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Modeling Elevator System With Coloured Petri Nets

M
Mohammed Assiri

The document describes the modeling of an elevator system using Colored Petri Nets (CPN) to address the complexities of controlling multiple elevators in buildings. It outlines various components such as the abstract and timing models, hall call and car call sub-models, and algorithms for elevator control, detailing the structure and functionalities of the system. The work aims to provide a flexible and formal model that can adapt to various algorithms governing real elevator systems.

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MODELING  ELEVATOR  SYSTEM     WITH  COLOURED  PETRI  NETS     By  MOHAMMED  ASSIRI   Jun  1,  2015   1  ©  Mohammed  Assiri  
1.  Introduction 2.  Coloured Petri Nets 3.  The Abstract Version of CPN-based Modelling of Elevator System 4.  The Timing Version of CPN-based Modelling of Elevator System 5.  The Parking Optimizer Model 6.  The Analyses 7.  Conclusion Outline:   Jun  1,  2015   2  ©  Mohammed  Assiri  
v Elevator Systems v The Objective v Related Works v The Contributions 1. Introduction : Jun  1,  2015   3  ©  Mohammed  Assiri  
•  Integral Part Of Buildings •  Very Complex o  Controlling Multiple Elevators By A Centralized Control Mechanism o  The Differences Among Buildings And Traffic Patterns v Elevator Systems Jun  1,  2015   4  ©  Mohammed  Assiri  
Proposing a model of elevator system that fulfillments the constraints of the following definition [Ghezzi et al. (2003)]*: An elevator system is to be installed in a building with m floors and n cars. The elevator and the control mechanisms are supplied by the manufacturer. The problem concerns the logistics of moving cars between floors according to the following : * Fundamentals of Software Engineering. Pearson Prentice Hall, 2nd edition. v The Objective Jun  1,  2015   5  ©  Mohammed  Assiri  
a.  Each elevator’s car has a set of buttons - one for each floor. Pressing these buttons signals the elevator to move to the corresponding floor. b.  On the wall outside the elevator each floor has two buttons (with the exception of the ground and the top floors). One button is pressed to request an upward moving elevator and another button is pressed to request a downward moving elevator. If both buttons are pressed, then each direction is assigned to a different car. c.  When an elevator has not received any requests for service, it should be held at its parking floor with its doors closed until it receives further requests. d.  All requests for elevators from floors (i.e. hall calls) must be serviced eventually. The applied algorithm controls the priority of floors. All requests for floors within elevators (i.e. car calls) must be serviced eventually, with floors usually serviced sequentially in the direction of travel. e.  Each elevator’s car has an emergency button which when pressed causes an alarm. The elevator is then deemed "out of service". Each elevator has a mechanism to cancel its "out of service" status. v The Objective (Cont.) Jun  1,  2015   6  ©  Mohammed  Assiri  
•  Elevator system is one of the software engineering benchmarks to test the expressive power, readability and convenience of various formal specification techniques [Ghezzi et al. (2003)] •  It has been modeled many times in past and that includes Petri Nets: 1.  Petri net based dynamic scheduling of an elevator system [Lin and Fu (1996)]. 2.  Dynamic scheduling of elevator systems over hybrid Petri net/rule modeling [Huang and Fu (1998)]. 3.  Timed Petri net based approach for elevator group controls [Cho et al. (1999)]. 4.  Abstract Petri net based approach to problem solving in real time applications [Etessami and Hura (1989)] 5.  Petri net-based modeling and control of the multi-elevator systems [Ahmad et al. (2014)] 6.  Simulation of the intelligent control circuit based on Petri net [Ye et al. (2011)]. 7.  Requirements Engineering for Reactive Systems: Coloured Petri Nets for an Elevator Controller [Fernandes et al. (2007)] 8.  Modeling and analysis of elevator system based on timed-Coloured Petri net [Liqian et al. (2004)] v Related Works Jun  1,  2015   7  ©  Mohammed  Assiri  
•  The independence of the number of floors and cars. •  Covering different stages of the elevator system in substantial details. •  The flexibility to adapt different algorithms and rules that govern real elevator system. •  May eventually evolve in a standard formal model of the elevator system. v The Contributions Jun  1,  2015   8  ©  Mohammed  Assiri  
v Overview v Definition v Computer Tools 2.  Coloured Petri Nets Jun  1,  2015   9  ©  Mohammed  Assiri  
•  Coloured Petri Nets (CPN) [Jensen (1981)*] is an extension of Petri Nets. It is a graphical language for constructing models of concurrent systems and analyzing their properties. •  CPN combines the capabilities of Petri Nets (as a graphical language) with the capabilities of Standard ML (as a high-level programming language). (next slides) * Coloured Petri Nets and the Invariant Method, Theoretical Computer Science v Overview Jun  1,  2015   10  ©  Mohammed  Assiri  
v The Structure of CPN-Based Model Jun  1,  2015   11   placetransition arc inscription colour set token colours [guards] priority value ©  Mohammed  Assiri  
•  The CPN ML language is a flexible, expressive, and extensible language founded on the functional programming Language: Standard ML (SML/NJ implementation). •  By CPN ML language, the CPN-based models have not only types and inscriptions, but also colour sets, token colours, variable declarations, and functions. v  CPN ML Language (A High-level Programming Language) Jun  1,  2015   12  ©  Mohammed  Assiri  
Structure    DefiniRons   v Demo Jun  1,  2015   13   unilluminated buttons Buttons 1`{floor_location=2,illumination=off}++ 1`{floor_location=3,illumination=off} unilluminate(button) button button illuminate(button) illuminated buttons 1`{floor_location=1,illumination=on} Buttons illuminate unilluminate ©  Mohammed  Assiri  
•  Semi-formal definition: A Coloured Peter Net is a tuple : CPN = (P,T,A,Σ,C,N,E,G,I) •  For more details and theory of CPN, please refer to Coloured Petri Nets Modelling and Validation of Concurrent Systems by Jensen and Kristensen (2009) v Definition Jun  1,  2015   14  ©  Mohammed  Assiri  
•  CPN Tools v.4.0 from AIS Group, Eindhoven University of Technology, The Netherlands. (www.cpntools.org) •  The CPN Tools is composed of a graphical editor, a state space tool, and a simulator. •  Visualization v.0.1 a visual aid was developed to observe the modeled system. v Computer Tools Jun  1,  2015   15  ©  Mohammed  Assiri  
3.  The Abstract Version of CPN-based Modelling of Elevator System Jun  1,  2015   16  ©  Mohammed  Assiri  
v The Abstract Car-Structure Sub-model Jun  1,  2015   17   CarsCarsCars DatabaseDatabaseDatabase Database initialize_database() Cars initialize_cars() ©  Mohammed  Assiri  
Colour  Sets     Defini1ons     Car  ID    {  i  |i  ∈  Z+  ∧  i  ≤  total  number  of  cars}     Range    {  r  |  r  ∈  Z+  ∧  lowest  floor  ≤  r  ≤  highest  floor}     Status    {  idle,  emergency,  out  of  service,  up,  down  }     Desired  Floors    {  [l]  |  l  ∈  Range}     Call  Issuer    {  request,  system,  non,  reservaRon}     Cars     {  (car  id,  current  floor,  status,  parking  floor,   desired  floors,  call  issuer)  |  car  id  ∈  Car  ID,   current  floor  ∈  Range,  status  ∈  Status,  parking   floor  ∈  Range,  desired  floors  ∈  Desired  Floors,   call  issuer  ∈  Call  Issuer}     v The Abstract Car-Structure Sub-model (Cont. 1) Jun  1,  2015   18  ©  Mohammed  Assiri  
Colour  Sets     Defini1ons     Car  Info     {(current  floor,  status,  desRnaRons,  car  id)  |   current  floor  ∈  Range,  status  ∈  Status,   desRnaRons  ∈  Desired  Floors,  car  id  ∈  Car  ID}     Database    {[d]  |  d  ∈  Car  Info}     v The Abstract Car-Structure Sub-model (Cont. 2) Jun  1,  2015   19  ©  Mohammed  Assiri  
Parameter     Legal  value   Cars’  number    {n  |  n  ∈  Z+}     Lowest  floor  number    {f  |  f  ∈  Z+  ∧  f  <  highest  floor}     Highest  floors  number    {h  |  h  ∈  Z+  ∧  lowest  floor  <  h}     v The Abstract Car-Structure Sub-model (Cont. 3) Jun  1,  2015   20  ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model Jun  1,  2015   21   counter selected floor's num requested call floor's number CarsCars DatabaseDatabasePrk SysPrk SysPrk Sys all floors' numbers watch generators log Release Random Number Release Assign Hall Call Assign Direction n rn_random() new_call new_call car hall_call snd_hcall (car,hall_call) n+1 i i-1 i i new_call hall_call i i+1 asn_dir(new_call) hall_call db upd_db (hall_call, db,car) INT 1`1 () Range Range selected_floor INT 1`1 Hall_Call Hall_Call [rn_guard(n,i)] [r_guard(i)] [asn_hcall_guard (hall_call,car,db)] Hall_Call Database Database initialize_database() initialize_cars() Cars Cars ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 1) Jun  1,  2015   22   requested call Hall_Call CarsCars initialize_cars() DatabaseDatabase initialize_database() Prk SysPrk Sys Hall_Call log Hall_Call Assign Hall Call [asn_hcall_guard (hall_call,car,db)] car hall_call snd_hcall (car,hall_call) hall_call hall_call db upd_db (hall_call, db,car) Hall  Call   {(hall  call  floor,  status)  |  hall  call  floor  ∈  Range,  status  ∈  Status}     ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 2) Jun  1,  2015   23   The Rules 1.  The selected car is either idle or travelling toward the direction of the hall call, 2. The selected car is not reserved, 3. The selected car is elected by the applied algorithm which could be the nearest-car algorithm , the minimum-waiting algorithm , or the scope algorithm . ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 3) Jun  1,  2015   24   •  The nearest-car algorithm [Barney (2003a)1]: 1.  Analysing the token of place Database. a.  The cars with proper status are extracted from the token. b.  The distances between hall-call floor and cars’ current floors are calculated. 2.  The hall call is assigned to the car with minimum distance to the hall call floor. •  The minimum waiting algorithm: 3.  Calculating the stop times consumed by the already placed and being served calls between the floor of the new hall call and each car’s current floor. 4.  The car with the expected minimum waiting-time is assigned to serve the new hall call •  The scope algorithm [Barney (2003b)2]: H ≤ A ≤ T. where: H = the head floor of car’s scope A = the answered hall-call floors T = the tail floor of car’s scope 1 Elevator Traffic Handbook: Theory and Practice. 2 VerRcal  transportaRon  in  tall  buildings.     ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 4) Jun  1,  2015   25   counter selected floor's num floor's number all floors' numbers watch generators Release Random Number Release n rn_random() new_call new_call n+1 i i INT 1`1 () Range Range selected_floor INT 1`1 [rn_guard(n,i)] [r_guard(i)] ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 5) Jun  1,  2015   26   Parameters   Legal  values     Producing  mode    {finite,  infinite}     Times  of  finite  hall  calls    {y  |  y  ∈  Z  ∧  0  ≤  y}     The  most  requested  floor    {r  |  r  ∈  Range}     DuplicaRon  of  most  requested  floor    {d  |  d  ∈  Z  ∧  0  ≤  d}     The  applied  algorithm    {minimum  waiRng,  nearest,  scope}     Producing’  pause  number∗    {p  |  p  ∈  Z  ∧  0  <  p}     ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 6) Jun  1,  2015   27   requested call floor's number Assign Direction new_call asn_dir(new_call) Range Hall_Call ©  Mohammed  Assiri  
v The Abstract Hall-Call Sub-model (Cont. 7) Jun  1,  2015   28   •  If the produced number equates the highest floor, then it is associated restrictedly with the down direction, •  Else if the produced number equates the lowest floor, then it is associated restrictedly with up direction. •  Otherwise, a produced number is associated non-deterministically with up direction or down direction. ü  Thus, a hall call of a valid floor’s number and an appropriate direction is produced correctly and completely. ©  Mohammed  Assiri  
v The Abstract Car-call Sub-model Jun  1,  2015   29   CarsCarsCars log car call all floors' numbers counter specific floors' num DatabaseDatabase watch generator Coordinate Release Floor's Number Reproduce archive(car,car_call, new_call,sf)car_callcar snd_ccall(car, new_call,sf) new_call rn_random() n+1 n sf place_calls (car,sf) db upd_db_ (new_call, db,car,sf) i+1 i i i-1 car_call reproduce(sf)sf car INT 1`1[rfn_guard(n,i)]() RangeINT 1`1 Specific_Floors initialize_sfloors() [rep_guard (sf,car,car_call)] 0Car_Calls initialize_log()initialize_cars() CarsDatabase initialize_database() [coord_guard(car_call,car,sf,new_call)] Database ©  Mohammed  Assiri  
v The Abstract Car-call Sub-model (Cont. 1) Jun  1,  2015   30   CarsCars log car call specific floors' num DatabaseDatabase Coordinate archive(car,car_call, new_call,sf)car_callcar snd_ccall(car, new_call,sf) new_call sf place_calls (car,sf) db upd_db_ (new_call, db,car,sf) Range Specific_Floors initialize_sfloors() Car_Calls initialize_log()initialize_cars() CarsDatabase initialize_database() [coord_guard(car_call,car,sf,new_call)] ©  Mohammed  Assiri   Specific  Floors    {(car  id,  specific  calls,  repeated  Rmes)  |  car  id  ∈  Car  ID,  Specific   calls  ∈  Desired  Floors,  repeated  Rmes  ∈  Z}    
v The Abstract Car-call Sub-model (Cont. 2) Jun  1,  2015   31   car call all floors' numbers counter watch generator Release Floor's Number rn_random() n+1 n i+1 i INT 1`1 [rfn_guard(n,i)]() RangeINT 1`1 ©  Mohammed  Assiri   specific floors' num Reproduce reproduce(sf)sf Specific_Floors initialize_sfloors() [rep_guard (sf,car,car_call)]
v The Abstract Car-call Sub-model (Cont. 3) Jun  1,  2015   32  ©  Mohammed  Assiri   Parameters     Legal  values     Producing  mode    {finite,  infinite}     Times  of  finite  car  calls    {x  |  x  ∈  Z  ∧  0  ≤  x}     Most  desired  floors    {[f]  |  f  ∈  Range}     Frequency  of  desired  floors    {d  |  d  ∈  Z  ∧  0  ≤  d}     Producing  pause  number    {p  |  p  ∈  Z+  }    
v The Abstract System-cycle Sub-model Jun  1,  2015   33   CarsCars Cars initialize_cars() Cars out of service Cars error log Cars DatabaseDatabase Database initialize_database() Databasesuccess log Cars Doors Doors initialize_doors () Database Database initialize_database() Database Maintain [mnt_guard(car)] 0 Restart [rst_guard(car)] Transfer [trn_guard(car)] Arrive [arr_guard(car,door)] suspend (car) car car car restart(car) car transfer(car) upd_trn(car,db) db cararrive(car) car doordoor upd_arr(car,db) db upd_susp (car,db) db db upd_rst (car,db) ©  Mohammed  Assiri  
v  The Abstract System-cycle Sub-model (The Maintenance) Jun  1,  2015   34   CarsCars out of service error log Database Database Maintain Restart suspend (car) car car car restart(car) upd_susp (car,db) db db upd_rst (car,db) Cars initialize_cars() [rst_guard(car)] Cars initialize_database() [mnt_guard(car)] 0 Cars ©  Mohammed  Assiri   Parameter     Legal  value     Restart  pending  cars  automaRcally     {”yes”,”no”  }    
v The Abstract System-cycle Sub-model (The Transition) Jun  1,  2015   35   CarsCars DatabaseDatabase Database Transfer car transfer(car) upd_trn(car,db) db Cars initialize_cars() [trn_guard(car)] initialize_database() ©  Mohammed  Assiri  
v The Abstract System-cycle Sub-model (The Arrival) Jun  1,  2015   36   CarsCars Cars initialize_cars() DatabaseDatabase Database initialize_database() success log Cars Doors Doors initialize_doors () Arrive [arr_guard(car,door)] cararrive(car) car doordoor upd_arr(car,db) db ©  Mohammed  Assiri  
4.  The Timing Version of CPN-based Modelling of Elevator System Jun  1,  2015   37  ©  Mohammed  Assiri   •  The abstract version concerns the logical movement of elevator system. In contrast, the timing version extends the abstract version to include the illumination of buttons , the calculation of waiting and serving times, and the limiting of cars’ stops.
v The Timing Car-Structure Sub-model Jun  1,  2015   38   CarsTiming Cars Timing_Cars initialize_tcars() DatabaseTiming Database Timing_Database initialize_tdatabase() Timing DatabaseTiming Cars ©  Mohammed  Assiri  
Colour  Sets     Defini1ons     Car  ID     {  i  |i  ∈  Z+  ∧  i  ≤  total  number  of  cars}     Range     {  r  |  r  ∈  Z+  ∧  lowest  floor  ≤  r  ≤  highest  floor}     Status   {  up,  down,  emergency,  idle,  out  of  service}     Desired  Floors   {  [l]  |  l  ∈  Range}     Call  Issuer   {  request,  system,  non,  reservaRon}     INT   {n  |  n  ∈  Z}     REAL   {r  |  r  ∈  R}   Timing  Hall  Call   {(hall  call,  direc1on,  1me)  |  hall  call  ∈  Range,  direc1on  ∈  Status,     1me  ∈  R}     Timing  Hall  Calls   {[h]  |  h  ∈  Timing  Hall  Call}     Timing  Cars   {(car  id,  current  floor,  status,  parking  floor,  desired  floors,  call  issuer,   Rme  period,  served  hall  calls,  stops  limitaRon  )  |  car  id  ∈  Car  ID,   current  floor  ∈  Range,  status  ∈  Status,  parking  floor  ∈  Range,  desired   floors  ∈  Desired  Floors,  call  issuer  ∈  Call  Issuer,  Rme  period  ∈  REAL,   served  hall  calls  ∈  Timing  Hall  Calls,  stops  limitaRon  ∈  INT}     v The Timing Car-Structure Sub-model (Cont. 1) Jun  1,  2015   39  ©  Mohammed  Assiri  
Parameter     Legal  value   Stops’  limitaRon    {s  |  s  ∈  Z+  ∧s=0  ∨  1  ≤  s}     v The Timing Car-Structure Sub-model (Cont. 2) Jun  1,  2015   40  ©  Mohammed  Assiri     (Pseudocode)     func%on  stops’  limita%on  value  ()  =                  if  the  parameter  "stops’  limita%on"  =  0  then    return  random(1,  floors’  number);   else    return  the  parameter  "stops’  limita%on";  
Colour  Sets     Defini1ons     Timing  Car’s  Data     {(current  floor,  status,  desRnaRons,  car  id,   Rme)  |  current  floor  ∈  Range,  status  ∈   Status,  desRnaRons  ∈  Desired  Floors,  car  id   ∈  Car  ID,  Rme  ∈  REAL}     Timing  Database    {[g]  |  g  ∈  Timing  Carʹ′s  Data}     v The Timing Car-Structure Sub-model (Cont. 3) Jun  1,  2015   41  ©  Mohammed  Assiri  
v The Timing Hall-Call Sub-model Jun  1,  2015   42   Prk Sys Hall_Call Prk Sys CarsTiming Cars Timing_Cars initialize_tcars() Coordinator Coordinator initialize_coordination() Hall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall's_Buttons Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Release Hall Call [releas_guard(HB,C)] Assign Hall Call [asn_guard(rhc,car,DB)] Cupd_coord(HB,C) illuminate_hall_btn(HB,C) carasn_hcall(car,rhc) (#hall_call rhc) rhc hall_call(HB,C,DB) released(C) C HB DB upd_asn (car,rhc,DB) DB DB Timing Cars Timing Database ©  Mohammed  Assiri  
v The Timing Hall-Call Sub-model (Releasing Hall Calls) Jun  1,  2015   43   Coordinator Coordinator initialize_coordination() Hall's_Buttons Hall's_Buttons initialize_halls'_buttons() Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Release Hall Call [releas_guard(HB,C)] Cupd_coord(HB,C) illuminate_hall_btn(HB,C) hall_call(HB,C,DB) HB DB DB ©  Mohammed  Assiri   Colour  Sets     Defini1ons     Hall  Call     {(hall  call  floor,  status)  |  hall  call  floor  ∈  Range,  status  ∈  Status  }     Hall  Calls     {[h]  |  h  ∈  Hall  Call}     Hall  BuOons     {(IB,  USB,  UUB)  |  IB  ∈  Hall  Calls,  USB  ∈  Hall  Calls,  UUB  ∈  Hall  Calls}     Coordinator   {(specified  call,  unspecified  call,  next  selec1on,  released  calls)  |  specified   call  ∈  Z,  unspecified  call  ∈  Z,  next  selec1on  ∈  Z,  released  calls  ∈  Z}    
v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 2) Jun  1,  2015   44  ©  Mohammed  Assiri   Rules: 1.  The unilluminated-specified buttons (USB) list and unilluminated-unspecified buttons (UUB) list are not both empty, 2.  If the limit of producing calls is finite, then it has been not already reached, 3.  The number of produced calls is less than the value of parameter pause number
v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 3) Jun  1,  2015   45  ©  Mohammed  Assiri   The choice of either USB list or UUB list is based on the following rules: 1.  When a list is empty, the other list is always selected. 2.  The difference between both lists’ length is less or equal to the value of parameter “The frequency of most requested hall calls”. 3.  The internal choice between tuples is sequential in USB list and arbitrary in UUB list.
v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 1) Jun  1,  2015   46  ©  Mohammed  Assiri   Parameters   Legal values   Producing mode   {finite, infinite}   Times of finite hall calls   {y | y ∈ Z ∧ 0 ≤ y}   The most requested hall calls   {[(floor number, direction)] | floor number ∈ Range, direction ∈ Status}   The frequency of most requested hall calls   {d | d ∈ Z ∧ 0 ≤ d}   The applied algorithm of hall calls   {minimum waiting,nearest, scope}   The travel time   {t | t ∈ R+}   The average time of stop   {s | s ∈ R+}   Pause number   {p | p ∈ Z+}  
v The Timing Hall-Call Sub-model (Assigning Hall Calls) Jun  1,  2015   47   Prk Sys Hall_Call CarsTiming Cars Timing_Cars initialize_tcars() Coordinator Coordinator initialize_coordination() Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Assign Hall Call [asn_guard(rhc,car,DB)] carasn_hcall(car,rhc) (#hall_call rhc) rhc released(C) C DB upd_asn (car,rhc,DB) ©  Mohammed  Assiri   Car’s Time   {(car id, time) | car id ∈ Car ID, time ∈ R}   Cars’ Times   {[c] | c ∈ Car′s Time}   Requested Hall Call   {(hall call, waiting times) | hall call ∈ Hall Call, waiting times ∈ Cars’ Times}   Coordinator     {(specified  call,  unspecified  call,  next  selecRon,  released  calls)  |  specified  call  ∈  Z,   unspecified  call  ∈  Z,  next  selecRon  ∈  Z,  released  calls  ∈  Z}    
v The Timing Car-Call Sub-model Jun  1,  2015   48   CarsTiming Cars Timing_Cars initialize_tcars() Calls_Counters Calls_Counters initialize_coord () DatabaseTiming Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Car's_Buttons Place Car Call [plc_gaurd(CB,CC,car) ] CCupd_ccoord(CB,CC) DBcarsnd_ccall(CB,CC,car) upd_db_(CB,CC,DB,car) CB illuminate_btn(CB,CC,car) Timing DatabaseTiming Cars ©  Mohammed  Assiri   Floors   {[f] | f ∈ Range}   Served Calls   {[(floor, time)] | floor ∈ Range, time ∈ R}   Cars’ Buttons   {(car id, ICB, USCB, UUCB) | car id ∈ Car ID, ICB ∈ Served calls, USCB ∈ Floors, UUCB ∈ Floors}   Calls’  Counters     {(specified call, unspecified call, next selection) | specified call ∈ Z, unspecified call ∈ Z, next selection ∈ Z}
v The Timing Car-Call Sub-model (Cont. ) Jun  1,  2015   49  ©  Mohammed  Assiri   Parameters   Legal values   Producing mode  {finite, infinite}   Times of finite car calls  {y | y ∈ Z ∧ 0 ≤ y}   The most desired floors  {[f] | f ∈ Range}   The frequency of most desired floors  {d | d ∈ Z ∧ 0 ≤ d}  
v The Timing System-cycle Sub-model Jun  1,  2015   50   CarsTiming Cars Timing_Cars initialize_tcars() Timing Cars out of service Timing_Cars DatabaseTiming Database Timing_Database initialize_tdatabase() Doors Doors initialize_counters () Database_Timing Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Car's_Buttons Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall's_Buttons warning to manager Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Maintain [mnt_guard(car,c)] 0 Restart [rst_guard(car)] Transfer [trn_guard(car)] Arrive [arr_guard(CB,car,cnt)] suspend(car) car car restart(car) car transfer(car) upd_trn(car,DB) DB cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB upd_susp(car,DB)DB DB upd_rst (car,DB) unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) reset_car's_btns(CB)CB return_hall_call (HB,car) HB log_hall(car) log_car(CB,CL,car)CL Timing Database Timing Database ©  Mohammed  Assiri  
v  The Timing System-cycle Sub-model (Maintenance Stage) Jun  1,  2015   51   CarsTiming Cars Timing_Cars initialize_tcars() out of service Timing_Cars Database_Timing Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() warning to manager Maintain [mnt_guard(car,c)] 0 Restart [rst_guard(car)] suspend(car) car car restart(car) upd_susp(car,DB)DB DB upd_rst (car,DB) reset_car's_btns(CB)CB return_hall_call (HB,car) HB ©  Mohammed  Assiri  
v The Timing System-cycle Sub-model (Arrival Stage) Jun  1,  2015   52   CarsTiming Cars Timing_Cars initialize_tcars() Doors Doors initialize_counters () Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Arrive [arr_guard(CB,car,cnt)] cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) log_hall(car) log_car(CB,CL,car)CL ©  Mohammed  Assiri  
v  The Timing System-cycle Sub-model (Arrival Stage Cont.) Jun  1,  2015   53   CarsTiming Cars Timing_Cars initialize_tcars() Doors Doors initialize_counters () Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Arrive [arr_guard(CB,car,cnt)] cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) log_hall(car) log_car(CB,CL,car)CL ©  Mohammed  Assiri   Colour  Sets     Defini1ons     Doors     {(car  id,  current  delivery  number,  deliveries’  total)  |  car  id  ∈  Car  ID,   current  delivery  number  ∈  Z  ,  deliveries’  total  ∈  Z}     Hall  Call  LOG     {(hall  call,  waiRng  Rme)  |  hall  call  ∈  Hall  Call,  waiRng  Rme  ∈  R}     Serving  Rmes     {[(floor,  serving  Rme)]  min  floor  ∈  Range,  serving  Rme  ∈  R}     Car  Call  LOG     {(car  id,  serving  Rmes)  |  car  id  ∈  Car  ID,  serving  Rmes  ∈  Serving   Times}    
5.  The Parking Optimizer Model Jun  1,  2015   54   elected floors Range Position ModelPosition Sub-modelPosition Sub-model Election ModelElection Sub-modelElection Sub-model Assignment ModelAssignment Sub-modelAssignment Sub-model ©  Mohammed  Assiri  
5.  The Parking Optimizer Model (Cont. ) Jun  1,  2015   55  ©  Mohammed  Assiri   The initial value of the parking floor is calculated generally by: 1.  Floors′ Number = (highest floor − lowest floor ) + 1 2.  Scope = |floors′ number ÷ cars′ number| 3.  Scope Head = ((scope ∗ car id) − (scope − 1)) + (lowest floor′s − 1) 4.  Scope Tail = (scope ∗ car id) + (lowest floor − 1) ∴ Spot(car id) = scope′s head (car id)
v The Election Sub-model Jun  1,  2015   56   elected floor counter INT 1`1 sorted list INT_List 1`[] candidate floors Floors_Statistics processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Prk SysPrk Sys Hall_Call Prk Sys elected floors Out Range Out Lock SysLock Sys INT 1`0 Lock Sys Elect Floor [elect_guard(tl,n,fs)] 3 Sort Floors' Recursion [sort_guard(n,fs)] 2 Count Call [count_guard(hall_call,fs,n,i)] 1 Sweepe Unelected Floors 5 upd_pcc(n,i,tl) hall_call upd_efc(tl,n) fs fs n update_list(tl,n) n count(hall_call,fs) i tlsort_recursion(fs,tl) n fsn+1 tl update_statistics(fs) (#floor fs) i 1i fs fs ©  Mohammed  Assiri  
v  The Election Sub-model (1. Counting The Placed Hall Calls) Jun  1,  2015   57   processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Prk SysPrk Sys Hall_Call Lock SysLock Sys INT 1`0 Count Call [count_guard(hall_call,fs,n,i)] 1 hall_call count(hall_call,fs)n fsn+1 i ©  Mohammed  Assiri   Floors  staRsRcs    {(floor,  Rmes)  |  floor  ∈  Range,  reputaRon  ∈  Z}     INT  List    {  [x]  |  x  ∈  Z  }    
v The Election Sub-model (2. Sorting The Floors) Jun  1,  2015   58   sorted list INT_List 1`[] candidate floors Floors_Statistics processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Lock SysLock Sys 1`0 Sort Floors' Recursion [sort_guard(n,fs)] 2 Sweepe Unelected Floors 5 fs fs n tlsort_recursion(fs,tl) update_statistics(fs) 1i fs ©  Mohammed  Assiri   Floors  staRsRcs    {(floor,  Rmes)  |  floor  ∈  Range,  reputaRon  ∈  Z}     INT  List    {  [x]  |  x  ∈  Z  }    
v  The Election Sub-model (3. Electing The Most Requested Floors) Jun  1,  2015   59   elected floor counter INT 1`1 sorted list INT_List 1`[] candidate floors Floors_Statistics elected floors Out Range Elect Floor [elect_guard(tl,n,fs)] 3 upd_efc(tl,n) update_list(tl,n) n tl (#floor fs) fs ©  Mohammed  Assiri  
v The Assignment Sub-model Jun  1,  2015   60   elected floor Range ID INT 1`0 identified floor Identified_Floor elected floors In Range In CarsCars Cars initialize_cars() Lock SysLock Sys INT 1`0 Lock Sys Count Elected Floors [count__guard()] 4 Assign ID to Floor 6 Alter Car's Parking Floor [alter_guard(car,f)] 7 n floor assign (n,floor) floor n-1 f car alter(car,f) iunlock(i) ii+1 nn+1 floor Cars ©  Mohammed  Assiri  
v The Assignment Sub-model (1. Processing The Floors) Jun  1,  2015   61   elected floor ID elected floors In Range Count Elected Floors Assign ID to Floor n floor floor n-1 nn+1 floor Range [count__guard()] 4 INT 1`0 6 ©  Mohammed  Assiri  
v  The Assignment Sub-model (2. Altering the Cars’ Parking Floors) Jun  1,  2015   62   identified floor Identified_Floor CarsCars Cars initialize_cars() Lock SysLock Sys INT 1`0 Assign ID to Floor 6 Alter Car's Parking Floor [alter_guard(car,f)] 7 assign (n,floor) f car alter(car,f) iunlock(i) ii+1 ©  Mohammed  Assiri   IdenRfied  Floor     {(floor  id,  floor’s  number)  |  floor  id  ∈  Car  ID,  floor’s  number  ∈  Range}    
v The Position Sub-model Jun  1,  2015   63   scopes req times Scope_Statistics cmpl nxt cmpl orders cmpl prv elected floors In Range new position Identified_Floor CarsCars Cars Lock SysLock Sys Identify Scope Count Scope's Elected Floors Identify Next Scope Decide Position Identify Previous Scope Alter Car's Parking Floor s s identify_prv(s,t) identify(s,floor) s s identify_nxt(s,t) s count_floors(s) decide(s) f car alter(car,f) iunlocksys(i) ii+1 t t floor s re_initialize(i) n INT 1`0 [scope_guard(s,floor)] 4 Scope initialize_scope() [n<>0] 6 Scope [prv_guard(s,t)] 7 Scope [nxt_guard(s,t)] 8 Scope 9 In [alter_guard(car,f)] 10 Cars Lock Sys initialize_cars() ©  Mohammed  Assiri  
v  The Position Sub-model (1. Identifying The Scope of Floors) Jun  1,  2015   64   scopes elected floors In Range Identify Scope identify(s,floor)s floor [scope_guard(s,floor)] 4 Scope initialize_scope() ©  Mohammed  Assiri   Scope   {(scope  id,  prev,  next,  elected  floors)  |  scope  id  ∈  Car  ID,  prev  ∈  Z,   next  ∈  Z,  elected  floors  ∈  INT  List}    
v  The Position Sub-model (2. Completing The Information of Scopes) Jun  1,  2015   65   scopes req times Scope_Statistics cmpl nxt cmpl orders cmpl prv Lock SysLock Sys Count Scope's Elected Floors Identify Next Scope Identify Previous Scope s s identify_prv(s,t) s s identify_nxt(s,t) count_floors(s) t t n INT 1`0 Scope initialize_scope() [n<>0] 6 Scope [prv_guard(s,t)] 7 Scope [nxt_guard(s,t)] 8 Scope ©  Mohammed  Assiri   Scope  StaRsRcs     {(scope  id,  floors’  number)  |  scope  id  ∈  Car  ID,  floors’  number  ∈  Z}    
v  The Position Sub-model (3. Altering the Cars’ Parking Floors) Jun  1,  2015   66   new position Identified_Floor CarsCars Cars Lock SysLock Sys Decide Position Alter Car's Parking Floor decide(s) f car alter(car,f) iunlocksys(i) ii+1 INT 1`0 9 [alter_guard(car,f)] 10 initialize_cars() ©  Mohammed  Assiri  
v  The Position Sub-model (3. Altering the Cars’ Parking Floors) Jun  1,  2015   67  ©  Mohammed  Assiri   The new parking floor of a scope is chosen according to the following rules: 1.  If the scope has many elected floors, then the floor of the highest reputation time is selected. 2.  If the scope has only one elected floor, then this floor is selected. 3.  If the scope has no elected floors, then the head floor or the tail floor of the scope is selected in account of elected floors of the lower and higher scopes.
v Introduction v Reachability Analysis v Simulation-based Performance Analysis 6.  The Analyses Jun  1,  2015   68  ©  Mohammed  Assiri  
v Introduction Jun  1,  2015   69  ©  Mohammed  Assiri   •  Various techniques and tools [van der Aalst and Stahl (2011)* ]. •  Reachability analysis is executed by the State Space tool to construct a graph of nodes and arcs, then report automatically some properties. •  Simulation-based performance analysis is by executing the model constantly while its data is being recorded, and then measured and compared. •  By simulator tool of CPN Tools and monitors (data-collectors and controller techniques) * Modeling Business Processes: A Petri Net-Oriented Approach. The MIT Press
v Reachability Analysis Jun  1,  2015   70  ©  Mohammed  Assiri   A  ParRal  Report  
v  The Report of The Data-collector of Simulation-based Performance Analysis Jun  1,  2015   71  ©  Mohammed  Assiri  
v  The Comparison between Two Algorithm though Simulation-based Performance Analysis. Jun  1,  2015   72  ©  Mohammed  Assiri  
v Discussion v Future Works v Questions 7.  Conclusion Jun  1,  2015   73  ©  Mohammed  Assiri  
v Future Works Jun  1,  2015   74  ©  Mohammed  Assiri   •  First, adopting more complex algorithms such as genetic algorithms. •  Second, resolving the state space explosion problem. •  Third, developing a Java-based extension that extracts and compares direct data from the proposed model with instance support of charts.
ü  Questions Jun  1,  2015   75  ©  Mohammed  Assiri  

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Modeling Elevator System With Coloured Petri Nets

  • 1. MODELING  ELEVATOR  SYSTEM     WITH  COLOURED  PETRI  NETS     By  MOHAMMED  ASSIRI   Jun  1,  2015   1  ©  Mohammed  Assiri  
  • 2. 1.  Introduction 2.  Coloured Petri Nets 3.  The Abstract Version of CPN-based Modelling of Elevator System 4.  The Timing Version of CPN-based Modelling of Elevator System 5.  The Parking Optimizer Model 6.  The Analyses 7.  Conclusion Outline:   Jun  1,  2015   2  ©  Mohammed  Assiri  
  • 3. v Elevator Systems v The Objective v Related Works v The Contributions 1. Introduction : Jun  1,  2015   3  ©  Mohammed  Assiri  
  • 4. •  Integral Part Of Buildings •  Very Complex o  Controlling Multiple Elevators By A Centralized Control Mechanism o  The Differences Among Buildings And Traffic Patterns v Elevator Systems Jun  1,  2015   4  ©  Mohammed  Assiri  
  • 5. Proposing a model of elevator system that fulfillments the constraints of the following definition [Ghezzi et al. (2003)]*: An elevator system is to be installed in a building with m floors and n cars. The elevator and the control mechanisms are supplied by the manufacturer. The problem concerns the logistics of moving cars between floors according to the following : * Fundamentals of Software Engineering. Pearson Prentice Hall, 2nd edition. v The Objective Jun  1,  2015   5  ©  Mohammed  Assiri  
  • 6. a.  Each elevator’s car has a set of buttons - one for each floor. Pressing these buttons signals the elevator to move to the corresponding floor. b.  On the wall outside the elevator each floor has two buttons (with the exception of the ground and the top floors). One button is pressed to request an upward moving elevator and another button is pressed to request a downward moving elevator. If both buttons are pressed, then each direction is assigned to a different car. c.  When an elevator has not received any requests for service, it should be held at its parking floor with its doors closed until it receives further requests. d.  All requests for elevators from floors (i.e. hall calls) must be serviced eventually. The applied algorithm controls the priority of floors. All requests for floors within elevators (i.e. car calls) must be serviced eventually, with floors usually serviced sequentially in the direction of travel. e.  Each elevator’s car has an emergency button which when pressed causes an alarm. The elevator is then deemed "out of service". Each elevator has a mechanism to cancel its "out of service" status. v The Objective (Cont.) Jun  1,  2015   6  ©  Mohammed  Assiri  
  • 7. •  Elevator system is one of the software engineering benchmarks to test the expressive power, readability and convenience of various formal specification techniques [Ghezzi et al. (2003)] •  It has been modeled many times in past and that includes Petri Nets: 1.  Petri net based dynamic scheduling of an elevator system [Lin and Fu (1996)]. 2.  Dynamic scheduling of elevator systems over hybrid Petri net/rule modeling [Huang and Fu (1998)]. 3.  Timed Petri net based approach for elevator group controls [Cho et al. (1999)]. 4.  Abstract Petri net based approach to problem solving in real time applications [Etessami and Hura (1989)] 5.  Petri net-based modeling and control of the multi-elevator systems [Ahmad et al. (2014)] 6.  Simulation of the intelligent control circuit based on Petri net [Ye et al. (2011)]. 7.  Requirements Engineering for Reactive Systems: Coloured Petri Nets for an Elevator Controller [Fernandes et al. (2007)] 8.  Modeling and analysis of elevator system based on timed-Coloured Petri net [Liqian et al. (2004)] v Related Works Jun  1,  2015   7  ©  Mohammed  Assiri  
  • 8. •  The independence of the number of floors and cars. •  Covering different stages of the elevator system in substantial details. •  The flexibility to adapt different algorithms and rules that govern real elevator system. •  May eventually evolve in a standard formal model of the elevator system. v The Contributions Jun  1,  2015   8  ©  Mohammed  Assiri  
  • 9. v Overview v Definition v Computer Tools 2.  Coloured Petri Nets Jun  1,  2015   9  ©  Mohammed  Assiri  
  • 10. •  Coloured Petri Nets (CPN) [Jensen (1981)*] is an extension of Petri Nets. It is a graphical language for constructing models of concurrent systems and analyzing their properties. •  CPN combines the capabilities of Petri Nets (as a graphical language) with the capabilities of Standard ML (as a high-level programming language). (next slides) * Coloured Petri Nets and the Invariant Method, Theoretical Computer Science v Overview Jun  1,  2015   10  ©  Mohammed  Assiri  
  • 11. v The Structure of CPN-Based Model Jun  1,  2015   11   placetransition arc inscription colour set token colours [guards] priority value ©  Mohammed  Assiri  
  • 12. •  The CPN ML language is a flexible, expressive, and extensible language founded on the functional programming Language: Standard ML (SML/NJ implementation). •  By CPN ML language, the CPN-based models have not only types and inscriptions, but also colour sets, token colours, variable declarations, and functions. v  CPN ML Language (A High-level Programming Language) Jun  1,  2015   12  ©  Mohammed  Assiri  
  • 13. Structure    DefiniRons   v Demo Jun  1,  2015   13   unilluminated buttons Buttons 1`{floor_location=2,illumination=off}++ 1`{floor_location=3,illumination=off} unilluminate(button) button button illuminate(button) illuminated buttons 1`{floor_location=1,illumination=on} Buttons illuminate unilluminate ©  Mohammed  Assiri  
  • 14. •  Semi-formal definition: A Coloured Peter Net is a tuple : CPN = (P,T,A,Σ,C,N,E,G,I) •  For more details and theory of CPN, please refer to Coloured Petri Nets Modelling and Validation of Concurrent Systems by Jensen and Kristensen (2009) v Definition Jun  1,  2015   14  ©  Mohammed  Assiri  
  • 15. •  CPN Tools v.4.0 from AIS Group, Eindhoven University of Technology, The Netherlands. (www.cpntools.org) •  The CPN Tools is composed of a graphical editor, a state space tool, and a simulator. •  Visualization v.0.1 a visual aid was developed to observe the modeled system. v Computer Tools Jun  1,  2015   15  ©  Mohammed  Assiri  
  • 16. 3.  The Abstract Version of CPN-based Modelling of Elevator System Jun  1,  2015   16  ©  Mohammed  Assiri  
  • 17. v The Abstract Car-Structure Sub-model Jun  1,  2015   17   CarsCarsCars DatabaseDatabaseDatabase Database initialize_database() Cars initialize_cars() ©  Mohammed  Assiri  
  • 18. Colour  Sets     Defini1ons     Car  ID    {  i  |i  ∈  Z+  ∧  i  ≤  total  number  of  cars}     Range    {  r  |  r  ∈  Z+  ∧  lowest  floor  ≤  r  ≤  highest  floor}     Status    {  idle,  emergency,  out  of  service,  up,  down  }     Desired  Floors    {  [l]  |  l  ∈  Range}     Call  Issuer    {  request,  system,  non,  reservaRon}     Cars     {  (car  id,  current  floor,  status,  parking  floor,   desired  floors,  call  issuer)  |  car  id  ∈  Car  ID,   current  floor  ∈  Range,  status  ∈  Status,  parking   floor  ∈  Range,  desired  floors  ∈  Desired  Floors,   call  issuer  ∈  Call  Issuer}     v The Abstract Car-Structure Sub-model (Cont. 1) Jun  1,  2015   18  ©  Mohammed  Assiri  
  • 19. Colour  Sets     Defini1ons     Car  Info     {(current  floor,  status,  desRnaRons,  car  id)  |   current  floor  ∈  Range,  status  ∈  Status,   desRnaRons  ∈  Desired  Floors,  car  id  ∈  Car  ID}     Database    {[d]  |  d  ∈  Car  Info}     v The Abstract Car-Structure Sub-model (Cont. 2) Jun  1,  2015   19  ©  Mohammed  Assiri  
  • 20. Parameter     Legal  value   Cars’  number    {n  |  n  ∈  Z+}     Lowest  floor  number    {f  |  f  ∈  Z+  ∧  f  <  highest  floor}     Highest  floors  number    {h  |  h  ∈  Z+  ∧  lowest  floor  <  h}     v The Abstract Car-Structure Sub-model (Cont. 3) Jun  1,  2015   20  ©  Mohammed  Assiri  
  • 21. v The Abstract Hall-Call Sub-model Jun  1,  2015   21   counter selected floor's num requested call floor's number CarsCars DatabaseDatabasePrk SysPrk SysPrk Sys all floors' numbers watch generators log Release Random Number Release Assign Hall Call Assign Direction n rn_random() new_call new_call car hall_call snd_hcall (car,hall_call) n+1 i i-1 i i new_call hall_call i i+1 asn_dir(new_call) hall_call db upd_db (hall_call, db,car) INT 1`1 () Range Range selected_floor INT 1`1 Hall_Call Hall_Call [rn_guard(n,i)] [r_guard(i)] [asn_hcall_guard (hall_call,car,db)] Hall_Call Database Database initialize_database() initialize_cars() Cars Cars ©  Mohammed  Assiri  
  • 22. v The Abstract Hall-Call Sub-model (Cont. 1) Jun  1,  2015   22   requested call Hall_Call CarsCars initialize_cars() DatabaseDatabase initialize_database() Prk SysPrk Sys Hall_Call log Hall_Call Assign Hall Call [asn_hcall_guard (hall_call,car,db)] car hall_call snd_hcall (car,hall_call) hall_call hall_call db upd_db (hall_call, db,car) Hall  Call   {(hall  call  floor,  status)  |  hall  call  floor  ∈  Range,  status  ∈  Status}     ©  Mohammed  Assiri  
  • 23. v The Abstract Hall-Call Sub-model (Cont. 2) Jun  1,  2015   23   The Rules 1.  The selected car is either idle or travelling toward the direction of the hall call, 2. The selected car is not reserved, 3. The selected car is elected by the applied algorithm which could be the nearest-car algorithm , the minimum-waiting algorithm , or the scope algorithm . ©  Mohammed  Assiri  
  • 24. v The Abstract Hall-Call Sub-model (Cont. 3) Jun  1,  2015   24   •  The nearest-car algorithm [Barney (2003a)1]: 1.  Analysing the token of place Database. a.  The cars with proper status are extracted from the token. b.  The distances between hall-call floor and cars’ current floors are calculated. 2.  The hall call is assigned to the car with minimum distance to the hall call floor. •  The minimum waiting algorithm: 3.  Calculating the stop times consumed by the already placed and being served calls between the floor of the new hall call and each car’s current floor. 4.  The car with the expected minimum waiting-time is assigned to serve the new hall call •  The scope algorithm [Barney (2003b)2]: H ≤ A ≤ T. where: H = the head floor of car’s scope A = the answered hall-call floors T = the tail floor of car’s scope 1 Elevator Traffic Handbook: Theory and Practice. 2 VerRcal  transportaRon  in  tall  buildings.     ©  Mohammed  Assiri  
  • 25. v The Abstract Hall-Call Sub-model (Cont. 4) Jun  1,  2015   25   counter selected floor's num floor's number all floors' numbers watch generators Release Random Number Release n rn_random() new_call new_call n+1 i i INT 1`1 () Range Range selected_floor INT 1`1 [rn_guard(n,i)] [r_guard(i)] ©  Mohammed  Assiri  
  • 26. v The Abstract Hall-Call Sub-model (Cont. 5) Jun  1,  2015   26   Parameters   Legal  values     Producing  mode    {finite,  infinite}     Times  of  finite  hall  calls    {y  |  y  ∈  Z  ∧  0  ≤  y}     The  most  requested  floor    {r  |  r  ∈  Range}     DuplicaRon  of  most  requested  floor    {d  |  d  ∈  Z  ∧  0  ≤  d}     The  applied  algorithm    {minimum  waiRng,  nearest,  scope}     Producing’  pause  number∗    {p  |  p  ∈  Z  ∧  0  <  p}     ©  Mohammed  Assiri  
  • 27. v The Abstract Hall-Call Sub-model (Cont. 6) Jun  1,  2015   27   requested call floor's number Assign Direction new_call asn_dir(new_call) Range Hall_Call ©  Mohammed  Assiri  
  • 28. v The Abstract Hall-Call Sub-model (Cont. 7) Jun  1,  2015   28   •  If the produced number equates the highest floor, then it is associated restrictedly with the down direction, •  Else if the produced number equates the lowest floor, then it is associated restrictedly with up direction. •  Otherwise, a produced number is associated non-deterministically with up direction or down direction. ü  Thus, a hall call of a valid floor’s number and an appropriate direction is produced correctly and completely. ©  Mohammed  Assiri  
  • 29. v The Abstract Car-call Sub-model Jun  1,  2015   29   CarsCarsCars log car call all floors' numbers counter specific floors' num DatabaseDatabase watch generator Coordinate Release Floor's Number Reproduce archive(car,car_call, new_call,sf)car_callcar snd_ccall(car, new_call,sf) new_call rn_random() n+1 n sf place_calls (car,sf) db upd_db_ (new_call, db,car,sf) i+1 i i i-1 car_call reproduce(sf)sf car INT 1`1[rfn_guard(n,i)]() RangeINT 1`1 Specific_Floors initialize_sfloors() [rep_guard (sf,car,car_call)] 0Car_Calls initialize_log()initialize_cars() CarsDatabase initialize_database() [coord_guard(car_call,car,sf,new_call)] Database ©  Mohammed  Assiri  
  • 30. v The Abstract Car-call Sub-model (Cont. 1) Jun  1,  2015   30   CarsCars log car call specific floors' num DatabaseDatabase Coordinate archive(car,car_call, new_call,sf)car_callcar snd_ccall(car, new_call,sf) new_call sf place_calls (car,sf) db upd_db_ (new_call, db,car,sf) Range Specific_Floors initialize_sfloors() Car_Calls initialize_log()initialize_cars() CarsDatabase initialize_database() [coord_guard(car_call,car,sf,new_call)] ©  Mohammed  Assiri   Specific  Floors    {(car  id,  specific  calls,  repeated  Rmes)  |  car  id  ∈  Car  ID,  Specific   calls  ∈  Desired  Floors,  repeated  Rmes  ∈  Z}    
  • 31. v The Abstract Car-call Sub-model (Cont. 2) Jun  1,  2015   31   car call all floors' numbers counter watch generator Release Floor's Number rn_random() n+1 n i+1 i INT 1`1 [rfn_guard(n,i)]() RangeINT 1`1 ©  Mohammed  Assiri   specific floors' num Reproduce reproduce(sf)sf Specific_Floors initialize_sfloors() [rep_guard (sf,car,car_call)]
  • 32. v The Abstract Car-call Sub-model (Cont. 3) Jun  1,  2015   32  ©  Mohammed  Assiri   Parameters     Legal  values     Producing  mode    {finite,  infinite}     Times  of  finite  car  calls    {x  |  x  ∈  Z  ∧  0  ≤  x}     Most  desired  floors    {[f]  |  f  ∈  Range}     Frequency  of  desired  floors    {d  |  d  ∈  Z  ∧  0  ≤  d}     Producing  pause  number    {p  |  p  ∈  Z+  }    
  • 33. v The Abstract System-cycle Sub-model Jun  1,  2015   33   CarsCars Cars initialize_cars() Cars out of service Cars error log Cars DatabaseDatabase Database initialize_database() Databasesuccess log Cars Doors Doors initialize_doors () Database Database initialize_database() Database Maintain [mnt_guard(car)] 0 Restart [rst_guard(car)] Transfer [trn_guard(car)] Arrive [arr_guard(car,door)] suspend (car) car car car restart(car) car transfer(car) upd_trn(car,db) db cararrive(car) car doordoor upd_arr(car,db) db upd_susp (car,db) db db upd_rst (car,db) ©  Mohammed  Assiri  
  • 34. v  The Abstract System-cycle Sub-model (The Maintenance) Jun  1,  2015   34   CarsCars out of service error log Database Database Maintain Restart suspend (car) car car car restart(car) upd_susp (car,db) db db upd_rst (car,db) Cars initialize_cars() [rst_guard(car)] Cars initialize_database() [mnt_guard(car)] 0 Cars ©  Mohammed  Assiri   Parameter     Legal  value     Restart  pending  cars  automaRcally     {”yes”,”no”  }    
  • 35. v The Abstract System-cycle Sub-model (The Transition) Jun  1,  2015   35   CarsCars DatabaseDatabase Database Transfer car transfer(car) upd_trn(car,db) db Cars initialize_cars() [trn_guard(car)] initialize_database() ©  Mohammed  Assiri  
  • 36. v The Abstract System-cycle Sub-model (The Arrival) Jun  1,  2015   36   CarsCars Cars initialize_cars() DatabaseDatabase Database initialize_database() success log Cars Doors Doors initialize_doors () Arrive [arr_guard(car,door)] cararrive(car) car doordoor upd_arr(car,db) db ©  Mohammed  Assiri  
  • 37. 4.  The Timing Version of CPN-based Modelling of Elevator System Jun  1,  2015   37  ©  Mohammed  Assiri   •  The abstract version concerns the logical movement of elevator system. In contrast, the timing version extends the abstract version to include the illumination of buttons , the calculation of waiting and serving times, and the limiting of cars’ stops.
  • 38. v The Timing Car-Structure Sub-model Jun  1,  2015   38   CarsTiming Cars Timing_Cars initialize_tcars() DatabaseTiming Database Timing_Database initialize_tdatabase() Timing DatabaseTiming Cars ©  Mohammed  Assiri  
  • 39. Colour  Sets     Defini1ons     Car  ID     {  i  |i  ∈  Z+  ∧  i  ≤  total  number  of  cars}     Range     {  r  |  r  ∈  Z+  ∧  lowest  floor  ≤  r  ≤  highest  floor}     Status   {  up,  down,  emergency,  idle,  out  of  service}     Desired  Floors   {  [l]  |  l  ∈  Range}     Call  Issuer   {  request,  system,  non,  reservaRon}     INT   {n  |  n  ∈  Z}     REAL   {r  |  r  ∈  R}   Timing  Hall  Call   {(hall  call,  direc1on,  1me)  |  hall  call  ∈  Range,  direc1on  ∈  Status,     1me  ∈  R}     Timing  Hall  Calls   {[h]  |  h  ∈  Timing  Hall  Call}     Timing  Cars   {(car  id,  current  floor,  status,  parking  floor,  desired  floors,  call  issuer,   Rme  period,  served  hall  calls,  stops  limitaRon  )  |  car  id  ∈  Car  ID,   current  floor  ∈  Range,  status  ∈  Status,  parking  floor  ∈  Range,  desired   floors  ∈  Desired  Floors,  call  issuer  ∈  Call  Issuer,  Rme  period  ∈  REAL,   served  hall  calls  ∈  Timing  Hall  Calls,  stops  limitaRon  ∈  INT}     v The Timing Car-Structure Sub-model (Cont. 1) Jun  1,  2015   39  ©  Mohammed  Assiri  
  • 40. Parameter     Legal  value   Stops’  limitaRon    {s  |  s  ∈  Z+  ∧s=0  ∨  1  ≤  s}     v The Timing Car-Structure Sub-model (Cont. 2) Jun  1,  2015   40  ©  Mohammed  Assiri     (Pseudocode)     func%on  stops’  limita%on  value  ()  =                  if  the  parameter  "stops’  limita%on"  =  0  then    return  random(1,  floors’  number);   else    return  the  parameter  "stops’  limita%on";  
  • 41. Colour  Sets     Defini1ons     Timing  Car’s  Data     {(current  floor,  status,  desRnaRons,  car  id,   Rme)  |  current  floor  ∈  Range,  status  ∈   Status,  desRnaRons  ∈  Desired  Floors,  car  id   ∈  Car  ID,  Rme  ∈  REAL}     Timing  Database    {[g]  |  g  ∈  Timing  Carʹ′s  Data}     v The Timing Car-Structure Sub-model (Cont. 3) Jun  1,  2015   41  ©  Mohammed  Assiri  
  • 42. v The Timing Hall-Call Sub-model Jun  1,  2015   42   Prk Sys Hall_Call Prk Sys CarsTiming Cars Timing_Cars initialize_tcars() Coordinator Coordinator initialize_coordination() Hall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall's_Buttons Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Release Hall Call [releas_guard(HB,C)] Assign Hall Call [asn_guard(rhc,car,DB)] Cupd_coord(HB,C) illuminate_hall_btn(HB,C) carasn_hcall(car,rhc) (#hall_call rhc) rhc hall_call(HB,C,DB) released(C) C HB DB upd_asn (car,rhc,DB) DB DB Timing Cars Timing Database ©  Mohammed  Assiri  
  • 43. v The Timing Hall-Call Sub-model (Releasing Hall Calls) Jun  1,  2015   43   Coordinator Coordinator initialize_coordination() Hall's_Buttons Hall's_Buttons initialize_halls'_buttons() Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Release Hall Call [releas_guard(HB,C)] Cupd_coord(HB,C) illuminate_hall_btn(HB,C) hall_call(HB,C,DB) HB DB DB ©  Mohammed  Assiri   Colour  Sets     Defini1ons     Hall  Call     {(hall  call  floor,  status)  |  hall  call  floor  ∈  Range,  status  ∈  Status  }     Hall  Calls     {[h]  |  h  ∈  Hall  Call}     Hall  BuOons     {(IB,  USB,  UUB)  |  IB  ∈  Hall  Calls,  USB  ∈  Hall  Calls,  UUB  ∈  Hall  Calls}     Coordinator   {(specified  call,  unspecified  call,  next  selec1on,  released  calls)  |  specified   call  ∈  Z,  unspecified  call  ∈  Z,  next  selec1on  ∈  Z,  released  calls  ∈  Z}    
  • 44. v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 2) Jun  1,  2015   44  ©  Mohammed  Assiri   Rules: 1.  The unilluminated-specified buttons (USB) list and unilluminated-unspecified buttons (UUB) list are not both empty, 2.  If the limit of producing calls is finite, then it has been not already reached, 3.  The number of produced calls is less than the value of parameter pause number
  • 45. v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 3) Jun  1,  2015   45  ©  Mohammed  Assiri   The choice of either USB list or UUB list is based on the following rules: 1.  When a list is empty, the other list is always selected. 2.  The difference between both lists’ length is less or equal to the value of parameter “The frequency of most requested hall calls”. 3.  The internal choice between tuples is sequential in USB list and arbitrary in UUB list.
  • 46. v  The Timing Hall-Call Sub-model (Releasing Hall Calls Cont. 1) Jun  1,  2015   46  ©  Mohammed  Assiri   Parameters   Legal values   Producing mode   {finite, infinite}   Times of finite hall calls   {y | y ∈ Z ∧ 0 ≤ y}   The most requested hall calls   {[(floor number, direction)] | floor number ∈ Range, direction ∈ Status}   The frequency of most requested hall calls   {d | d ∈ Z ∧ 0 ≤ d}   The applied algorithm of hall calls   {minimum waiting,nearest, scope}   The travel time   {t | t ∈ R+}   The average time of stop   {s | s ∈ R+}   Pause number   {p | p ∈ Z+}  
  • 47. v The Timing Hall-Call Sub-model (Assigning Hall Calls) Jun  1,  2015   47   Prk Sys Hall_Call CarsTiming Cars Timing_Cars initialize_tcars() Coordinator Coordinator initialize_coordination() Requested Hall Call Requested_Hall_Call DatabaseTiming Database Timing_Database initialize_tdatabase() Assign Hall Call [asn_guard(rhc,car,DB)] carasn_hcall(car,rhc) (#hall_call rhc) rhc released(C) C DB upd_asn (car,rhc,DB) ©  Mohammed  Assiri   Car’s Time   {(car id, time) | car id ∈ Car ID, time ∈ R}   Cars’ Times   {[c] | c ∈ Car′s Time}   Requested Hall Call   {(hall call, waiting times) | hall call ∈ Hall Call, waiting times ∈ Cars’ Times}   Coordinator     {(specified  call,  unspecified  call,  next  selecRon,  released  calls)  |  specified  call  ∈  Z,   unspecified  call  ∈  Z,  next  selecRon  ∈  Z,  released  calls  ∈  Z}    
  • 48. v The Timing Car-Call Sub-model Jun  1,  2015   48   CarsTiming Cars Timing_Cars initialize_tcars() Calls_Counters Calls_Counters initialize_coord () DatabaseTiming Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Car's_Buttons Place Car Call [plc_gaurd(CB,CC,car) ] CCupd_ccoord(CB,CC) DBcarsnd_ccall(CB,CC,car) upd_db_(CB,CC,DB,car) CB illuminate_btn(CB,CC,car) Timing DatabaseTiming Cars ©  Mohammed  Assiri   Floors   {[f] | f ∈ Range}   Served Calls   {[(floor, time)] | floor ∈ Range, time ∈ R}   Cars’ Buttons   {(car id, ICB, USCB, UUCB) | car id ∈ Car ID, ICB ∈ Served calls, USCB ∈ Floors, UUCB ∈ Floors}   Calls’  Counters     {(specified call, unspecified call, next selection) | specified call ∈ Z, unspecified call ∈ Z, next selection ∈ Z}
  • 49. v The Timing Car-Call Sub-model (Cont. ) Jun  1,  2015   49  ©  Mohammed  Assiri   Parameters   Legal values   Producing mode  {finite, infinite}   Times of finite car calls  {y | y ∈ Z ∧ 0 ≤ y}   The most desired floors  {[f] | f ∈ Range}   The frequency of most desired floors  {d | d ∈ Z ∧ 0 ≤ d}  
  • 50. v The Timing System-cycle Sub-model Jun  1,  2015   50   CarsTiming Cars Timing_Cars initialize_tcars() Timing Cars out of service Timing_Cars DatabaseTiming Database Timing_Database initialize_tdatabase() Doors Doors initialize_counters () Database_Timing Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Car's_Buttons Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall's_Buttons warning to manager Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Maintain [mnt_guard(car,c)] 0 Restart [rst_guard(car)] Transfer [trn_guard(car)] Arrive [arr_guard(CB,car,cnt)] suspend(car) car car restart(car) car transfer(car) upd_trn(car,DB) DB cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB upd_susp(car,DB)DB DB upd_rst (car,DB) unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) reset_car's_btns(CB)CB return_hall_call (HB,car) HB log_hall(car) log_car(CB,CL,car)CL Timing Database Timing Database ©  Mohammed  Assiri  
  • 51. v  The Timing System-cycle Sub-model (Maintenance Stage) Jun  1,  2015   51   CarsTiming Cars Timing_Cars initialize_tcars() out of service Timing_Cars Database_Timing Database Timing_Database initialize_tdatabase() Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() warning to manager Maintain [mnt_guard(car,c)] 0 Restart [rst_guard(car)] suspend(car) car car restart(car) upd_susp(car,DB)DB DB upd_rst (car,DB) reset_car's_btns(CB)CB return_hall_call (HB,car) HB ©  Mohammed  Assiri  
  • 52. v The Timing System-cycle Sub-model (Arrival Stage) Jun  1,  2015   52   CarsTiming Cars Timing_Cars initialize_tcars() Doors Doors initialize_counters () Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Arrive [arr_guard(CB,car,cnt)] cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) log_hall(car) log_car(CB,CL,car)CL ©  Mohammed  Assiri  
  • 53. v  The Timing System-cycle Sub-model (Arrival Stage Cont.) Jun  1,  2015   53   CarsTiming Cars Timing_Cars initialize_tcars() Doors Doors initialize_counters () Car's_ButtonsCar's_Buttons Car's_Buttons initialize_car's_buttons () Hall's_ButtonsHall's_Buttons Hall's_Buttons initialize_halls'_buttons() Hall Call LOG Hall_Call_LOG Car Call LOG Car_Call_LOG initialize_car_call_log () Arrive [arr_guard(CB,car,cnt)] cararrive(car,cnt) upd_cnt(car,cnt) cnt upd_arr(car,DB) DB unilluminate_hall_btn (HB,car) HBCB unilluminate_btn (CB,car) log_hall(car) log_car(CB,CL,car)CL ©  Mohammed  Assiri   Colour  Sets     Defini1ons     Doors     {(car  id,  current  delivery  number,  deliveries’  total)  |  car  id  ∈  Car  ID,   current  delivery  number  ∈  Z  ,  deliveries’  total  ∈  Z}     Hall  Call  LOG     {(hall  call,  waiRng  Rme)  |  hall  call  ∈  Hall  Call,  waiRng  Rme  ∈  R}     Serving  Rmes     {[(floor,  serving  Rme)]  min  floor  ∈  Range,  serving  Rme  ∈  R}     Car  Call  LOG     {(car  id,  serving  Rmes)  |  car  id  ∈  Car  ID,  serving  Rmes  ∈  Serving   Times}    
  • 54. 5.  The Parking Optimizer Model Jun  1,  2015   54   elected floors Range Position ModelPosition Sub-modelPosition Sub-model Election ModelElection Sub-modelElection Sub-model Assignment ModelAssignment Sub-modelAssignment Sub-model ©  Mohammed  Assiri  
  • 55. 5.  The Parking Optimizer Model (Cont. ) Jun  1,  2015   55  ©  Mohammed  Assiri   The initial value of the parking floor is calculated generally by: 1.  Floors′ Number = (highest floor − lowest floor ) + 1 2.  Scope = |floors′ number ÷ cars′ number| 3.  Scope Head = ((scope ∗ car id) − (scope − 1)) + (lowest floor′s − 1) 4.  Scope Tail = (scope ∗ car id) + (lowest floor − 1) ∴ Spot(car id) = scope′s head (car id)
  • 56. v The Election Sub-model Jun  1,  2015   56   elected floor counter INT 1`1 sorted list INT_List 1`[] candidate floors Floors_Statistics processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Prk SysPrk Sys Hall_Call Prk Sys elected floors Out Range Out Lock SysLock Sys INT 1`0 Lock Sys Elect Floor [elect_guard(tl,n,fs)] 3 Sort Floors' Recursion [sort_guard(n,fs)] 2 Count Call [count_guard(hall_call,fs,n,i)] 1 Sweepe Unelected Floors 5 upd_pcc(n,i,tl) hall_call upd_efc(tl,n) fs fs n update_list(tl,n) n count(hall_call,fs) i tlsort_recursion(fs,tl) n fsn+1 tl update_statistics(fs) (#floor fs) i 1i fs fs ©  Mohammed  Assiri  
  • 57. v  The Election Sub-model (1. Counting The Placed Hall Calls) Jun  1,  2015   57   processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Prk SysPrk Sys Hall_Call Lock SysLock Sys INT 1`0 Count Call [count_guard(hall_call,fs,n,i)] 1 hall_call count(hall_call,fs)n fsn+1 i ©  Mohammed  Assiri   Floors  staRsRcs    {(floor,  Rmes)  |  floor  ∈  Range,  reputaRon  ∈  Z}     INT  List    {  [x]  |  x  ∈  Z  }    
  • 58. v The Election Sub-model (2. Sorting The Floors) Jun  1,  2015   58   sorted list INT_List 1`[] candidate floors Floors_Statistics processed call counter INT 1`0 floors statistics Floors_Statistics initialize_statistics() Lock SysLock Sys 1`0 Sort Floors' Recursion [sort_guard(n,fs)] 2 Sweepe Unelected Floors 5 fs fs n tlsort_recursion(fs,tl) update_statistics(fs) 1i fs ©  Mohammed  Assiri   Floors  staRsRcs    {(floor,  Rmes)  |  floor  ∈  Range,  reputaRon  ∈  Z}     INT  List    {  [x]  |  x  ∈  Z  }    
  • 59. v  The Election Sub-model (3. Electing The Most Requested Floors) Jun  1,  2015   59   elected floor counter INT 1`1 sorted list INT_List 1`[] candidate floors Floors_Statistics elected floors Out Range Elect Floor [elect_guard(tl,n,fs)] 3 upd_efc(tl,n) update_list(tl,n) n tl (#floor fs) fs ©  Mohammed  Assiri  
  • 60. v The Assignment Sub-model Jun  1,  2015   60   elected floor Range ID INT 1`0 identified floor Identified_Floor elected floors In Range In CarsCars Cars initialize_cars() Lock SysLock Sys INT 1`0 Lock Sys Count Elected Floors [count__guard()] 4 Assign ID to Floor 6 Alter Car's Parking Floor [alter_guard(car,f)] 7 n floor assign (n,floor) floor n-1 f car alter(car,f) iunlock(i) ii+1 nn+1 floor Cars ©  Mohammed  Assiri  
  • 61. v The Assignment Sub-model (1. Processing The Floors) Jun  1,  2015   61   elected floor ID elected floors In Range Count Elected Floors Assign ID to Floor n floor floor n-1 nn+1 floor Range [count__guard()] 4 INT 1`0 6 ©  Mohammed  Assiri  
  • 62. v  The Assignment Sub-model (2. Altering the Cars’ Parking Floors) Jun  1,  2015   62   identified floor Identified_Floor CarsCars Cars initialize_cars() Lock SysLock Sys INT 1`0 Assign ID to Floor 6 Alter Car's Parking Floor [alter_guard(car,f)] 7 assign (n,floor) f car alter(car,f) iunlock(i) ii+1 ©  Mohammed  Assiri   IdenRfied  Floor     {(floor  id,  floor’s  number)  |  floor  id  ∈  Car  ID,  floor’s  number  ∈  Range}    
  • 63. v The Position Sub-model Jun  1,  2015   63   scopes req times Scope_Statistics cmpl nxt cmpl orders cmpl prv elected floors In Range new position Identified_Floor CarsCars Cars Lock SysLock Sys Identify Scope Count Scope's Elected Floors Identify Next Scope Decide Position Identify Previous Scope Alter Car's Parking Floor s s identify_prv(s,t) identify(s,floor) s s identify_nxt(s,t) s count_floors(s) decide(s) f car alter(car,f) iunlocksys(i) ii+1 t t floor s re_initialize(i) n INT 1`0 [scope_guard(s,floor)] 4 Scope initialize_scope() [n<>0] 6 Scope [prv_guard(s,t)] 7 Scope [nxt_guard(s,t)] 8 Scope 9 In [alter_guard(car,f)] 10 Cars Lock Sys initialize_cars() ©  Mohammed  Assiri  
  • 64. v  The Position Sub-model (1. Identifying The Scope of Floors) Jun  1,  2015   64   scopes elected floors In Range Identify Scope identify(s,floor)s floor [scope_guard(s,floor)] 4 Scope initialize_scope() ©  Mohammed  Assiri   Scope   {(scope  id,  prev,  next,  elected  floors)  |  scope  id  ∈  Car  ID,  prev  ∈  Z,   next  ∈  Z,  elected  floors  ∈  INT  List}    
  • 65. v  The Position Sub-model (2. Completing The Information of Scopes) Jun  1,  2015   65   scopes req times Scope_Statistics cmpl nxt cmpl orders cmpl prv Lock SysLock Sys Count Scope's Elected Floors Identify Next Scope Identify Previous Scope s s identify_prv(s,t) s s identify_nxt(s,t) count_floors(s) t t n INT 1`0 Scope initialize_scope() [n<>0] 6 Scope [prv_guard(s,t)] 7 Scope [nxt_guard(s,t)] 8 Scope ©  Mohammed  Assiri   Scope  StaRsRcs     {(scope  id,  floors’  number)  |  scope  id  ∈  Car  ID,  floors’  number  ∈  Z}    
  • 66. v  The Position Sub-model (3. Altering the Cars’ Parking Floors) Jun  1,  2015   66   new position Identified_Floor CarsCars Cars Lock SysLock Sys Decide Position Alter Car's Parking Floor decide(s) f car alter(car,f) iunlocksys(i) ii+1 INT 1`0 9 [alter_guard(car,f)] 10 initialize_cars() ©  Mohammed  Assiri  
  • 67. v  The Position Sub-model (3. Altering the Cars’ Parking Floors) Jun  1,  2015   67  ©  Mohammed  Assiri   The new parking floor of a scope is chosen according to the following rules: 1.  If the scope has many elected floors, then the floor of the highest reputation time is selected. 2.  If the scope has only one elected floor, then this floor is selected. 3.  If the scope has no elected floors, then the head floor or the tail floor of the scope is selected in account of elected floors of the lower and higher scopes.
  • 68. v Introduction v Reachability Analysis v Simulation-based Performance Analysis 6.  The Analyses Jun  1,  2015   68  ©  Mohammed  Assiri  
  • 69. v Introduction Jun  1,  2015   69  ©  Mohammed  Assiri   •  Various techniques and tools [van der Aalst and Stahl (2011)* ]. •  Reachability analysis is executed by the State Space tool to construct a graph of nodes and arcs, then report automatically some properties. •  Simulation-based performance analysis is by executing the model constantly while its data is being recorded, and then measured and compared. •  By simulator tool of CPN Tools and monitors (data-collectors and controller techniques) * Modeling Business Processes: A Petri Net-Oriented Approach. The MIT Press
  • 70. v Reachability Analysis Jun  1,  2015   70  ©  Mohammed  Assiri   A  ParRal  Report  
  • 71. v  The Report of The Data-collector of Simulation-based Performance Analysis Jun  1,  2015   71  ©  Mohammed  Assiri  
  • 72. v  The Comparison between Two Algorithm though Simulation-based Performance Analysis. Jun  1,  2015   72  ©  Mohammed  Assiri  
  • 74. v Future Works Jun  1,  2015   74  ©  Mohammed  Assiri   •  First, adopting more complex algorithms such as genetic algorithms. •  Second, resolving the state space explosion problem. •  Third, developing a Java-based extension that extracts and compares direct data from the proposed model with instance support of charts.
  • 75. ü  Questions Jun  1,  2015   75  ©  Mohammed  Assiri