DEEM User`s Manual
Contents
1. number func_basic func_name arith_opl gt SQRT arith_op2 gt s er Xf Mer NAD arith_opn gt min max mean number gt digit digit digit exponent digit Digit digit exponent digit gt 30 b an 39 exponent gt e digit digit func_basic gt mark place_name number of Token in lt place_name gt place name y Nu uu Nu Nu uN VAR variable_name declaration of variable lt variable_name gt predicate gt predicate NOT predicate predicate bool_arith predicate func compare func TRUE FALSE bool_arith gt AND OR EOR NOR NAND compare gt lt gt gt lt gt lt Chapter 2 User Interface Same examples VAR A mark Place_2 e IF mark Place_1 lt 2 AND mark Place_2 0 THEN VAR M ELSE 0 001 The Enabling Function syntax is nab gt predicat predicate gt predicate NOT predicate predicate bool_arith predicate func compare func TRUE FALSE Same examples mark Place_2 gt 1 e mark Place_1 1 OR mark Place_3 lt 4 The property window associated with the arcs Figure 2 4 contains the following fields Place specifies the name of the place the arc is a2. element The property window of an object can also be opened by clicking with the right button on it 2 3 2 Property Window A property window is associated with each element place transition or arc Place Name Paces Tokens fa Capacity no limit footy cance Figure 2 2 Property window associated with the place The property window associated with a place shown in Figure 2 2 contains the following fields Place Name specifies the name of the place Token defines the number of tokens that the place contains at the beginning of the computation 1 N B in the following we will call DEEM_buttons all the buttons shown by the DEEM interface in the working window Chapter 2 User Interface Capacity specifies the maximum number of tokens that a place can have during the computation Name Trans _1 Orientation wv Horizontal Vertical Transition Type Timed 1 Deterministic Time Function IMARK Place_1 2 Enabling function Copy from list to Rate function field 1 Copy Apply Cancel Help Figure 2 3 Property window associated with the transition The property window associated with the transitions shown in Figure 2 3 contains the following fields Transition Name specifies the name of the transition Orientation specifies the horizontal or vertical orientation of the transition Transition Type specifies the type of the transition Trans
3. equation V t E t K t V t where K t and E t are the global and local kernel matrices 4 and is the convolution operator Instead of directly attacking the solution of the generalised Markov renewal equation by numerical algorithms or Laplace Stiltjes transform DEEM computes matrix V t according to the analytical method proposed in 5 6 5 2 The solution algorithm The following equation r 1 Q Q6 V _ t Ile A ad e allows to evaluate V t through the separate analysis of the various alternative paths which compose the mission and only requires the derivation of matrix exponentials eQit and Ai j gt i j 1 2 n which can be automatically obtained when the reachability graph is generated The solutions of the DSPN model is thus reduced to the cheaper problem of solving a set of homogeneous time continuos smaller Markov chains To compute the dependability figures of the system DEEM derives the probability vector P t of each marking in SN at time t We can obtain P r from the transient probability matrix V t with the equation P t P V t where P is the initial probability vector of the DSPN To compute P t and then the dependability figures of the system the solution engine of DEEM takes as input the DSPN model and its initial probability vector P and performs the following algorithm 1 Chapter 4 Results and output files Builds RGP the reachability graph of the PhN sub model This graph
4. Graphical User Interface of DEEM 2 1 Some general information about DEEM DEEM possesses a GUI inspired by 2 and realized using an X11 installation with Motif runtime Libraries which the user employs to define his model of a MPS DEEM provides two logically separate parts to represent MPS models One is the System Net SN which represents the failure repair behaviour of system components the other is the Phase Net PhN which represents the execution of the various phases For this reason the working area is split in two fields as shown in Figure 2 1 fe DEEM 1 0 beta 15 unnamed File Edit Insert i DEEM 1 0 beta 15 2000 University of Horence and CNUCE CNR Pisa J Figure 2 1 DEEM interface The SN area may contain only exponentially distributed and immediate transitions whereas in the PhN area the transitions may be deterministic or immediate In a PhN model a token in a place represents the execution of a phase and the firing of a deterministic transition the beginning of the next phase In general the execution of a phase is represented by each marking enabling only one deterministic transition DEEM employs the DSPN formalism 1 to model a MPS DSPN extends Generalised Stochastic Petri Nets and Stochastic Reward Nets so to allow the exact modelling of events with deterministic occurrence times Chapter 2 User Interface According to this the GUI uses the following objects to create a model Places e
5. confirm Following the specifications of our SMS example properties to the places of figure 3 9 are assigned as follows Change the name Place_1 in P1 P1 represents the phase of Mission 1 and its initial number of tokens is 1 The global mission starts at place P1 Change the name Place_2 in Stop1 Stop is necessary because Mission 2 can begin only if component A did not fail If A failed the system waits in Stop1 the repair of this component Change the names Place_3 and Place_4 in P2 and P3 respectively These places represent the two phases of Mission2 Change the name Place_5 in Stop2 Stop2 is necessary because Mission 1 can begin only if component A and B did not fail If A and B failed the system waits in Stop2 the repair of the component s Change the name Place_6 in Count Count is the place that stores the number of cycles executed Change the name Place_7 in Aok Aok represents the state healthy of component A Its initial number of tokens is 1 at start time the component is healthy 15 Chapter 3 How to create and solve a Model an example Change the name Place_8 in Afail A token in Afail represents the failure of component A Change the name Place_9 in Bok Bok represents the state healthy of component B It s initial number of tokens is 1 at start time the component is healthy Change the name Place_10 in Bfail A token in Bfail represents the failure of component B Change th
6. contains the measures evaluated for the study studyname in a format which can be further elaborated by gnuplot It is possible to open the file Filename studyname spreadsheet using some spreadsheets programs like EXCEL Microsoft for any graphical representation An example of this type of file is shown below KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKK KAKK DEEM Dependability Modeling and Evaluation K Version 1 0 beta 2 C 2000 by Istituto CNUCE CNR Ghezzano Pisa ITALY a KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KKK EK This file was generated Tue Jul 11 15 03 21 2000 STUDY_NAME Study_3 STUDY_variables_setting Time 1 500000e 03 lb 0 0001 0 01 10 p 9 500000e 01 alfa 1 2 5 REW_MEASURE_NAME Reliability PREDICATE mark Afail mark Bfail lt 2 REW_FUNCTION 1 lb alfa 1 000000e 00 2 000000e 00 5 000000e 00 25 Chapter 4 Results and output files 1 000000e 04 9 941818e 01 9 907599e 01 9 813445e 01 1 000000e 03 9 440268e 01 9 132017e 01 8 353453e 01 1 000000e 02 6 015980e 01 4 783397e 01 3 020994e 01 REW_MEASURE_NAME Unreliability PREDICATE mark Afail mark Bfail 2 REW_FUNCTION 1 lb alfa 1 000000e 00 2 000000e 00 5 000000e 00 1 000000e 04 5 818176e 03 9 240130e 03 1 865547e 02 1 000000e 03 5 597324e 02 8 679829e 02 1 646547e 01 1 000000e 02 3 984020e 01 5 2
7. for the MPS from P according to the standard computation algorithms The main computational cost of the DEEM solution algorithm is that required for the transient solutions steps 2 and 3 and the multiplications in step 5 2 of the algorithm sketched in the previous section Notice that the DEEM approach to generate the required matrices ever requires to handle the entire state space of the MRGP process 28 Appendix Installation To use DEEM do the following visit http bonda cnuce cnr it DEEM to obtain the license file deemlicense and drop this file in your home directory unzip and untar the file deem releasenumber bin arch tar gz set the environment variable DEEM_HOME to the path of the installation directory of DEEM here is an example of lines that could be added to someone s cshre assuming use of C shell to execute deem T T EMHOME deem_models SDEEMHOME bin deems amp alias deem cd D T EM_HOME where is DEEM setenv D to invoke DEEM run deem from the command line prompt Please report any bugs to silvano chiaradonna cnuce cnr it Tool Oraganization and File Structure This paragraph gives the organization of DEEM and its file structure Figure A 1 input output flow gt execute program data file D executable program netname Parameters List Studies List PhN and SN Description Reward
8. instantaneous It is possible to define several measures to be evaluated together in a study Click on the Apply button and a new row for inserting the name reward function and analysis type flag will appear below the previously defined measure s E g if the Unreliability would have been of interest too click on Apply and fill the new field with the appropriate values that is 1 Unreliability ii IF mark Afail mark Bfail gt 2 THEN 1 both components A and B are failed thus leading to the failure of the system ii click on instantaneous To confirm and close the Measure window click on OK The figure 3 13 shows how the measures are defined 19 Chapter 3 How to create and solve a Model an example Figure 3 13 Measures defined for the SMS model 3 6 Transient analysis The model evaluation follows the above described steps To evaluate a model select Transient Analysis in Compute Menu The study under evaluation is the current study as defined in the parameters window To start the analysis click on OK The figure 3 14 shows an example Figure 3 14 Transient analysis for the study Study_1 20 Results and output files The Transient analysis produces various types of files with different extensions Some describe intermediate information useful for debugging a model or to trace the evaluation process they are the files mc and rg others contain numerical results of the evaluation This c
9. iterations that has to be considered by the transient solution method When Run in the Background mode is selected graphic interface of DEEM can still be used while the solver is running In the Verbose mode more information about the solution is showed on the shell while the solver is running In Computation Time Info mode information about the analysis times is produced Save State Distr mode permits to save in file netname studyname sdistro the state distribution of the net at the end of the transient analysis Load State Distr mode permits to load from file netname studyname sdistri the state distribution of the net at initial time of the transient analysis The field Current Study shows the study selected for the analysis and the field Measure shows the measures that are calculated The OK button makes the analysis to start 2 8 Menu The Menu contains some information about DEEM version Xserver Xclient the creator The figure 2 8 shown this window DEEM Project DEpendability Evaluation of Multiple phased mission systems Version 1 0 beta 15 Elaborated in 2000 by Andrea Bondavalli University of Florence Silvano Chiaradonna Istituto CNUCE CNR Pisa Roberto Filippini Istituto CNUCE CNR Pisa Ivan Mura Istituto CNUCE CNR Pisa Simona Poli Istituto CNUCE CNR Pisa Francesca Sandrini Istituto CNUCE CNR Pisa x server pcbonda cnuce cnr it x client mammolo cnuce cnr it 0 0 Figure 2 8 Informatio
10. 16603e 01 6 979006e 01 Figure 4 14 shows the plot of the Reliability generated by EXCEL Microsoft from the output file of the DEEM transient analysis Reliability 1 00E 00 9 00E 01 8 00E 01 7 00E 01 6 00E 01 5 00E 01 4 00E 01 3 00E 01 2 00E 01 1 00E 01 0 00E 00 1 00E 04 1 00E 03 1 00E 02 Failure rate of B Figure 4 14 Reliability of the system 26 Transient Solver DEEM provides a specific and efficient analytical solution for MPS models This chapter describes the DEEM s solution algorithm 5 1 The analytical technique The specialised solution finds its ground by observing that the only deterministic transitions in a DSPN model of a MPS are the phase duration and that these transitions are enabled one at a time Thus the marking process M t t20 of the DSPN is a Markov Regenerative Process MRGP 4 for which the firing times of the deterministic transitions are indeed regeneration points Moreover the following property holds of the DSPN model of a MPS Property 1 in every non absorbing marking of the DSPN there is always one deterministic transition enabled which corresponds to the phase being currently executed The general solution method for MRGP processes considers computing matrix V t whose entry m m is the occupation probability of marking m at time t20 given the initial marking m Matrix V t is the solution to the generalised Markov renewal
11. Contents TUCO OR ater cas asf penal E choc A eid lds ee tata eas die esate 1 User Imterlace n sen enia re akae na E EEEE EET ASEE 2 2 1 Some general information about DEEM ssssssssssssresssrrrrerererrrereesesss 2 22 File UMC Wed taal asr E E E E ES 3 2D TU IGT E E E A E ha ete Ue 3 2 5 1 Baoit COMMANAS iscissi noi a a yaad eyedi eases eeeeset yeas 4 2 3 2 Property WWATIOOW 6 o5 550 vce sa we tae aaa sae ocean oa oe dana es ee eaten 4 24 Insert Menti rosers Sueteeratils sur secte tel uneden E AE EEA ren culty cues ely 8 2 5 Special Ment esas ecw dati aa E a aia ra eek Ge a aa 8 2 6 ZOOM Menu ei osred inane Ea TEOT ETE SEA R EIEEE RETETE TEE Maw INEA 9 Ze C mp te Menis etna chou r ae TE E EEE E E RETEN 9 shell Parameters e eea R e E ETEA ea atlas 9 T MESE T a AT SA 10 2 7 3 Transient Analysis lt j sscjeddceskeeuageedasea pedis edb seg eaderdegaevedas sends 12 De PINE ance asco At way eae eae tated Gea ao 7 oe a Nas OERA T TO E T 13 How to create and solve a Model an example ccceeeceeeeee ence eeneeeaes 14 Sol Ar working example ssiri sce heaved i nE ER hones serenade sizhann desde 14 3 2 Creation of the graphical Model gii33564 esigissaceicasneddeneeasoerdssvaavaowiaageeas 14 3 3 Properties of places transitions and arcs cece eee cece cence een eeeeeeees 15 3 4 Values of the parameters and studies osssesessseeessseeresssersesseere 17 3 5 Definition of the MEASTIT ES a5 5 laisse sects anaes s
12. Count In reachgraph 0_1 0_0 6 1 000000e 00 means that state 0_1 can be reached from state 0_0 by the firing of transition 6 T1 which rate is 1 000000e 00 KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK DEEM Dependability Modeling and Evaluation Version 1 0 beta 2 C 2000 by Istituto CNUCE CNR Ghezzano Pisa ITALY X kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkxkxkxkkxkxkxkxkxkxkxkxkxkkkkxkxkkkkkkxkxx k This file was generated Tue Jul 11 15 02 24 2000 _nplace 11 _ntrans 11 _places 0 P1 14 EP23 22 B37 3 Aok 4 Afail 5 Count 6 Stop2 7 Bok 8 Bfail 9 Stopl 10 repair_B _transitions 0 Yes_repair_A 1 yes_repair_B 22 g 1 _ntanmark _nabsmark _nvanmark _nvanloop _nentries _reachset 0 Ort 0 Tcount Tstopl ok_repair nok_repair T1 T2 fA T3 B 150 1 0 150 0_t 0 1 tot Lely 226 221g 3 2t 0 4 t 1 5_t 2 6_t 0 Second part of file _reachgraph 0_0 o_1 0_0 6 0_2 0137 0_3 0_2 9 0_4 Owe 0_5 0_4 7 0_6 O59 1 000000e4 1 000000e4 1 000000e4 1 000000e4 1 000000e4 1 000000e1 00 00 00 00 00 00 23 Chapter 4 Results and output files Chapter 4 Results and output files 4 2 The files created for each phase The transient analysis creates three different files during the a
13. Measures List Composed Measures List netname studyname distri Initial States Distribution by command line by command line Transient Solver Graphical User Interface Report Generator 4 option Final States Distribution Evaluated Measures Evaluated Measures netname studyname distro netname studyname spreadsheet netname studyname gnuplot netname information in LATEX format netname tex Figure A 1 Organization of DEEM and its file structure 1 Bibliography M Ajmone Marsan and G Chiola On Petri nets with deterministic and exponentially distributed firing times Lecture Notes in Computer Science Vol 266 pp 132 145 1987 S Allmaier and S Dalibor PANDA Petri net analysis and design assistant in Proc Performance TOOLS 97 Saint Malo France 1997 A Bondavalli I Mura and K S Trivedi Dependability Modelling and Sensitivity Analysis of Scheduled Maintenance Systems in Proc EDCC 3 European Dependable Computing Conference Prague Czech Republic 1999 pp 7 23 H Choi V G Kulkarni and K S Trivedi Transient analysis of deterministic and stochastic Petri nets in Proc 14th International Conference on Application and Theory of Petri Nets Chicago IL 1993 pp 166 185 I Mura and A Bondavalli Markov Regenerative Stochastic Petri Nets to Model and Evaluate the Dependability of Phased Missions IEEE Transactions on Computers to appear Vol pp 2001 I M
14. Study The window shows the study list and the values of the variables of the current study Figure 2 5 Value ny f A Fi ia Current Study Study _1 Open Study New Study Delete Study oK Cancel Help Figure 2 5 Parameters and studies window Chapter 2 User Interface The values of the variables can be specified in the following way value gt number example A 0 01 range example A 1 7 2 1 3 5 7 or A 1 8 2 1 2 4 8 value_set example A 0 0002 0 009 0 002 0 09 0 02 The first two values of range represent the interval of variability for the parameter A the last value represents the incremental step to be added or multiplied to obtain the intermediate values in the set As a default the incremental step is added and it is represented by a or nothing before the last value For a multiplying incremental step a has to be put before the last value Each set of values of the variables one numerical value for each variable corresponds to an experiment evaluation run 2 7 2 Measures Compute gt Measures permits to define the measures Measures are defined by a Name a reward function and an analysis type flag ist cum or tim_av for instantaneous cumulated and timed averaged analysis respectively The analysis type flag is set clicking on the relative button Composed measures also can be defined through an expression co
15. Transitions Arcs Besides the introduction of deterministic transitions DEEM makes available a set of modeling features that significantly improve DSPN expressiveness the firing rates of timed transitions may be specified through arbitrary marking dependent functions these functions may be employed to include additional enabling conditions guards to the specification of the transitions rewards rates can be defined as arbitrary marking dependent functions arcs cardinalities may depend on the marking of the model To draw a correct PhN it is necessary that the reachability graph associated with the PhN be a tree or an acyclic graph Even if the behaviour of the system is represented by a loop after n phases the some phases are repeated that is the only condition to draw a correct PhN 2 2 File Menu The File Menu is used to create a new model to open or close a model to save the created or modified model to assign a name to the net and to quit DEEM File gt New or Ctrl N creates a new model If a model is already opened it is closed a confirmation box is shown and a new net can be drawn File gt Open or Ctrl L opens a model from the directory deem_models File gt Save or Ctrl S saves in the current directory the opened model The default name for new models is unnamed File gt Save As With this option a new name can be assigned to a model The file is written in the directory deem_models If
16. a file with the same name exists in deem_models a warning massage File already exists Overwrite it appears in a window and the choice to overwrite the file is given File gt Close closes the drawn model File gt Save Options permits an automatic backup by making on automatic save every k steps where k is a number File gt Exit or Ctrl X quits DEEM 2 3 Edit Menu The Edit Menu is used to undo or redo some actions to refresh the window to delete cut copy paste one or more objects to define the properties of places transitions and arcs Chapter 2 User Interface 2 3 1 Edit commands Edit gt undo or Ctrl U removes one by one all the modifications to the model made since the last saved model The same command can be executed by clicking the DEEM_ button El Edit gt redo restores the modifications removed by Edit gt undo The same command can be executed by clicking DEEM_button E Edit gt Refresh or Ctrl R refreshes the DEEM window To select an object click with the left button on it and the following commands became available Edit gt Delete or Ctrl D removes the selected object The same command can be executed by clicking the DEEM_ button K Edit gt Copy Node or Ctrl E copies the selected place Edit gt Copy Edit gt Cut and Edit gt Paste to copy cut and past the selected part of the net Edit gt properties or Ctrl O open the property window associated with the selected
17. ance Systems SMS MPS are very general since their phases can be distinguished along a wide variety of differentiating features e During a specific phase an MPS is devoted to the execution of a particular set of tasks which may be different from the activities performed within other phases e The performance and dependability requirements of an MPS can be completely different from one phase to another e During some phases the system may be subject to a particularly stressing environment thus experiencing dramatic increases in the failure rate of its components e In order to accomplish its mission a MPS may need to change its configuration over time to adopt the most suitable one with respect to the performance and dependability requirements of the phase being currently executed or simply to be more resilient to a hazardous external environment e The successful completion of a phase as well as the activities performed therein may bring a different benefit to the MPS with respect to that obtained with other phases Many examples of MPS can be found in various application domains Representative examples are systems for the aided guide of aircraft whose mission time is divided into several phases such as take off cruise landing with completely different requirements A very important sub class of MPS is represented be the so called Scheduled Maintenance Systems encountered in almost all the application domains where an artefac
18. ange the name in yes_repair_B This transition represents the possible scheduled maintenance action for component B backup unit B is subject to a partial check at the end of each amp pairs of missions It is an immediate transition with probability 1 and priority 2 it must fire before transitions Tstop1 and Tcount yes_repair_B is enabled if i the place Afail 16 Chapter 3 How to create and solve a Model an example does not have tokens ii it is the end of Mission 1 or 2 and iii it is the end of one of the amp pairs of missions Trans_10 and Trans_11 change those names in ok_repair and nok_repair respectively ok_repair represents a successful repair action it has a probability equal to p nok_repair represents the failure of the repair action it has a probability equal to 1 p They are enabled only just before the starting of Mission 1 there are not tokens in places Stop1 and Stop2 The figure 3 10 shows an example of rate and enabling function The rate of the exponential transition is 0 001 if there is a token in place P1 otherwise it is 0 002 Name fa Orientation Horizontal v Vertical Transition Type Timed Rate Function iF mark P1 1 THEN 0 001 ELSE 0 002 Enabling function mark Count lt 50 Copy from list to Rate function field COPY PI a Fe P3 Aok Afail Figure 3 10 Definition of rate and enabling function If there are arcs wit
19. aw an input arc click with the left button on the starting place then on the destination transition with the right button To draw an output arc click with the left button on the starting transition then on the destination place with the right button To draw an inhibit arc from a place to a transition the property window associated with the arc has to be opened Input output arcs can also be inserted clicking the DEEM_button whereas O inhibit arcs can be inserted by clicking the DEEM_button Zl 2 5 Special Menu The Special Menu is used to change the look of DEEM window or to move the net or part of it Special gt View gt Designer border shows hides the border of the PhN and SN area Node names shows hides the places name Place init Value shows hides the initial number of tokens of each place Place capacity shows hides the places capacity Trans Rate Probability shows hides the transitions rate probability Multiplicity Arc shows hides the arcs multiplicity Trans Priority shows hides the immediate transitions priority Panel shows hides the panel on the left side of the DEEM window Special gt Net Size defines the size of the DEEM window default 800x600 Special gt Move Net opens a new window with 4 arrows to move the global net PhN and SN Chapter 2 User Interface Special gt Move Part of Net moves the selected part of the net in the desired position chosen by left clicking Special gt Colo
20. e multiplicity of values is given the variable assumes all the values in the set and a different transient analysis is performed for each of them File Edit Insert J X l Ub lo la lu x N Tcount SH _ JTS5i3 i DEEM 1 0 be 2 15 2000 University of Horence and CNUCE CNR Pisa cL HELENE a cantnciotnnsesciesenereuisnesnsciotencnenoieniieseiii Figure 3 11 SMS model To create a study click on New Insert the name of the study and click Apply Now assignments to the variables can be performed as illustrated in Figs 3 12a and 3 12b Open Study New Study Delete Study Figure 3 12a The window where insert the name of the new study Chapter 3 How to create and solve a Model an example Value 1500 0 0001 0 01 10 Current Study Study 3 Study_1 Open Study Study _2 Study 3 ____ New study Delete Study L Figure 3 12b A definition of study 3 5 Definition of the measures To define the measures to be evaluated select Measures in Compute Menu For each measure it is required the definition of i a name ii a reward function and iii the analysis type flag instantaneous cumulated and timed averaged analysis In our example we are interested in evaluating the Reliability of the system Therefore i Reliability ii IF mark Afail mark Bfail lt 2 THEN 1 atleast one component must be up ii click on
21. e name Place_11 in repair_B A token in repair_B indicates that component B is under repair For each transition open the property window select the place and a click on Properties of the Edit Menu or b click with the right button of the mouse and assign the name to the transition By clicking on Transition Type the choice between immediate or timed can be made If immediate is selected the firing probability and possibly the priority have to be inserted If timed is selected instead a new choice between Deterministic and Exponential has to be performed both requiring the insertion of the transition rate Click Apply to confirm The probability rate of firing can be marking dependent if this is the case the field Rate Function must be filled using the appropriate syntax defined in Chapter 2 If the firing of the transition is marking dependent the field Enabling Function must be filled too Following the specifications of our SMS example properties to the transitions of figure 3 9 are assigned as follows Trans_1 change the name in T1 T1 is a deterministic transition that model the time 10 hours needed for the system to perform the phase of mission 1 This transition is enabled if the number of tokens in place Count is less than 50 Trans_2 change the name in Tstop1 Tstop1 is an immediate transition with probability 1 and priority 1 It may be enabled only if the state of component A is healthy This condition is
22. easosacaadaadandtessacesevebsess 19 3 6 Transient analysis 1 sseesicecdaaseuads diag avgeaaescdyauvessssdagavgeisesscpaaeesaeseeas 20 Results cand output fre Saaana a ate ee cae 21 4 Ae PIN leS weona ierni ea E E e E E E i 21 4 2 The files created for each phase essnessenessseesseeesseesssseessersssseesss 24 4 3 The files created for each Study 023 5 vecescitesasseedadesus chyudaaeredeageious ieee 25 Transient Solvei verorren cocci aces ue E T peers tea cate T eevee 27 5 L Theanalytical te hini Que sissi farsa eiseue ddaeatsob de eacn tiseaedrete neue E a 27 5 2 The solution algorithm eeeeesesssesesereerrrrrreresrrsresssrerererreeereeeeus 2T AppendiR soere eeann EEKE Erh AEEA odes sabusia pdcaaayudi dade TEDN EAA SE 29 Stall ati On ein i ian EERE E E ETE SOE Dae AEE E EA T aS 29 Tool Oraganization and File Structure 0 ce cece ence eee cence eeneeeeneeenaees 29 Bibliography nenii i eddies be hana EEE EEE dha ee Saeed OEE ER EA NEREA 30 Introduction Many systems devoted to control and management of critical activities have to perform a series of tasks that must be accomplished in sequence Their operational life consists of a sequence of non overlapping periods called phases These systems are often called Multiple Phased Systems MPS They include several classes of systems that have been object of active research during the last decades such as those known as Phased Mission Systems PMS and Scheduled Mainten
23. gt AND OR EOR NOR NAND compare gt lt gt y gt Ve gt lt e 11 Chapter 2 User Interface The syntax of predicate and impulse_predicate is predicate gt predicate NOT predicate predicate bool_arith predicate func compare func TRUE FALSE impulse_predicat gt fire trans_name 2 Some examples IF mark Place_1 1 THEN mark Place_2 ELSE 1 e IF mark Place_1 gt 1 AND mark Place_2 0 THEN 1 IF fire Trans_1 THEN 5 As a future work it will be given the possibility also to define some derived measures obtained as functions of the measures evaluated by the tool in phase of post processing example measures of performability or cost 2 7 3 Transient Analysis Compute gt Transient Analysis permits to enter the parameters for the transient analysis Figure 2 7 _ Run in the Background 1 Verbose Computation Time Info Save State Distr Load State Distr Parameters for the Transient Analysis Epsilon ie 10 Maxiter 10000 E Current Study sway 1 5 Measure 4 OK Cancel Help Figure 2 7 Transient analysis window 2 Not yet implemented in the release 1 0 beta 15 12 Chapter 2 User Interface The field Epsilon represents the error tolerance Maxiter the maximum number of
24. h a multiplicity different from 1 the property window associated with those arcs has to be opened select the arc and a click on Properties of the Edit Menu or b click with the right button of the mouse To set the multiplicity the field Weight can be filled with an integer number for example 2 or if the multiplicity is marking dependent insert the appropriate function in the field Multiplicity Function for example mark Place_1 In this last case the multiplicity changes as a function of the number of tokens of the place s it depends on In the SMS example we are working on all arcs have multiplicity 1 The figure 3 11 shows the complete model obtained 3 4 Values of the parameters and studies To assign values to all the model parameters select Parameters in Compute Menu A window will appear listing all the variables included in the model with associated an undefined value no_def Assignments to such variables may be performed through the insertion of i a constant number it is the case of A 4 and A 4 whose values are 0 001 and 0 002 or ii a set of values e g 0 00001 0 001 0 0015 0 002 0 5 or iii a range of values e g 0 001 0 01 0 001 where the first two numbers represent the extreme values assumed by the variable and the third number is the step to be added or multiplied to make the variable assume intermediate values in the range If a 17 Chapter 3 How to create and solve a Model an exampl
25. hapter lists and explains the output files of DEEM 4 1 The PHN files The Transient analysis creates two different PhN files e Filename_PhN mc describes the Markov Chain MC of the PAN A part of this file is shown below _nstates represents the number of states of the model _order TOFROM represents the type of order arrive on state X if the current state is Y The MC is represented by _matrix with the following syntax destination_state origin_state probability KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKAKKK DEEM Dependability Modelling and Evaluation s Version 1 0 xx xx 00 me C 2000 by Institute CNUCE CNR Ghezzano Pisa ITALY KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK KK KKK K This file was generated Tue Jun 27 12 57 22 2000 _firstindex 0 _nstates 154 _nentries 153 _order _TOFROM _matrix o_o O_1 0_0 1 000000000000e 00 0_2 0_1 1 000000000000e 00 0_3 0_2 1 000000000000e 00 0_4 0_3 1 000000000000e 00 Chapter 4 Results and output files e Filename_PhN rg describes the Reachability Graph RG of the PhN Two parts of these files are shown below All places and transitions have associated an integer number used in reachset and reachgraph In reachset O_4 t 1 1 5 1 represents the marking of state 0_4 t In this state there is a token within place 2 P2 and a token within place 5
26. has exactly one stable marking m for each phase i 1 2 2 the MPS may perform 2 Call deem_solver 1 P 0 init init The recursive algorithm of deem_solver i P t is 1 Builds the reachability graph RGS m of the whole DSPN model when marking m is the only one permitted for the PhN From RGS m obtains the transition rate matrix Q of the continuous time Markov chain describing the evolution of the DSPN during the execution of phase 7 init If there are not phases next to phase 7 or t lt t 7 then derivate the transient state probability vector P t pint gl and return else continue to step 3 Derivate the transient state probability vector P Pe Builds the reachability graph RGS m next m where next m m m k es of the whole DSPN model when the initial marking of the PhN is Mm and transition 4 is the only deterministic one allowed to fire Each marking m is reachable from m through the firing of some istantaneous transition next the Det io firing of t For each stable marking M phase j performs the following steps 5 1 From RGS m next m obtains the branching probability matrix A for the transition from phase i to phase Ja 5 2 Derivate the initial state probability vector of the phase j pe PA ija init init 5 3 Call deem_solver jp P ti 7 In this solution algorithm DEEM evaluates the specific dependability measure of interest
27. itions can be immediate represented by a thin line or timed in this case they may have exponentially distributed firing times and they are represented by empty rectangles or deterministic firing times only for PhN represented by filled rectangles When a type is chosen a new window appears to define in more details the transition If the immediate type is chosen the new window allows to specify the probability and priority associated with it When a timed transition is chosen instead the new window allows to define the firing rate of the transition The values can be constants or variables To define a variable the following syntax has to be respected VAR variable_name Rate Function defines the firing rate of the transitions and can be an arbitrary marking dependent function Enabling Function defines the enabling condition or guard of the transition It can be an arbitrary marking dependent function Copy from list to adds the place selected from the list of all the places of the net in the Rate Function field or in the Enabling Function field by clicking the copy button Chapter 2 User Interface In this window the Help button shows the syntax of the probability rate and enabling function The probability and rate function syntax is func gt fune arith_opl func func arith_op2 func arith_opn func func IF predicate THEN func CELSE func
28. mposing the evaluated reward based measures refered with the construct FUN as showed at bottom in Figure 2 6 Measure Name Reward Function Analysis Type fi I A ist vam sy tim_av FE Composed Measure Name Composed Measure x z oK Apply Cancel Help Figure 2 6 Measures window The syntax of Reward Functions is Reward_Function gt IF predicate THEN func CELSE func IF impulse_predicate THEN impulse_func 10 Chapter 2 User Interface where the sintax of the func and impulse_func is func gt func Y arith_opl func func arith_op2 func arith_opn func func Y IF predicate THEN func CELSE func number func_basic func_name impulse_func gt impulse_ func arith_opl impulse_func impulse_func arith_op2 impulse_func arith_opn impulse_func impulse_func number VAR variable_name arith_opl gt SQRT arith_op2 gt 4 wer Sya igr j NAr arith_opn gt min max mean number gt digit digit digit exponent digit Digit digit exponent digit oO Pas 89 exponent gt e digit digit func_basic gt mark place_name number of Token in lt place_name gt place_name oD id nv nv AA AAI bool_arith
29. n window of DEEM 13 How to create and solve a Model an example This chapter describes how to create and solve a model with DEEM by applying the process to a real example of Scheduled Maintenance System SMS 3 3 1 A working example Consider a system equipped with two components Component A is a primary unit providing some functionality to the system and component B acts as a backup unit for component A The system is equipped with a switching logic so that when A fails the control of operation is immediately passed to B The system executes cyclically two different types of mission Mission 1 encompasses a single phase of fixed duration t where Mission 2 is a two phase mission whose phases have duration 72 and 722 respectively The time to failure of component A is exponentially distributed with parameter A during the mission of type 1 and parameter A during the mission of type 2 whereas the time to failure of component B is constantly Ag The following scheduled maintenance actions are undertaken during system lifetime e The system is subject to a complete maintenance check every 100 missions Primary unit A is replaced at the end of each mission if failed After the replacement A takes again the role of primary unit Backup unit B is subject to a partial check at the end of each amp pairs of missions After 100 missions all the components are checked and the system is restored to the initial condi
30. nalysis e Filename mc describes the Markov Chain MC It has the same format of file mc of PhN e Filename rg describes the Reachability Graph RG It has the same format of file rg of PhN e Filename trsolv contains the state probability distribution at time t and average probability to being in that state at time t A part of this file is shown below KKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK DEEM Dependability Modeling and Evaluation i Version 1 0 beta 2 C 2000 by Istituto CNUCE CNR Ghezzano Pisa ITALY kkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkxkkxkxkxkxkkxkxkxkxkkxkxkxkxkkkxkxkxkkkkkkxkxx k This file was generated Tue Jul 11 15 02 25 2000 a gt PHASE NUMBER 0 STATE PROBABILITY EXPECTED TOTAL TIME TIMEAVG GJ _timepoint 1 500000e 01 O21 8 478937040879e 01 9 2185633886lle O01 0 2 1 281427233714e 02 6 757151638498e 03 03 1 372182355086e 01 7 068102093397e 02 O_4 2 073788052551le 03 7 054885648605e 04 24 Chapter 4 Results and output files 4 3 The files created for each study The last files that the transient analysis creates are the files of the defined studies one for each study e Filename studyname spreadsheet contains the measures evaluated for the study studyname in a format which can be further elaborated by spreadsheet programs e Filename studyname gnuplot
31. obtained by giving the greater priority to the immediate transition Yes_repair_A that represents the repair of component A Trans_3 and Trans _4 change those names in T2 and T3 respectively They are deterministic transitions that model the time 5 and 10 hours respectively needed for the system to perform the two phases of Mission 2 Trans_5 change the name in Tcount Tcount is an immediate transition with probability 1 and priority 1 It may be enabled only if the state of component A is healthy and it is the end of the amp i th mission i 1 L50 o Trans_6 change the name in fA fA is an exponential transition with firing time equal to 0 001 A if Mission 1 is the active mission otherwise it is equal to 0 002 24 fA is enabled if the number of tokens in place Count is less than 50 Trans_7 change the name in Yes_repair_A This transition represents the scheduled maintenance action for component A which is replaced at the end of each mission if failed It is an immediate transition with probability 1 and priority 2 it must fire before transitions Tstop1 and Tcount Yes_repair_A is enabled if 1 the place Bfail does not have tokens ii the number of tokens in place Count is less than 50 and 111 it is the end of Mission 1 or 2 Trans_8 change the name in fB fB is an exponential transition with firing time s fB is enabled if the number of tokens in place Count is less than 50 Trans_9 ch
32. rs allows to choose the combination of colours for places transitions etc In the Colour Groups list a set of pre defined colour combinations is given After a combination is chosen by left clicking on it it can be assigned clicking on lt New combinations can be inserted in the list clicking on gt and assigning them a name A combination can be deleted by selecting it and clicking the delete button Special gt Project Report allows to create the documentation of the MPS model producing a LATEX file containing all model information 2 6 Zoom Menu The Zoom Menu is used to change the size of the global net by 25 50 75 or 100 the original size 2 7 Compute Menu In Compute Menu is possible to set parameters to define some measures of interest and to activate the transient analysis 2 7 1 Parameters Compute gt Parameters opens a new window in which all the variables defined within the model are shown The variable Time is always present When a variable is inserted in the model it is automatically added to the variable list the field Name showing the name of the variable and field Value the default no_def When a variable is removed from the model it is automatically removed from the variable list A set of values for each variable represents a study In the same window it is possible to create a new Study open an old one selected from a list of studies that becomes the current one or remove a
33. t is to be used for long time and is periodically subject to maintenance actions An SMS is easily formulated as a MPS considering that the system is run for a number of operational phases and then undergoes a maintenance phase DEEM DEpendability Evaluation of Multiple phased system is a dependability modeling and evaluation tool specifically tailored for MPS This tool supports the methodology proposed in 5 6 for the dependability modeling tool and evaluation of MPS This methodology relies upon Deterministic and Stochastic Petri Nets DSPN as a modeling tool and on Markov Regenerative Processes MRGP for the model solution Due to their high expressiveness DSPN models are able to cope with dynamic structure of MPS and allow defining very concise models DEEM models are solved with a very simple and computationally efficient analytical solution technique based on the separation of the MRGP underlying the DSPN of a MPS This manual is organized as follows Chapter 2 describes the user interface defining all menus with their functionalities Chapter 3 shows how to create a model in DEEM and how to solve it Chapter 4 specifies the files the results of the analysis are stored in and it describes how to interpret those files Chapter 5 describes the specialized solution algorithm implemented by DEEM In Appendix all the steps to install DEEM are shown User Interface This chapter is a reference guide for the various options provided by the
34. tion We want to evaluate the Reliability R of the SMS defined as the not occurrence of a failure in both A and B 3 2 Creation of the graphical Model To execute DEEM write the command deem the window in Figure 2 1 will then appear As already described in Chapter 2 the deem window for the model representation is composed of two parts the PhN window up part for the model of the phases and the SN window low part for the failure repair model of the system components Using the graphical commands Insert Menu introduced in Chapter 2 the models for the PhN and SN of our SMS running example can be constructed as illustrated in Fig 3 9 Chapter 3 How to create and solve a Model an example File Edit Insert Special Zoom Compute 7 Figure 3 9 A sketch of the SMS model The PhN has 6 places 5 transitions and arcs linking places and transitions The SN has 5 places 6 transitions and arcs that linking places and transitions Default names to places and transitions are automatically assigned by the tool To save the model click on Save As File Menu in Chapter 2 3 3 Properties of places transitions and arcs Now properties have to be assigned to each object places transitions and arcs For each place open the property window select the place and a click on Properties of the Edit Menu or b click with the right button of the mouse Assign name number of tokens and capacity to the place Click Apply to
35. ttached to Transition specifies the name of the transition the arc is attached to Type specifies the type of the arc input output or inhibit Weight specifies the multiplicity of the arc Multiplicity Function defines the multiplicity of the arc as a function It can be a marking dependent function example mark place_name Place Prace 1 Transition rans 1 Type input y Output Inhibit Weight fi Multiplicity Function i test cnca Figure 2 4 Property window associated with the arc Chapter 2 User Interface If a multiplicity function is defined the field weight is not considered and the multiplicity of the arc is defined by this function 2 4 Insert Menu The Insert Menu is used to insert places transitions or arcs Insert gt Place or Ctrl P draws a place in the DEEM window by clicking with the left button in the desired position The same command is executed by clicking the DEEM_ button o Insert gt Transition Horizontal or Ctrl H draws in the DEEM window a horizontal transition by clicking with the left button in the desired position The same command is executed by clicking the DEEM_button El Insert gt Transition Vertical or Ctrl V draws in the DEEM window a vertical transition by clicking with the left button in the desired position The same command is executed by clicking the DEEM_ button 0 Insert gt ARC or Ctrl A draws an input output or inhibit arc To dr
36. ura A Bondavalli X Zang and K S Trivedi Dependability Modeling and Evaluation of Phased Mission Systems a DSPN Approach in Proc DCCA 7 Dependable Computing for Critical Applications San Jose CA 1999 pp 319 337
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