Int. J. Communications, Network and System Sciences, 2012, 5, 815-824 Published Online December 2012 (
Modeling Components and Services of LTE Mobile
Communications System
Ishtiaq Ahmed Choudhry1, Nazir Ahmad Zafar2
1Department of Communication and Networking, King Faisal University, Al-Ahsa, KSA
2Department of Computer Science, King Faisal University, Al-Ahsa, KSA
Received October 8, 2012; revised November 10, 2012; accepted November 18, 2012
The latest wireless broadband network standard is LTE (Long Term Evolution) which is developed by 3GPP (3rd Gen-
eration Partnership Project). It will enable mobile devices such as smart phones, tablets and laptops to access Internet at
a very high speed along with lots of multimedia services. There are many issues that are yet to be solved due to dynamic
complex nature of wireless systems, multimedia software applications and software requirements. Poor service quality,
service disconnections due to mobility, seamless handover, handover interruption time and downward compatibility to
other Radio Access Networks (RAN) are some of the key issues for the current LTE systems that are addressed very
recently in the scientific literature. Formal method is one of the promising software engineering techniques that assure
quality and perfection in software system models. Formal methods use mathematical language to explicitly specify sys-
tem specifications and requirements that serve as initial grounds for further development and implementation. It effi-
ciently handles all component connections and resource management parameters using discrete structures. Z Schema
language is used to model static aspects of LTE communications system. All the schemas are being verified using
Z/Eves toolset. The aim is to provide sound mathematical foundation for system validation and verification that eventu-
ally results in a more reliable, scalable and complete software system.
Keywords: LTE Communications System; Formal Methods; Emerging Software; Mathematical Language; Z Notation
1. Introduction
Long Term Evolution (LTE), a wireless broadband tech-
nology, is designed to support roaming Internet use and
access via mobiles phones and other such handset de-
vices. LTE is also referred as fourth generation (4G)
technology and provides significant improvements over
previous cellular communication networks. LTE is the
latest wireless standard for International Mobile Tele-
communication (IMT) system which has been deployed
in many countries and few others are in pipeline for its
deployment. LTE can operate in different bandwidths
ranging from 1.4 MHz to 20 MHz and will provide a data
rate of 100 Mbps to 1 Gbps depending upon the mobility
of the user equipment. LTE—Advanced Release 10 is set
to provide higher bit rate (DL 3Gbps, UL 1.5 Gbps). The
IMT system is a complex one due to its different Radio
Access Networks (RAN) and protocols. International
Mobile Telecommunication systems allow users to ac-
cess services and information at any time and at any
place. However, these telecommunication systems pro-
vide mobility services with different requirements, re-
sources and constraints. For example, poor quality of
service, service interruptions due to mobility, seamless
handover, interruption time at handovers and downward
compatibility to other Radio Access Networks are some
of the common key issues that are addressed in the scien-
tific literature [1-7]. There are many other issues which
need to be addressed due to complexity and dynamic
nature of wireless systems, new information technology
infrastructure, multimedia applications and software re-
LTE offers many real time multimedia applications by
integrating with the existing technologies. Although there
exists a lot of research in this area but still there is an
uncertainty and sufficient improvement are required in it
due to complexity and flexibility of the system. The
telecom industry is still discovering the system, network
approaches and optimization techniques with the support
and cooperation of academics and researches around the
globe. Because LTE will integrate many heterogeneous
networks and services, the seamless implementation for a
complete development of LTE communications system is
an open research problem.
Formal methods are mathematical techniques used to
model software systems. It enables us to write system
specification in such a way that it helps us understanding
opyright © 2012 SciRes. IJCNS
states of the system and its properties in a rigorous way.
Formal methods are effective abstraction technique for
managing complexity of large scale, dynamic and dis-
tributed systems. By use of formal methods, systems
requirements, specification and limitations are addressed
at early stages of systems and software development. In
this way, a thorough development processes leads to a
complete, consistent and robust model. The most impor-
tant benefit of using formal methods is that we can move
gradually from informal requirements to a detailed model
maintaining the system properties and constraints.
In the existing work [8], Milner extended the system
from Calculus of Communication System to pie-calculus
developing a dynamic communication model which can
be used to describe the mobility issues. In this work, mo-
bility is assumed as movement of links between the con-
nected components. Acharya et al., [9] have used formal
techniques to overcome the consistency issue at various
phases of development process in wireless mobile com-
munication networks. Formal models are applied in [10],
[11] using Z and object Z, however, few discrepancies
are identified and the systems are not addressed com-
pletely. Duke et al., [12] have presented several case
studies to illustrate application of formal methods. One
of his study regarding mobile phone system which keeps
track of several states of mobiles with limited number of
operations, is an interesting example. The same case
study is extended by Battaz in [13] to address the mobil-
ity issues explicitly using Z specification language. To
further extend the same system, Battaz has described
handover procedure among two objects in more details.
The requirements capturing and analysis of LTE system
is presented in [14]. In our paper, LTE is developed by
the 3G Partnership Group (3GPP) [15] and its specifica-
tions is laid out mainly focusing on model abstraction.
In this paper, formal specification of static structures
of the LTE system is presented using Z notation. First of
all, fundamental definitions used in the model are pre-
sented. Then formal specification of few important ser-
vices, phone book, messages and call record is described.
In the next, formal description of user equipment is given
based on the above definitions. Further, formal descrip-
tion of core components, namely, evolved Node B, Home
Subscriber Server, Serving Gateway and Mobility Man-
agement Entity is described. Finally, LTE system is pre-
sented after composition of the above structures. The
relationships among the components are defined for well-
definedness. An integration of the components is de-
scribed in terms of properties. The description of the
formal specification is provided by Z notation. The speci-
fication of the system is analyzed using Z/Eves toolset.
Rest of the paper is organized as: In Section 2, basic
model of the LTE communications system is introduced.
Formal model using Z notation is provided in Section 3.
Model analysis is presented in Section 4. Finally, conclu-
sions and future work are addressed in Section 5.
2. Long Term Evolution System
The previous cellular systems were unable to provide
connectivity to packet switched networks and hence were
not able to share services. The LTE has been designed to
provide seamless Internet Protocol (IP) connectivity be-
tween user equipment (UE) and the packet data network
(PDN), without any disruption to the applications run by
end user during mobility. While the term “LTE” encom-
passes the evolution of the Universal Mobile Telecom-
munications System (UMTS) radio access through the
Evolved UTRAN (E-UTRAN), it is accompanied by an
evolution of the non-radio aspects under the term “Sys-
tem Architecture Evolution” (SAE), which includes the
Evolved Packet Core (EPC) network. Together LTE and
SAE comprise the Evolved Packet System (EPS) [16].
The LTE architecture is composed of separate compo-
nents that includes UE (User Equipment), eNB (evolved
Node B—more commonly known as base station in
UMTS), SGW (Serving Gateway), MME (Mobility Ma-
nagement Entity), HSS (Home Subscriber Server), and
PDN-GW (Packet Data Network Gateway). We have
dedicated this section to define LTE components. After
defining the system and its functional components formal
description of the system will be provided.
2.1. Evolved Radio Access Network
The evolved RAN for LTE consists of a single node, i.e.,
the eNodeB (eNB) that interfaces with the user equip-
ment (UE). The architecture of all eNBs is called a flat
architecture. The eNB is responsible for all radio-related
functions. It offers Radio Resource Control (RRC) func-
tionality corresponding to the control plane. It performs
many functions including Radio Resource Management
(RRM), Admission Control (AC), radio mobility control,
scheduling and dynamic allocation of resources to UEs in
both uplink and downlink. Another function performed
by eNBs is header compression to ensure efficient use of
radio interface by compressing the IP packet headers that
could otherwise represent a significant overhead, espe-
cially for small packets such as VoIP. When UE and eNB
is connected, then all data sent over the radio interface is
On the network side, all of these functions reside in the
eNBs, each of which can be responsible for managing
multiple cells. Unlike some of the previous second- and
third-generation technologies, LTE integrates the radio
controller function into the eNB. This allows tight inter-
action between the different protocol layers of the radio
access network (RAN), thus reducing latency and im-
proving efficiency. Such distributed control eliminates
Copyright © 2012 SciRes. IJCNS
the need for a high-availability, processing-intensive
controller, which in turn has the potential to reduce costs
and avoid “single points of failure.” Furthermore, as LTE
does not support soft handover there is no need for a
centralized data-combining function in the network [16].
2.2. Serving Gateway
All user data packets (IP packets) are transferred through
Serving Gateway, while also acting as the mobility an-
chor for the user plane during inter-eNB handovers. It
also serves as the mobility anchor for interworking with
other 3GPP technologies such as general packet radio
service (GPRS) and UMTS. For idle state of user equip-
ment, the serving gateway terminates the download link
data path and triggers paging when the data arrives for
the UE. It manages and stores UE contexts, e.g. parame-
ters of the IP bearer service, and network internal routing
information. It performs replication of the user traffic in
case of lawful interception. In addition, SGW performs
some administrative functions in the visited network such
as collecting information for charging (for example, the
volume of data sent to or received from user).
2.3. Mobility Management Entity
The MME is the key control-node for the LTE access-
network. MME is the control node that processes the
signaling between the UE and the Core Network (CN).
The protocols running between the UE and the CN are
known as the Non Access Stratum (NAS) protocols. It is
also responsible for idle mode UE tracking and paging
procedure including retransmissions. It is involved in the
carrier activation/deactivation process and is also respon-
sible for choosing the SGW for a UE at the initial attach
and at time of intra-LTE handover involving CN node
relocation. It is responsible for authenticating the user
(by interacting with the HSS). The Non-Access Stratum
(NAS) signaling terminates at the MME and it is also
responsible for generation and allocation of temporary
identities to UEs. It checks the authorization of the UE to
camp on the service termination point in the network for
ciphering/integrity protection for NAS signaling and
handles the security key management. Lawful intercep-
tion of signaling is also supported by the MME. The
MME also provides the control plane function for mobil-
ity between LTE and 2G/3G access networks with the S3
interface terminating at the MME from the SGSN. The
MME also terminates the S6a interface towards the home
HSS for roaming UEs.
2.4. Home Subscriber Server
The Home Subscribe Server is the main Internet Multi-
media Server IMS database which also acts as database
in evolved packet core EPC networks. The HSS is a su-
per HLR that combined legacy HLR and AUC (Authen-
tication Center) functions together for circuit switched
(CS) and packet switched (PS) domains. The AUC gen-
erates the vectors for authentication and security keys. In
the IMS architecture, the HSS connects to application
servers as well as the Call Session Control Function
(CSCF) using the DIAMETER protocol. HSS is the
master repository for subscriber profiles, device profiles,
and state information. As a mandatory control plane func-
tion in the LTE Evolved Packet Core (EPC), the HSS
manages subscriber identities, service profiles, authen-
tication, authorization, and quality of service (QoS) for
LTE and IP Multimedia Subsystem (IMS) networks. An
architecture of the LTE System, its components and rela-
tionship among the components is presented in the Fig-
ure 1 (reproduced from
2.5. Packet Data Network Gateway
Another very important component is the PDN gateway.
The PDN Gateway is responsible for IP address alloca-
tion for the UE, as well as QoS enforcement and flow-
based charging according to rules from the PCRF (Policy
Control and Charging Rules Function). It is responsible
for the filtering of downlink user IP packets into the
different QoS-based carriers. This is performed based on
Traffic Flow Templates (TFTs). The P-GW performs
QoS enforcement for guaranteed bit rate (GBR) carriers.
It also serves as the mobility anchor for interworking
with non-3GPP technologies such as CDMA2000 and
WiMAX® networks. This component is partially model-
ed in this paper, however, a more completed function
will be modeled later.
From the above model it is clear that this system is
very much complex in terms of hardware equipment,
communication protocols, and multimedia applications.
3. Formal Specification
Formal specification of the LTE system is provided in
this section. Z is used for the formal specification and
Z/Eves tool is used for the model analysis. Schema is a
powerful structure in Z used for variables definitions,
components encapsulation and defining properties in
terms of invariants. In the formal model, first of all, fun-
damental definitions used in the LTE system are pre-
sented. In these definitions, phone book, messages and
call record facilities are considered for services descrip-
tion. Then major components namely user equipment,
eNB, HSS and SGW are defined. In the next section,
formal definition of an important component, MME is
described. Finally, LTE communications system is pre-
sented based on composition of the above structures.
Copyright © 2012 SciRes. IJCNS
Copyright © 2012 SciRes. IJCNS
Figure 1. An architecture of LTE system.
3.1. Services main of function mobiles and person in range of mobiles,
it holds that type of mobile is MOBILE; 2) For each
equipment identifier in domain of function officials and
person in range of officials, the type of mobile is OFFI-
CIAL; 3) For each equipment identifier in domain of
function personals and person in range of the personals,
the type of mobile is described as PERSONAL.
Formal definition of phone book is described below by
using schema PhoneBook which consists of four compo-
nents, namely, mobiles, officials, personal and type. The
first three variables are defined as functions of type
equipment identifier to Person. The schema person con-
tains two variables, that is, name and address. The last
one variable in definition of PhoneBook is used to repre-
sent type of the phone number, i.e., home, official or
mobile. The schema consists of two parts in addition to
the name of the schema written in the first horizontal line.
Definitions of variables used are given in first part of the
schema and invariants are defined in the second part.
[String, EquipmentId]; PType ::=MOBILE | OFFICE | HOME
»_Person ________________________
Æname: seq String
Æaddress: seq String
Formal definition of messages s described below by
using the schema Messages. The schema consists of four
components, inbox, sent, outbox and type. The variables
inbox, sent and outbox are defined as functions of type
equipment identifier to Message. The schema Message
consists of three variables, namely, equipment identifier,
data stored and sending or receiving time. The data sent
or received is defined as a sequence of strings. The
sending or receiving times are denoted by Time.
Æmobiles, officials, personals: EquipmentId f Person
Ætype: PType
ÆAeid: EquipmentI d; person: Person|eid e dom mobiles
Æperson e ran mobiles
Æ • (eid, person) e mobiles type = MOBILE
ÆAeid: EquipmentId; person: Person
Æ | eid e dom officials person e ran officials
Æ • (eid, person) e officials type = OFFICE
ÆAeid: EquipmentId; person: Person
Æ | eid e dom personals person e ran personals
Æ • (eid, person) e personals type = HOME
Æueid: EquipmentId
Ædata: seq String
Ætime: Time
Invariants: 1) For each equipment identifier in do-
»_Messages _______________________
Æinbox, sent, outbox: EquipmentId f Message; type: MType
ÆAeid: EquipmentId; message: Message | eid e dom inbox
Æmessage e ran inbox
Æ • (eid, message) e inbox type = RECEIVED
ÆAeid: EquipmentId; message: Message | eid e dom sent
Æmessage e ran sent
Æ • (eid, message) e sent type = DELIVERED
ÆAeid: EquipmentId; message: Message | eid e dom outbox
Æmessage e ran outbox
Æ • (eid, message) e outbox type = FAILED v type =
Invariants: 1) For each equipment identifier in
domain of function inbox and message in range of the
inbox, it holds that status of message is RECEIVED; 2)
For each equipment identifier in domain of function sent
and message in range of the sent, the status of message is
DELIVERED; 3) For each equipment identifier in do-
main of function outbox and message in range of outbox
the status of the message is represented as DEFFERED.
Formal specification of calls record is described by the
schema CallsRecord which consists of outgoing, incom-
ing, missed and type. The first three variables are de-
scribed by the functions of type equipment identifier to
Call. The schema Call consists of two variables, that is,
equipment identifier and sending or receiving time.
Æoutgoing: EquipmentId f Call
Æincoming: EquipmentId f Call
Æmissed: EquipmentId f Call
Ætype: CType
ÆAeid: EquipmentId; call: Call | eid e dom outgoing call e
Æran outgoing
Æ • (eid, call) e outgoing type = OUTGOING
ÆAeid: EquipmentId; call: Call | eid e dom incoming call e
Æran incoming
Æ • (eid, call) e incoming type = INCOMING
ÆAeid: EquipmentId; call: Call | eid e dom missed call e
Æran missed • (eid, call) e missed type = MISSED
»_Call _________________________
Æueid: EquipmentId
Ætime: Time
Invariants: 1) For each equipment identifier in do-
main and call in range of the outgoing function, it is sat-
isfied that status of the call is OUTGOING; 2) For each
equipment identifier in domain and call in range of the
incoming, it is satisfied that status of the call is IN-
COMING; 3) For each equipment identifier in domain
and call in range of the missed function, the property
holds that status of the call is MISSED.
3.2. LTE Components
The formal description of User equipment, eNB, HSS
and SGW are presented here. User equipment is a device
used directly by an end-user to communicate with other
connected users. It can be a telephone, laptop or any
other such device connected to the base station. The user
equipment is defined by the schema UserEquipment
given below. The equipment identifier is denoted by the
EquipmentId. The equipment has three states that is ac-
tive, idle or detached. The Phone Book, Messages and
Call Record schemas are called to define the user equip-
ment. The equipment has information about its position
which is defined in terms of latitude and longitude. Each
variable has two parts that is an integral and fractional.
The user equipment contains information about its state,
i.e., active, idle or detached. Further, it contains sim
identifier and key. The equipment has other two variables
called control and voice frequencies. The value of fre-
quency will be either allocated or null. In predicate part
of the schema, it is described that control frequency has
allocated status if and only if the equipment status is ac-
tive or idle. The control frequency is null if and only if
the equipment is detached.
 Limit: N
»_Position ________________________
Ænorth, nfrac: N; west, wfrac: N
Æ0 ¯ north north ¯ 180 0 ¯ west west ¯ 360
Æ0 ¯ nfrac nfrac ¯ Limit 0 ¯ wfrac wfrac ¯ Limit
[SimKey, SimId, Frequency]
Æueid: EquipmentId; PhoneBook
Æmessages: Messages; calls: CallsRecord
Æposition: Position; uestate: UEState
Æsimid: SimId; simkey: SimKey
Æcfstatus, vfstatus: FStatus; cfreq, vfreq: Frequency
Æcfstatus = ALLOCATED ¤ uestate e {IDLE, ACTIVE}
Æcfstatus = NULL ¤ uestate = DETACHED
An evolved Node B is the radio access part of LTE
which contains at least one radio transmitter, receiver and
control section. The receiver contain resource manage-
Copyright © 2012 SciRes. IJCNS
ment and logic control functions. The evolved Node B is
denoted by the schema eNB given below. The schema
consists of seven components. The first one node is iden-
tifier denoted by NodeId. The next three components are
frequencies, namely, total set of frequencies, control and
voice frequencies. The next component is a set of
equipment connected to the evolved Node B. Finally,
two functions for control frequencies and voice frequen-
cies are described from a set of frequency to equipment
identifier. The node identifier is of type Node.
Æenb: Node; uequipments: F UserEquipment
Æfrequencies; cfrequencies ;vfrequencies: F Frequency
Æcalloc; valloc: Frequency f EquipmentId
Æcfrequencies Î 0 vfrequencies Î 0
Æcfrequencies I vfrequencies = 0
Æfrequencies = cfrequencies U vfrequencies
ÆAue: UserEquipment | uequipments Î 0
Æ ue e uequipments ue . cfreq e cfrequencies ue .
Ævfreq e vfrequencies
ÆAf1, f2: Frequency; ei: EquipmentId | (f1, ei) e calloc (f2,
Æei) e calloc f1 = f2
ÆAf1, f2: Frequency; ei: EquipmentId | (f1, ei) e valloc (f2,
Æei) e valloc f1 = f2
ÆAfr: Frequency | fr e dom calloc fr e cfrequencies
ÆAfr: Frequency | fr e dom valloc fr e vfrequencies
ÆAue1: EquipmentId | ue1 e ran calloc
Æ • Eue2: UserEquipment | ue2 e uequipments ue1 = ue2
Æ. ueid
ÆAue1: EquipmentId | ue1 e ran calloc
Æ • Eue2: UserEquipment | ue2 e uequipments ue1 = ue2
Æ. ueid
Invariants: 1) Control and voice frequencies are non-
empty; 2) Intersection of control and voice frequencies is
an empty set; 3) The union of control and voice frequen-
cies is equal to set of total frequencies; 4) The control
and voice frequencies of each equipment connected to
evolved node are in the set of total frequencies in the
node; 5) The control frequency is a one to one function; 6)
The voice frequency is a one to one function that is a
voice frequency can be assigned to only one equipment;
7) The control frequency in the domain of frequency al-
location function to each user equipment, is in the set of
control frequencies of evolved node; 8) The voice fre-
quency in the domain of frequency allocation function to
each user equipment, is in the set of voice frequencies of
evolved node; 9) The range of control frequency is subset
of set of equipments of evolved node; 10) The range of
voice frequency function is sub-set of set of equipments
of evolved node.
The HSS manages subscription related information
and supports the network control layer. It consists of
various components some of the important information is
given below in schema HSS. The first one component is
its identifier. The second one is access having value
granted or not denied. The next three components are for
storing record about sim identifiers, sim keys and equip-
ment identifiers. The relationship between sim identifiers
with keys and equipment are also defined. Home location
and visitor location registers are represented by hlrs and
vlrs respectively which are power set of location register
(LR). Three types of networks, GERAN, UTRAN and
2G/3G, are considered in the schema. The sim is de-
scribed by the schema sim which consists of sim key,
sim’s owner, balance to call, render and other informa-
tion. The last one component is added because this sche-
ma can be extended in our future work to have more in-
formation needed for the definition of sim.
Æsimkey: SimKey; owner: seq String
Æbalance: N; render: Render; otherinfo: seq String
[LR, HId]; Access ::= GRANTED | DENIED
RAN ::= GERAN | UTRAN | G23 ; BalLimit: N
Æhid: Hid ; access: Access; sims: SimId f Sim
Æsrecord: SimId f EquipmentId; simkeys: F SimKey
Æhlrs, vlrs: F LR ; networktype: RAN
ÆAsid: SimId; sim: Sim | sid e dom sims sim e ran sims
Æ(sid, sim) e sims
Æ sim . balance ˘ BalLimit access = GRANTED
ÆAsid: SimId; sim: Sim | sid e dom sims sim e ran sims
Æ(sid, sim) e sims sim . balance < BalLimit access =
ÆAsid: SimId | sid e dom sims sid e dom srecord
ÆAsid: SimId | sid e dom srecord sid e dom sims
ÆAsid: SimId; sim: Sim | sid e dom sims sim e ran sims
Æ(sid, sim) e sims sim . simkey e simkeys
ÆAlr: LR lr e hlrs lr vlrs lr e vlrs lr hlrs
Invariants: 1) Each sim identifier in the HSS is in the
domain of sims function. If the sim balance is more than
the minimum limit than permission for call is guaranteed;
2) If the sim balance is less than the minimum required
limit then permission for call is not guaranteed; 3) Each
sim in the domain of sim function is in the domain of
sim-equipment function; 4) Each sim in the domain of
sim-equipment function is in the domain of sims function;
Copyright © 2012 SciRes. IJCNS
5) Each sim key in the sim record function is in the HSS;
6) The intersection of sets, home location and visitors
location registers, is empty.
The primary functionality of Serving Gateway (SGW)
is to manage user mobility and act as a segregation point
between the radio access network and the other core
networks. The SGW maintains data movement between
evolved nodes and the PDN Gateway. In a functional
point of view, SGW is a termination point of the packet
data network interface. Considering functionality of SGW,
formal specification of SGW is given below by using the
schema SGW. The schema consists of four components,
namely, identifier, internet protocol, data and networks.
The data is defined as a basic set type. The radio access
network types are same as defined above in the definition
of HSS schema. In the predicate part of the schema, it is
stated that the data packet is sent towards a network
based on the request of sender.
[Data]; IP ::= IP 1 | IP2 | IP3
Æsgw: seq N; iprotocol: IP; data: Data; network : RAN
Æiprotocol = IP1 network = GERAN
Æiprotocol = IP2 network = UTRAN
Æiprotocol = IP3 network = G23
The Mobility Management Entity (MME) is the key
control node for the Long Term Evolution network. The
primary functionality of MME is monitoring tracking and
paging procedure for idle mode user equipment. It is in-
volved in activation and deactivation processes and is
responsible for choosing the SGW for user equipment at
the initial process. It is responsible for security issues
including authentication of the user by interacting with
the HSS. It verifies authorization of user equipment to
site on the service provider and enforces the equipment
roaming restrictions. Furthermore, the MME provides the
control function for mobility between Long Term Evolu-
tion and other access networks.
Formal specification of Mobility Management Entity
is given below using the schema MME. The schema con-
sists of five components, namely, evolved nodes, home
subscriber servers, serving gateways, verification and
request. The formal definitions of the components are
already given in terms of schemas. In MME schema,
evolved nodes, home subscriber servers and serving gate-
ways are assumed as power sets. Similar to above, all
sets are assumed as finite collections of the components.
Request has two values either success or failure. Simi-
larly verification is either done or rejected.
Verification ::= VERIFIED | REJECTED
Æenbs: F eNB; hsss: F HSS; sgws: F SGW
Æverification: Verification; request: Request
ÆAenb: eNB | enb e enbs
Æ • Aue: UserEquipment | ue e enb . uequipments
Æ • Ehss: HSS | hss e hsss
Æ • Esid: SimId; uei: EquipmentId | (sid, uei) e hss . srecord
Æ ue . ueid = uei ue . simid = sid
ÆAenb: eNB | enb e enbs
Æ • Aue: UserEquipment | ue e enb . uequipments
Æ • Ehss: HSS | hss e hsss
Æ • Esk: SimKey | sk e hss . simkeys ue . simkey = sk
ÆAenb: eNB | enb e enbs
Æ • Aue: UserEquipment | ue e enb . uequipments
Æ verification = VERIFIED request = SUCCESS
ÆAenb: eNB | enb e enbs
Æ • Aue: UserEquipment | ue e enb . uequipments
Æ verification = REJECTED request = FAILURE
Invariants: 1) For each evolved node and for each
user equipment in the node there exists home subscriber
server which contains the sim identifier of the equipment;
2) For an evolved node and for each equipment in the
node there exists home subscriber server containing sim
identifier of the equipment; 3) For each user equipment,
if identity is verified, it is successful; 4) For an equip-
ment, if the identity is not verified then it is a failure.
Finally, formal specification of LTE is given below
using LTE schema which consists of five components,
namely, set of evolved nodes, set of home subscriber
servers, set of serving gateways, set of mobile manage-
ment entities and network. The components definitions
are given in first part and invariants are defined in the
second part of the schema.
ÆsGWS: F SGW ; mMES: F MME ; networks: RAN
ÆAmm: MME | mm e mMES • Aenb: eNB | enb e mm . enbs
Æ• enb e eNBS
ÆAmm: MME | mm e mMES • Ahs: HSS | hs e mm . hsss
Æ• hs e hSSS
ÆAmm: MME | mm e mMES • Asg: SGW | sg e mm . sgws
Æ• sg e sGWS
Invariants: 1) For each mobile management entity
and for every evolved node, the node is in the LTE sys-
tem; 2) For each mobile management entity and for every
Copyright © 2012 SciRes. IJCNS
Copyright © 2012 SciRes. IJCNS
There exist various tools for analyzing Z specification,
Z/Eves is one of the powerful tools used in this research
for analyzing the formal specification of long term evo-
lution communications system. A snapshot of the part of
the specification analysis is provided in Figure 2. First
column on the left of the figure shows status of the syn-
tax checking and the second column represents the proof
correctness of the specification. The symbol “Y” stands
that specification is correct syntactically and proof is also
correct. The symbol “N” is used that errors exist which
needs to be fixed by further analysis. Formal specifica-
tion of our systems is fully analyzed to be correct and
hence “N” does not appear in the figure. All the schemas
are checked to be correct in syntax and has a correct
home subscriber server, the server is in the LTE system;
3) For each mobile management entity and for every
serving gateway, the gateway is in the LTE system.
4. Model Analysis
Formal analysis of the specification is provided here in
this section. Since there does not exist any computer tool
which may assure about complete correctness of a formal
model, therefore, even the specification is well-written, it
may contain potential errors. Hence, an art of writing
specification does not provide guarantee about correct-
ness of a system. However, if the specification is analyz-
ed and validated with the rigorous computer tools, it
certainly improves confidence by identifying errors if
exists. Summary of the results is presented in Table 1 given
Figure 2. Model analysis using Z/Eves tool.
Table 1. Results of model analysis.
Schema Name Syntax Type Check Domain Check Reduction Proof
Person Y Y NA Y
PhoneBook Y Y NA Y
Message Y Y NA Y
Messages Y Y NA Y
Call Y Y NA Y
CallsRecord Y Y NA Y
Position Y Y NA Y
UserEquipment Y Y NA Y
Sim Y Y NA Y
below. Name of the schema is given in first column of
the table. The symbol “Y” in second column indicates
that all schemas are proved automatically. Similarly,
domain checking, reduction and proof by reduction are
represented in columns 3, 4 & 5 respectively. The “NA”
in column four is used that reduction was not required on
the predicates and, hence, the formal specification is well-
written and meaningful.
5. Conclusions and Future Work
Modeling of complex systems has become a challenging
task due to specifications and integration of their com-
ponents. The Long Term Evolution (LTE) is a complex
mobile communications system providing real time mul-
timedia applications. Literature review reveals that some
research work on addressing various issues of this system
has been considered, however, LTE needs much more
research contributions for its modeling, specifications,
optimization and maintenance due to its complexity and
distributed nature [17,18]. The telecom industry with the
support of academia is discovering networks modeling
and integration techniques for the systems and their im-
plementation. Since LTE will integrate many heteroge-
neous networks and services, the seamless implementa-
tion for a complete development of LTE communications
system is an open research problem [19-22]. In this paper,
formal methods [23] in terms of Z notation are applied
for modeling, specification and analysis of the LTE sys-
tem. It is observed that the use of Z notation was effect-
tive to model and verify properties of the system because
of its abstraction and expressive power. Further, the Z
notation has a rigorous computer tool support addressing
complexity of the system. At first, formal specification of
services including messages and call record was provided.
Then description of LTE components was presented. In
the next section, formal description of the LTE system
was described after composition of the schemas describ-
ing services and LTE components. Formal specification
is analyzed using Z/Eves toolset. Based on our experi-
ence, it is observed that Z notation was useful at re-
quirements analysis for further modeling and develop-
ment of the system. The Z/Eves toolset facilitated and
boosted our confidence for a complete and consistent des-
cription of the LTE model.
The preliminary results of this research were presented
in [24] where LTE system was described at higher level
of abstraction. In this paper, a detailed model is presented
for addressing various issues including services, compo-
nents and interaction protocols at software level of the
LTE system. The other challenges, for example, quality
of service, security issues and optimization techniques in
this heterogeneous environment will be addressed in our
future work.
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