecom, ICME, WCNC, and PIMRC conferences. He was the recipient
network operator in Japan. From October 2005 until March 2006, he worked of the Best Paper Award from the IEEE ICC 2012 and ACM MSWiM 2005.