The Formal Design Model of an Automatic Teller Machine _ATM_ - DOC

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					  The Formal Design Model of an Automatic Teller Machine
                         (ATM)
                                   Yingxu Wang, University of Calgary, Canada


                                                     Abstract

    An Automated Teller Machine (ATM) is a safety-critical and real-time system that is highly complicated in
design and implementation. This paper presents the formal design, specification, and modeling of the ATM system
using a denotational mathematics known as Real-Time Process Algebra (RTPA). The conceptual model of the ATM
system is introduced as the initial requirements for the system. The architectural model of the ATM system is created
using RTPA architectural modeling methodologies and refined by a set of Unified Data Models (UDMs), which
share a generic mathematical model of tuples. The static behaviors of the ATM system are specified and refined by a
set of Unified Process Models (UPMs) for the ATM transition processing and system supporting processes. The
dynamic behaviors of the ATM system are specified and refined by process priority allocation, process deployment,
and process dispatch models. Based on the formal design models of the ATM system, code can be automatically
generated using the RTPA Code Generator (RTPA-CG), or be seamlessly transformed into programs by
programmers. The formal models of ATM may not only serve as a formal design paradigm of real-time software
systems, but also a test bench for the expressive power and modeling capability of exiting formal methods in
software engineering.

    Keywords: Software science, software engineering, RTPA, ATM, real-time systems, formal design models,
system architecture specification, system behaviour specification, unified data models, UDM, unified process
models, UPM, design frameworks, design reuse


                                                INTRODUCTION

     The modeling and description of an Automated Teller Machine (ATM) are a typical design case in safety-critical
and real-time systems (Laplante, 1977; Hayes, 1985; McDermid, 1991; Corsetti et al., 1991; Liu, 2000; Wang, 2002,
2007). As a real-time control system, the ATM system is characterized by its high degree of complexity, intricate
interactions with hardware devices and users, and necessary requirements for domain knowledge. All these factors
warrant the ATM system as a complex but ideal design paradigm in large-scale software system design in general
and in real-time system modeling in particular.

     There is a lack of systematical and detailed documentation of design knowledge and modeling prototypes of
ATM systems and a formal model of them in denotational mathematics and formal notation systems (Wang, 2008a,
2008b). This paper presents the formal design, specification, and modeling of the ATM system using a denotational
mathematics known as Real-Time Process Algebra (RTPA) (Wang, 2002, 2003, 2007, 2008a, 2008c, 2008d). RTPA
introduces only 17 meta-processes and 17 process relations to describe software system architectures and behaviors
with a stepwise refinement methodology (Wang, 2007, 2008c). According to the RTPA methodology for system
modeling and refinement, a software system can be specified as a set of architectural and operational components as
well as their interactions. The former is modeled by Unified Data Models (UDMs, also known as the component
logical model (CLM)) (Wang, 2008c), which is an abstract model of system hardware interfaces, an internal logic
model of hardware, and/or an internal control structure of the system. The latter is modeled by static and dynamic
processes using the Unified Process Models (UPMs) (Hoare, 1978, 1985; Bjorner and Jones, 1982; Wang, 2007,
2008c; Wang and King, 2000).

    This paper develops a formal design model of the ATM system in a top-down approach on the basis of the
RTPA methodology. This work demonstrates that the ATM system can be formally modeled and described by a set
of real-time processes in RTPA. In the remainder of this paper, the conceptual model of the ATM system is
described as the initial requirements for the system. The architectural model of the ATM system is created based on
the conceptual model using the RTPA architectural modeling methodologies and refined by a set of UDMs. Then,
the static behaviors of the ATM system are specified and refined by a set of processes (UPMs). The dynamic
behaviors of the ATM system are specified and refined by process priority allocation, process deployment, and
process dispatching models. With the formal and rigorous models of the ATM system, code can be automatically
generated by the RTPA Code Generator (RTPA-CG) (Wang, 2007), or be seamlessly transferred into program code
manually. The formal models of ATM may not only serve as a formal design paradigm of real-time software
systems, but also a test bench for the expressive power and modeling capability of exiting formal methods in
software engineering.


                             THE CONCEPTUAL MODEL OF THE ATM SYSTEM

    An ATM system is a real-time front terminal of automatic teller services with the support of a central bank
server and a centralized account database. This paper models an ATM that provides money withdraw and account
balance management services. The architecture of the ATM system, as shown in Fig. 1, encompasses an ATM
processor, a system clock, a remote account database, and a set of peripheral devices such as the card reader,
monitor, keypad, bills storage, and bills disburser.


                                    Card
                                   Reader                 ATM                   Bills
                                    [1]                                       Disburser
                                                        Processor                [1]


                                  Keypad

                                    [1]
                                                                                Bills
                                                                               Storage
                                                                                 [1]
                                  Monitor

                                    [1]


                                                           [1]                 System
                                  Account
                                                                               Clock
                                  Database
                                                                                 [1]
                                    [1]


                                   Fig. 1 The conceptual model of the ATM system

     The conceptual model of an ATM system is used to be described by a Finite State Machine (FSM), which adopts
a set of states and a set of state transition functions modeled by a transition diagram or a transition table to describe
the basic behaviors of the ATM system. On the basis of the conceptual model of the ATM system as given in Fig. 1,
the top level behaviors of ATM can be modeled in a transition diagram as shown in Fig. 2.

   Corresponding to the transition diagram of the ATM as given in Fig. 2, a formal model of the ATM system as an
FSM, ATMST, is defined as a 5-tuple as follows:

                                             ATMST  (S, , s, F, )                                                 (1)
where

       S is a set of valid states that forms the domain of the ATM, S = {s0, s1, …, s7} where the states are: s0 –
        System, s1 – Welcome, s2 - Check PIN, s3 – Input withdraw amount, s4 - Verify balance, s5 - Verify bills
        availability, s6 - Disburse bills, and s7 - Eject card, respectively;
        is a set of events that the ATM may accept and process,  = {e0, e1, …, e10} where e0 - Start, e1 - Insert
        card, e2 - Correct PIN, e3 - Incorrect PIN, e4 – Request  max, e5 – Request > max, e6 - Cancel transaction, e7 -
        Sufficient funds, e8 - Insufficient funds, e9 - Sufficient bills in ATM, and e10 - Insufficient bills in ATM;
       s is the start state of the ATM, s = s1 (Welcome);
       F is a set of ending states, F = {s1};
       δ is the transition function of the ATM that determines the next state of the FSM, si+1, on the basis of the

                                                           2
        current state si and a specific incoming event ei, i.e., si+1 = δ (si, ei), where

                                                              δ = f: S  ∑ → S                                                        (2)

which can be rigorously defined in the transition table as shown in Table 1 corresponding to the conceptual model of
the ATM behaviors as shown in Fig. 2.



                                                                               System


                                                                                         start


                                                                              Welcome
                                                          insert
                                                           card
                                                                              cancel
                                                                           transaction
                                 incorrect   Check PIN                                                     Eject card
                                   PIN
                                                                            cancel
                                                                         transaction
                                                       correct
                                                        PIN

                                   request   Input withdraw                                                                Disburse
                                    > max       amount                           insufficient                                bills
                                                                                    funds              insufficient
                                                                                                      bills in ATM
                                                       Request
                                                         max
                                                                         sufficient
                                                                           funds                                  sufficient bills
                                                Verify                                      Verify bills             in ATM
                                                balance                                     availability


                                    Fig. 2 The transition diagram of the ATM behaviors


                                       Table 1. The State Transition Table of the ATM

                                                  si                ei           si+1 = δ(si, ei)
                                                  s0               e0                   s1
                                                  s1               e1                   s2
                                                  s2               e2                   s3
                                                  s2               e3                   s2
                                                  s2               e6                   s7
                                                  s3               e4                   s4
                                                  s3               e5                   s3
                                                  s3               e6                   s7
                                                  s4               e7                   s5
                                                  s4               e8                   s7
                                                  s5               e9                   s6
                                                  s5               e10                  s7
                                                  s6                -                   s7
                                                  s7                -                   s1

        Based on the above conceptual models and descriptions, an abstract FSM model of the ATM system can be
    described as shown in Fig. 3.




                                                                             3
                                                                 s0


                                                                  e0


                                                                 s1
                                                 e1                         -

                                                            e6
                            e3         s2                                       s7


                                            e2              e6                            -


                            e5         s3                               e10                   s6
                                                         e8

                                            e4
                                                                                     e9
                                                       e7
                                       s4                              s5



                                 Fig. 3 The Abstract FSM Model of the ATM behaviors

   The top level framework of the ATM system can be modeled by a set of architecture, static behaviors, and
dynamic behaviors using RTPA (Wang, 2002, 2008a) as follows:

                                    §(ATM)  ATM§.ArchitectureST
                                                 || ATM§.StaticBehaviorsPC
                                                 || ATM§.DynamicBehaviorsPC                                           (3)
where || indicates that these three subsystems related in parallel, and §, ST, and PC are type suffixes of system, system
structure, and process, respectively.

    The conceptual models of ATM as presented in Figs. 1 through 3 describe the configuration, basic behaviors,
and logical relationships among components of the ATM system. According to the RTPA methodology for system
modeling, specification, and refinement (Wang, 2008a, 2008b), the top level model of any system may be specified
in a similar structure as given in Eq. 3. The following sections will extend and refine the top level framework of
ATM§ into detailed architectural models (UDMs) and behavioral models (UPMs).

                          THE ARCHITECTURAL MODEL OF THE ATM SYSTEM

     The architecture of a hybrid hardware/software system, particularly a real-time system, is a system framework
that represents the overall structure, components, processes, and their interrelationships and interactions. This
sections specifies the architecture of the ATM system, ATM§.ArchitectureST, by a high-level architectural
framework based on its conceptual model as provided in Fig. 1. Then, each of its architectural components will be
refined as a UDM (also known as Component Logical Model (CLM)) (Wang, 2002, 2007, 2008c).

The Architectural Framework of the ATM System

    System architectures, at the top level, specify a list of structural identifiers of UDMs and their relations. A UDM
may be regarded as a predefined class of system hardware or internal control models, which can be inherited or
implemented by corresponding UDM objects as specific instances in the succeeding architectural refinement
processes for the system.
    Corresponding to the conceptual model of ATM as shown in Figs. 1 to 3, the high-level specification of the
architecture of ATM, ATM§.ArchitectureST, is given in Fig. 4 in RTPA. ATM§.ArchitectureST encompasses parallel
structures of a set of UDMs such as the ATMProcessorST, CardReaderST, KeypadST, MonitorST, BillStorageST,



                                                                 4
BillsDisburserST, AccountDatabaseST, and SysClockST, as well as a set of system events @EventsS and a set of
statuses StatusBL. The numbers in the angel brackets indicate the configuration of how many data objects that share
the same UDM.

                               ATM§.ArchitectureST  <ATMProcessor : ST | [1]>
                                                     || <CardReader : ST | [1]>
                                                     || <Keypad : ST | [1]>
                                                    || <Monitor : ST | [1]>
                                                    || <BillStorage : ST | [1]>
                                                    || <BillsDisburser : ST | [1]>
                                                    || <SysClock : ST | [1]
                                                    || <SysDatabase : ST | [1]>
                                                    || <@EventsS>
                                                    || < StatusBL>

                                 Fig. 4 The architectural framework of the ATM system

     The set of events of ATM are predefined global control variables of the system, as given in Eq. 4, which
represent an external stimulus to a system or the occurring of an internal change of status such as an action of users,
an updating of the environment, and a change of the value of a control variable. Types of general events, @EventS,
that may trigger a behavior in a system can be classified into operational (@eS), time (@tTM), and interrupt (@int)
events where @ is the event prefix, and S, TM, and ⊙ the type suffixes of string, time, and interrupt, respectively, i.e.:
                        ATM§.ArchitectureST.EventsST  @SysInitialS
                                                                | @tTM = §thh:mm:ss
                                                                | @SysClock100msInt⊙
                                                                                                                       (4)

    In RTPA, a status denoted by ⓢsBL is an abstract model of system state in Boolean type with a status prefix ⓢ,
such as an operation result and an internal condition. The ATM statuses as a set of predefined global control
variables are as follows:

                          ATM§.ArchitectureST.StatusST   CardReadStatusBL
                                                        | MonitorStatusBL
                                                        |  KeypadStatusBL
                                                        |  BillStorageStatusBL
                                                        |  BillsDisburserStatusBL
                                                        |  BillsDisburseEngineStatusBL
                                                        |  BillsAvailableBL
                                                        |  BillsDisbursedBL
                                                        |  CardInsertedBL
                                                        |  CardEjectedBL
                                                        |  CancellKeyPressedBL
                                                        |  EnterKeyPressedBL
                                                        |  DataEnteredBL
                                                        |  TimeOutBL
                                                        |  ServiceCompletedBL
                                                        |  ServiceCancelledBL
                                                        |  SystemFailureBL
                                                        |  SysShutDownBL
                                                        |  ValidAmountBL
                                                        |  ValidBalanceBL
                                                        |  ValidCardBL
                                                        |  ValidPINBL
                                                                                                                       (5)


                                                            5
The UDM Structures of the ATM System

    As modeled in Fig. 4, the ATM system encompasses eight UDMs for modeling the system hardware interfaces
and internal control structures. It is recognized that UDMs are a powerful modeling means in system architectural
modeling (Wang, 2002, 2007, 2008c), which can be used to unify user defined complex data objects in system
modeling, and to represent the abstraction and formalization of domain knowledge and structural information. The
generic mathematical model of UDMs is tuples. Each of the eight UDMs of the ATM system is designed and
modeled in the following subsections, except that the ATMProcessorST will be embodied by its static and dynamic
behavioral models (UPMs) in other sections.

(a) The UDM of the Card Reader

    The card reader of the ATM system, CardReaderST, is an architectural model of the interface device, which
accepts an inserted bank card, scans predesigned identification information on the card, and returns the card to users.
The UDM model of CardReaderST specifies seven functional fields as shown in Fig. 5. The card input port is an
input structure consisting of two fields known as the CardInputAddressH and CardInputN. The card insert port is an
output structure consisting of two fields known as the CardInsertAddressH and CardInsertEngineBL. The card eject
port is another output structure consisting of two fields known as the CardEjectAddressH and CardEjectEngineBL.
There are three CardReaderST operating statuses modeled in the fields of CardReadStatusBL, CardInsertStatusBL, and
CardEjectStatusBL.


           CardReaderST  (<PORTST(<CardInputAddress : H | CardInputAddressH = FF00H>,
                                        <CardInput : N | 0  CardInputN  1000000>)>,
                              <CardReadStatus : BL | CardReadStatusBL = {(T, Normal), (F, Faulty)}>,
                             <PORTST(<CardInsertAddress : H | CardInsertAddressH = FF01H>,
                                       <CardInsertEngine : BL | CardInsertEngineBL = {(T, On), (F, Off)}>)>,
                              <CardInsertStatus : BL | CardInsertStatusBL = {(T, Normal), (F, Faulty)}>,
                              <PORTST(<CardEjectAddress : H | CardEjectAddressH = FF01H>,
                                       <CardEjectEngine : BL | CardEjectEngineBL = {(T, On), (F, Off)}>)>,
                              <CardEjectStatus : BL | CardEjectStatusBL = {(T, Normal), (F, Faulty)}>
                            )


                                  Fig. 5 The refined UDM model of the card reader

(b) The UDM of the Keypad

     The keypad of the ATM system, KeypadST, is an architectural model of the interface device for users entering
required information such as the personal identification number (PIN) and withdraw amount of money. The UDM
model of KeypadST specifies five functional fields with certain design constraints as shown in Fig. 6. The field of
PortAddressH represents the physical input address of the keypad. The field of InputDigitsH represents information (
4 digits) entered from the keypad. The field of KeypadStatusBL represents the working conditions of the keypad. The
fields of EnterPressedBL and CancelPressedBL represent a valid or invalid input entered by the keypad, respectively.


                KeypadST  (<PORTST(<PortAddress : H | PortAddressH = FF10H>,
                                         <InputDigits : N | 0  InputDigitsN  1000>)>,
                               <KeypadStatus : BL | KeypadStatusBL = {(T,Normal), (F, Faulty)}>,
                               <EnterPressed : BL | EnterPressedBL = {(T, Pressed), (F, Unpressed>,
                               <CancelPressed : BL | CancelPressedBL = {(T, Pressed), (F, Unpressed)}>
                              )

                                     Fig. 6 The refined UDM model of the keypad




                                                           6
(c) The UDM of the Monitor

    The monitor of the ATM system, MonitorST, is an architectural model of the output device that displays system
operational and status information to users. The UDM model of MonitorST specifies four functional fields with
certain design constraints as shown in Fig. 7. The field of PortAddressH represents the physical output address to the
monitor. The field of OutputInformationS represents a string of letters ( 255 characters) that will be displayed on the
monitor. The field of MonitorStatusBL represents the operational conditions of the monitor. The field of
CurrentDisplyS is a system feedback of the latest output information on the monitor.


              MonitorST  (<PORTST(<PortAddress : H | PortAddressH = FF20H>,
                                          <OutputInformation : S | 0 < #(Output InformationS)  255>)>,
                                 <MonitorStatus : BL | MonitorStatusBL = {(T, Normal), (F, Faulty)}>,
                                <CurrentDisplay : S | 0  #(CurrentDisplayS)  255>)>
                               )

                                        Fig. 7 The refined UDM model of the monitor

(d) The UDM of the Bills Storage

     The bills storage of the ATM system, BillStorageST, is an architectural model of the internal device that stores
bills in different notes, which can be sent to the bills disburser in various combinations. The UDM model of
BillStorageST specifies six functional fields with certain design constraints as shown in Fig. 8. The bills storage port
is an output structure consisting of two fields known as the BillStorageAddressH and BillsAmountN. The bills deliver
port is an output structure consisting of two fields known as the BillsDeliverAddressH and BillsDeliverEngineBL. The
field of BillStorageStatusBL represents the operational conditions of the bills storage. The field of BillsLevelN
represents the current level of bills in the bills storage.


         BillStorageST  (<PORTST(<BillStorageAddress : H | BillStorageAddressH = FF30H>,
                                         <BillsAmount : N | 1  BillsAmountN  1000>)>,
                               <PORTST(<BillsDeliverAddress : H | BillsDeliverAddressH = FF31H>,
                                         <BillsDeliverEngine : BL | BillsDeliveryEngineBL = {(T, On), (F, Off)}>)>,
                               <BillStorageStatus : BL | BillStorageStatusBL = {(T, Normal), (F, Faulty)}>,
                               <BillsLevel : N | 0  BillsLevelN  MaxLevelN>
                           )

                                      Fig. 8 The refined UDM model of the bills storage

(e) The UDM of the Bills Disburser

     The bills disburser of the ATM system, BillsDisburserST, is an architectural model of the output device that
delivers bills of requested amount from the bills storage to the customer. The UDM model of BillsDisburserST
specifies four functional fields with certain design constraints as shown in Fig. 9. The disburser drive port is an
output structure consisting of two fields known as the DisburserDriveAddressH and DisburseEngineBL. The field of
BillsDisburserStatusBL represents the operational conditions of the bills disburser. The field of AmountDisbursedN is
a system feedback signal of bills disbursed to the customer in the current transaction.

           BillsDisburserST  (<PORTST(<DisburserDriveAddress : H | DisburserDriveAddressH = FF41H>,
                                         <DisburseEngine : BL | DisburseEngineBL = {(T, On), (F, Off)}>)>,
                               <BillsDisburserStatus : BL | BillsDisburserStatusBL = {(T, Normal), (F, Faulty)}>,
                               <AmountDisbursed : N | 1  AmountDisbursedN  1000>)>
                              )

                                     Fig. 9 The refined UDM model of the bills disburser


                                                               7
(f) The UDM of the System Clock
    The system clock of the ATM system is an architectural model for event timing, process duration manipulation,
and system synchronization. The UDM model of the system clock, SysClockST, is designed as given in Fig. 10.
SysClockST provides an absolute (calendar) clock CurrentTimehh:mm:ss as the logical time reference of the entire
system and a relative clock §tN as a generic counter of the ATM system. The InterruptCounterN is adopted to transfer
the system timing ticks at 100ms interval into the second signal. The real-time system clock is updated by the
process SysClockPC, which will be described in the following section on system static behaviors.

                      SysClockST  ( <§t : N | 0  §tN  1,000,000>,
                                               <CurrentTime : hh:mm:ss | 00:00:00 
                                                                           CurrentTimehh:mm:ss  23:59:59>,
                                               <MainClockPort : H | MainClockPortB = FFF1H>,
                                               <ClockInterval : N | ClockIntervalN = 100ms>,
                                               <InterruptCounter : N | 0  InterruptCounterN  9>
                                           )


                                    Fig. 10 The refined UDM model of the system clock

(g) The UDM of the System Database
    The system database of the ATM system, SysDatabaseST, is an architectural model of the internal centralized
database located in the bank`s server where the ATM connects to. The ATM uses the card number scanned from a
bank card and the PIN entered from the keypad to access the system database in order to verify the validity of the
card and information recorded in the corresponding account in SysDatabaseST, such as the card holder, current
balance, and withdraw constraints.
    The UDM model of SysDatabaseST specifies a set of accounts with seven functional fields as shown in Fig. 11.
The field of AccountNumN represents a specific account existed in the system that is corresponding to the number
assigned to the bank card. The field of AccountStatusBL represents the current status of an account such as active or
inactive in the system. The field of PINH represents a user defined PIN ( 4 digits) recorded in the system. The field
of CardHolderS records the name of person that holds the account. The field of BalanceN represents the current
remaining money in the given account. The field of MaxAllowableWithdrawN represents the limit set by the bank for
the given account. The field of CurrentWithdrawN specifies the valid user requested amount of withdraw in the
current transaction.

                                1000000
              SysDatabaseST     R
                                 iN=0
                                          SysAccount(iN)ST:

                                           (<AccountNum : N | 0  AccountNumN  1000000>) :
                                            <AccountStatus : BL | AccountStatusBL = {(T, Active), (F, Inactive)}>,
                                            <PIN : N | 0000  PINN  9999>,
                                            <CardHolder : S | 0 < #( CardHolderS)  255>,
                                            <Balance : N | 0  BalanceN  10000>,
                                            <MaxAllowableWithdraw : N | MaxAllowableWithdrawN = 1000>,
                                            <CurrentWithdraw : N | 5  CurrentWithdrawN  MaxAllowableWithdrawN>
                                          )


                                 Fig. 11 The refined UDM model of the system database
     The system architectural models specified in this section provide a set of abstract object models and clear
interfaces between system hardware and software. By reaching this point, the co-design of a real-time system can be
carried out in parallel by separated hardware and software teams. It is recognized that system architecture
specification by the means of UDMs is a fundamental and difficult phase in software system modeling, while
conventional formal methods hardly provide any support for this purpose. From the above examples in this
subsection, it can be seen that RTPA provides a set of expressive notations for specifying system architectural
structures and control models, including hardware, software, and their interactions. On the basis of the system
architecture specification and with the work products of system architectural components or UDMs, specification of
the operational components of the LDS system as behavioral processes can be carried out directly as elaborated in
the following sections.


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