Using the RTPN model for the modelling of complex Workflow systems Abdia Hamdani Abdelkrim Abdelli Ibn-Khaldoun University of Tiaret. LSI laboratory, USTHB university, Algiers. hh abla@yahoo.fr Abdelli@lsi-usthb.dz of the workflow system. This may include dif- ferent mechanisms ( e.g., sequence, choice, paral- Abstract lelism and synchronizations), usually called work- flow patterns [Aal05]. For instance, synchroniza- Dealing with synchronization in time tion in workflow system can be seen as a meeting constrained workflow is becoming a point during the process where a set of tasks has challenging issue. In this paper, we to wait for others according to a given scheme (e.g present a modelling approach based on the AND-join synchronizer pattern). Nowadays, Petri nets formalism for timed workflow the real challenge in workflow systems is to deal systems with complex synchronization with situations where a variable number of tasks is among tasks of different privileges (Mas- processed under different synchronization and time ter/Slave). To this aim, we consider the constraints patterns. Indeed, adapting, replan- concept of rendezvous already introduced ning, and synchronizing workflows in response to in the RTPN (Time Petri Nets with an unexpected progress, delays, or technical con- rendezvous), to define a subclass of ditions are necessary to maintain the safety of the RTPNs called Time Workflow-nets with systems. Furthermore, such requirements are be- Rendezvous (RTWF-nets). We discuss coming critical aspects in many domains as for ex- how this model can cover a large range of ample healthcare workflows [Car09]. For example, timed synchronization patterns in a very in transplantation surgery activity, we require the smart and compact framework. concurrent presence of the organ to be implanted, blood for the patient and the patient, that must ar- rive within the same hour at the hospital to avoid Keywords – Workflow, Real-time systems, their functional degradation. Rendezvous, Petri nets, Patterns. In this paper, we propose the use of RTPN (Time Petri Nets with Rendezvous) [Ham17], for the 1 Introduction modelling and the analysis of complex workflow systems that include synchronization and time In the late of the 70’s, the research on workflow constraints among tasks. The RT P N introduces systems has started and a lot of approaches and the paradigm of rendezvous to define various syn- powerful tools have been proposed and developed. chronization schemes under different time con- Generally, workflows represent processes describ- straint orchestrations. With its expressiveness ing how and when their elementary tasks should power, RTPN provides a compact framework to be accomplished, thus describing the control flow represent complex workflow systems in elegant Copyright c by the paper’s authors. Copying permitted for way, that could hardly be handled by other existing private and academic purposes. models. After presenting and discussing the work- In:Proceedings of the 3rd Edition of the International flow patterns provided by RTPN, we define a sub- Conference on Advanced Aspects of Software Engineer- class of RTPN, called RTWFN (Time Workflow- ing (ICAASE18), Constantine, Algeria, 1,2-December-2018, nets with Rendezvous ), which is dedicated for the published at http://ceur-ws.org Page 76 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 specification of workflow systems. specify workflow systems, as the use of computa- The remaining of this paper is organized as follows: tional tree logic (CT L) in [Rus91], the event alge- Section 2 discusses the related works. In section 3, bra in [Els09], multi-agent theory in [Alf16], UML we present our workflow model with timed ren- activity diagrams in [Arn16], and State Charts dezvous patterns. Section 4 presents the RTPN [Wen12]. However, all the previous works do not and RTWFN models before presenting the mod- consider time constraints. To deal with the lat- elling approach. In section 5, case-study examples ter, the authors in [Eder15] introduce the Timed are presented. Finally, conclusions and comments Workflow Graph (TWG) defining a graph which is on future work are given. composed of a set of nodes (activities) and edges (control flow). Each activity is characterized by its 2 Related Works duration and earliest and latest ending time. How- ever, no delay between activities is defined, thus, In this section, we review the key works defined in leading to incorrect time evaluation. the literature that address workflow systems mod- elling and analysis. 3 Our workflow model a)-Petri Nets based Models : Basic Petri nets have been used for the represen- Workflow modelling and analysis are very impor- tation, the validation and the verification of busi- tant aspects and become more complex when con- ness procedures in [Aal05]. In [Aal98], the authors sidering, in addition, synchronization and time introduce the WorkFlow net (WF-net) to specify constraints. We present in this section the the processing of a workflow. Afterwards, the WF- essence of our approach by describing the differ- net has been extended to deal with data, time and ent paradigms used in our modelling framework. other aspects. A various extensions are proposed: (i) the extension with time [Ada98]; (ii) the ex- 3.1 Tasks, rendezvous, locality and delay tension with color to model data [Rus09] ; (iii) the parameters extension with hierarchy to structure large mod- In our model, we consider a set of elementary els [Aal08]; (iv) and finally combining some of the work units called tasks, that collectively achieve previous features [Fra17]. the whole process. An atomic task is an activity Different other models have been proposed in that cannot be divided into sub-processes. Tasks the literature : In [Wan08], the authors intro- can have different privileges (Master or Slave) and duce the R/NT-WF Net to model workflows con- are associated with a time interval defining the strained by resources and a non-determined time. earliest and the latest times within which they A procedure is given to compute the earliest should occur. A Rendezvous is a time point dur- and the latest times to start each activity. In ing the workflow process where a set of tasks [Bou08], a new formalism called the Time Re- has to wait for others in order to perform a syn- cursive ECATNets (T-RECATNets) is proposed chronization. A rendezvous, noted R, is the tu- for modelling and analysing time constrained re- ple (Tm , Ts , (Loc− , Loc+ ), (α− , α+ , δ − , δ + )), such configurable workflows. In [Ber12] component- that: based timed-arc Petri Nets (CTAPN) are defined - Tm denotes the non empty set of master tasks to model collaborative healthcare workflows. The involved in the scheme; Ts is the set of slave tasks. authors in [Cic13] consider the TSPN model for In the sequel, we note Tr = Ts ∪ Tm , and we as- modelling and enactment of complex workflows. sume that each task t is characterized by its own The authors in [Yeh05], introduce the WFCS-nets time constraints, given in the form of an interval (workflow with critical sections nets), to deal with [x(t), y(t)]. synchronization and time constraints among activ- - (Loc− , Loc+ ) denotes the localities on which re- ities while considering critical sections. In [Aal13] fer the delay parameters. Loc− is called the early [Sai17], patterns are adapted to cope with inter- time locality and Loc+ is the latest time locality. organisational workflows (IOWF). An approach - The delay parameters (α− , α+ , δ − , δ + ) are posi- describing how the qualitative and quantitative tive rational numbers from Q+ ∪ {+∞} that spec- analysis of the framework can be performed by us- ify the tolerable drifts between the synchronizing ing TCTL model checking is presented in [Bou14]. tasks in the rendezvous. The parameters α− and -b) Others Models : δ − are associated with the early time locality, while Other formalisms have been also considered to α+ and δ + are with the latest time locality. International Conference on Advanced Aspects of Software Engineering Page 77 ICAASE, December, 01-02, 2018 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 - no later than δ + time units after the occurrence of the locality Loc+ ; It is noteworthy that the parameters α− and δ are associated with the locality Loc− , while − α+ and δ + are associated with the locality Loc+ . Let be M AX: the maximum value between the earliest time of the last master task that started its execution and the latest time of the first master task that ends its execution. Likewise, M IN : the smallest value between the earliest time of the last master task that started its execution and the latest time of the first master task that ended its execution. Figure 1: Localities and delays in a rendezvous According to the value of the delay parameters, the two localities, we define and discuss in the According to the type of synchronization pat- sequel a panel of useful synchronization patterns tern, the early time locality Loc− can refer to one that are derived from the concept of rendezvous: of the two following dates (see Fig.1): Loc− := M AX {x(t)}, namely at the earliest time of the a-Cobegin rendezvous: This regroups all ∀t∈Tm the patterns such that the earliest time of the ren- last master task that started its execution; or dezvous is determined by the earliest start of one Loc− := M AX {x(t)}, namely at the earliest time ∀t∈Tr task among masters tasks or all the tasks, leading of the last task that started its execution. to different variants, as for example: Likewise, Loc+ can take two different dates: -1) if we have (α− = 0) and (δ − = 0 or ∞), Loc+ := M IN {y(t)}, namely at the latest time then, the earliest time of the synchronization oc- ∀t∈Tm of the first master task that ends its execution; or curs at the earliest time of the last master task Loc+ := M IN {y(t)}, namely at the latest time of that started its execution. We call this pattern ∀t∈Tr the cobegin master Synchronized rendezvous (see the first task that ends its execution. Fig 2.a)). Example: let’s consider the example of For the sake of simplification, in the sequel the ex- the transplantation surgery activity: if the organ pression of the value of both localities will refer arrives between [1, 3], the blood between [2, 3] and only to the set of transitions considered in the op- the patient between [2, 5], the earliest time the ren- erators M IN or M AX, namely Tm or Tr rather dezvous occurs is 2. than considering the whole expression. However, -2) If we have(α− = ∞) and (δ − = 0 ), then the whatever the synchronization pattern in the Ren- earliest time of the synchronization occurs at M IN dezvous we consider, it should be noticed that at (see Fig 2.b). This is called a strict cobegin ren- least one of the two localities Loc− and Loc+ of dezvous. Assuming the same example, if the organ the rendezvous must refer to the set of master tasks arrives between [1, 2], the blood at [3, 3] and the Tm . This is because the rendezvous must be driven patient between [2, 5]. The earliest time the ren- by master tasks. dezvous occurs is the minimum between (3, 2) = 2. -3) If we have(α− = ∞) and (δ − = ∞ ), then 3.2 Timed Rendezvous patterns the earliest time of the synchronization occurs at: Let R = (Tm , Ts , (Loc− , Loc+ ), (α− , α+ , δ − , δ + )) - if Loc− = Tm : The earliest time of the first mas- be a rendezvous. As illustrated in Fig.1, the earli- ter task that stated its execution. We call this pat- est time to hold the rendezvous must occur: tern, cobegin master-relaxed rendezvous (see Fig - no earlier than α− time units before the occur- 4.g)). rence of the locality Loc− ; and - if Loc− = Ts : The earliest time of the first task - no later than δ − time units after the occurrence that stated its execution. We call this rendezvous of the locality Loc− . cobegin-relaxed rendezvous The latest time to hold the rendezvous must oc- cur: b-Coend related rendezvous: This regroups - no earlier than α+ time units before the occur- all the patterns such that the latest time of the rence of the locality Loc+ ; and rendezvous is determined by the latest ending time International Conference on Advanced Aspects of Software Engineering Page 78 ICAASE, December, 01-02, 2018 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 Figure 2: Cobegin related Rendezvous Figure 4: Relaxed rendezvous. of the fist task (among masters tasks or all the tasks); this leads to different variants, for instance: -1) If we have (δ + = 0) and (α+ = 0 or ∞), then the latest time of the synchronization occurs at the latest time of the first master task that ends its execution. We call this pattern the coend master Synchronized rendezvous (see Fig 3.c). Example: Let’s consider the previous example, if the organ arrives between [1, 3], the blood between [2, 3] and Figure 5: Fully synchronized rendezvous. the patient between [2, 5], the latest time of the rendezvous is 3. 1. A Fully master synchronized rendezvous is -2) If we have(δ + = ∞) and (α+ = 0 or ∞), both a cobegin master Synchronized and a co- then the latest time of the synchronization occurs end master Synchronized rendezvous. (see Fig at M AX (see Fig 3.d). This is called a hard Coend 5.e,f) rendezvous. Example: if the organ arrives between [1, 2], the blood at [3, 3] and the patient between 2. A Relaxed rendezvous is both a cobegin relaxed [2, 5], the latest time the rendezvous occurs is the and a coend relaxed rendezvous (see Fig 4.g,h). maximum between (3, 2) = 3. 3. A Critical rendezvous, is a rendezvous such -3) If we have (δ + = ∞) and (α+ = ∞), then that Loc+ = Loc− . In other terms the ear- the latest time of the synchronization occurs at: liest and the latest time of the occurrence of - (if Loc+ = Tm ): The latest time of the last master the rendezvous are the same. The rendezvous task that ends its execution. We call this pattern has to be executed in urgency and cannot be the coend master-relaxed rendezvous. By taking delayed once its offered. the previous example, the synchronisation occurs at 5. 3.3 Discussion - (if Loc+ = Ts ): The latest time of the last task that ends its execution. We call this pattern the A large range of synchronization schemes defined coend relaxed rendezvous. in the literature are covered by our model, and By combining the previous patterns, or by con- many others. For example for the basic rules sidering specific conditions, we can define new sub- of the T SP N model [Cic13], the Synchronized patterns, as for example: rendezvous coincides with either the And or the P ur − And rules (when considering a different variants of disjointed interval relations). This ex- presses that all tasks are present during the ren- dezvous. The Relaxed rendezvous is referred to the Or rule of T SP N , for instance. The Cobegin Synchronized rendezvous covers: the And, P ur − And, W eak − And, And − M aster, rules, whereas, the (Coend Synchronized) rendezvous covers: the And, P ur − And, Strong − Or, StrongM aster Figure 3: Coend related Rendezvous. rules. The Cobegin Relaxed rendezvous covers the : Or, Strong − Or, Or − M aster, rules, whereas, International Conference on Advanced Aspects of Software Engineering Page 79 ICAASE, December, 01-02, 2018 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 the Coend Relaxed covers the W eak − And, Or, values. We write Is (t) = [x0 (t), y0 (t)]. This gives W eak − M aster,rules. Our model covers also, the the static time interval within which the transition wait constraints of the parallel pattern [Car09]. t can fire, such that 0 ≤ x0 (t) ≤ y0 (t); However, our model is more expressive as it con- RDVs denotes a finite set of synchronous siders time constraints in form of intervals (not in- Rendezvous. A Rendezvous R of RDVs is stants) and at different levels (not only between a synchronisation scheme that has the form tasks), while assuming different privileges. For the (Tm , Ts , (Loc− , Loc+ ), (α− , α+ , δ − , δ + )), where best of our knowledge, no related works have ad- Tm and Ts are subsets of transitions. Tm ∩ Ts = ∅ dressed the timed synchronization between work- and we note Tr = Tm ∪ Ts .Tm is a non empty flow tasks of different privileges. Synchronization and finite set of master transitions, and Ts the and time constraints are generally studied sepa- finite set of slave transitions. (Loc− , Loc+ ) are rately. the localities considered in the rendezvous, values of which are in {(Tm , Tm ), (Tm , Tr ), (Tr , Tm )}. Fi- 4 Time Workflow net with Ren- nally, α− , α+ , δ + and δ − are the delay parameters dezvous: RTWFN that take their values in Q+ ∪ {+∞}. In the RT P N model, a transition can be in- In this section, we first present the syntax and volved in more that one rendezvous. This denotes the semantics of the RTPN model as introduced the case where an event or a process ( modelled in [Ham17], then we introduce a subclass of by the transition) is subject to different alterna- RTPN, called Workflow nets with timed ren- tive synchronization schemes. The selection of the dezvous RTWFN. This model is dedicated to rendezvous to execute is handled in non determin- specify workflow systems. Finally, we present a istic manner. However, a priority function on the RTWFN based modelling approach for workflow set of rendezvous can be introduced as an addi- systems. tional parameter to solve the non determinism. In other respects, a transition that is not involved in 4.1 Time Petri net with Rendezvous: any rendezvous of the RT P N is to progress in an RT P N asynchronous manner since it is not compelled by A classical Petri net (PN) is a directed bipartite any synchronisation scheme. The RT P N model graph with two types of nodes, called places and evolves by firing a rendezvous at each step. This transitions. The nodes are connected via directed implies the firing of all its transitions providing arcs and connections between two nodes of the that some conditions are satisfied. Firing a ren- same type are not allowed. Places are represented dezvous relies on the marking and on the corre- by circles and transitions by rectangles. We as- sponding synchronization pattern which entails to sume that the reader is familiar with Petri nets meet the dynamic time constraints of the model. theory. In the RTPN model, time intervals are as- Different semantics can be considered : a mono- sociated with each transition thus defining a Time server semantics, namely for any marking only one Petri net (TPN). The TPN is then extended with instance of a transition and by extension a ren- a set of synchronization rules defined by the con- dezvous can be enabled (see the paper [Ham17] for cept of rendezvous introduced previously. We re- more details); or a multi-server one which consid- call hereafter the syntax and the semantics of the ers that a transition and hence a rendezvous can be RT P N model. Formally, the syntax of the RT P N enabled more than once for a given marking (refer model is defined as follows: to the papers [Abd15] [Bouch13]). Definition An RT P N is given by the tuple (P, T, B, F, M0 , Is , RDVs ) where: P and T 4.2 Time Workflow Net with Rendezvous: are respectively two non empty disjoint sets of RTWFN places and transitions; ; B and F are respec- tively the backward and the forward incidence We introduce, in the following, the RTWFN model functions B : P × T −→ N = {0, 1, 2, ..}; which is a particular case of a RTPN. F : P × T −→ N ; M0 is the initial marking Definition A RTWFN noted RTw is a tuple function that associates with each place a number (RT, pb , pe ), such that: of tokens M0 : P −→ N ; Is is the delay interval -RT = (P, T, B, F, M0 , Is , RDVs is a Time Petri mapping function; Is : T −→ Q+ × Q+ ∪ {∞} , Net with rendezvous. where Q+ is a set of null or positive rational -pb is a special place of P called the beginning place International Conference on Advanced Aspects of Software Engineering Page 80 ICAASE, December, 01-02, 2018 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 of the workflow net, and we have: •pb = ∅ and M0 (pb ) 6= 0; -pe is a special place of P called the ending place of the workflow, and we have: pe • = ∅ and M0 (pe ) = (x) 0 ; where: •x denotes the set of input transitions connected to the place x while x•: gives the set of output transitions connected to x . The place pb denotes the source of the net while the place pe the sink of the net. The RTWFN should verify that there exists a run from the ini- Figure 6: Modelling approach with RTWFN tial marking including the place pb to a final mark- ing including the place pe ; we say that the net is strongly connected. 4.4.1 Example-1 Let’s consider the example of ”An online vendor 4.3 Modeling Workflow with synchroniza- workflow ”, already presented in [Bet02]. The tion and time delay using RTWF-Net figure 7 depicts a portion of the whole RT W F N specification. In the problem description, different The RTWFN model of the whole workflow con- types of synchronization and time constraints have strained by synchronization and time delays can to be considered to ensure that all the products be obtained by the following approach: are delivered to the customer in a due time to -1)First we create the places pe and pb . better manage the warehouse resources. A and -2) A single task: Each elementary unit:(task ) B correspond to the shipments that have to be is mapped into a transition t ∈ T and an in- made by two suppliers (of the same privilege). put place p ∈ P . For time constraints a time The task A, resp B is denoted by the transitions interval is associated with each transition’s task Ab and Ae (Beginning and and end of A) resp. I(t) = [x(t), y(t)], thus, defining the earliest and the transitions Bb and Be (Beginning and the end the latest time delay of the task. If no time con- of B). Both A and B must occur respectively straint are imposed, this means that I(t) = [0, ∞), between [3, 7] and [1, 3] after the the ending of contrarily, with I(t) = [0, 0] the task cannot be de- the operation OP that lasts between [1, 10]. The layed and must occur as soon as the input place is tasks A and B have a duration between [1, 5]. marked (See Fig.6.(x)). If the task is the first in Finally, the beginning of the local delivery task the process then its input place is pb . If it is the LD (denoted by the transition LDb), has to last in the workflow then its output place is pe . occur as soon as A and B complete. The final -3) Sequence: In the example of Fig 6.a, tasks delivery task must begin after that all products t1 and t2 are executed sequentially, representing are made available and none of the products precedence constraints of task execution in the must wait more than 2 time units at the ware- workflow; house. To express the previous synchronization requirements we introduce the following set of -4) Choice: In Fig 6.b, t1 and t2 are in conflict rendezvous RDV = {R1 , R2 } such that: R1 = and can never occur both; ({tAb , tBb }, ∅, ({tAb , tBb }, {tAb , tBb }), (0, 0, 0, 0)) -5) Concurrency: In Fig 6.c, tasks are in con- which means no temporal delay is considered currency; they occur in parallel and are not in con- at the beginning of A and B and represents a flict. Their execution can be governed by synchro- fully synchronized rendezvous as well as a Critical nization patterns that are expressed in the form of rendezvous. R1 can fire within: # rendezvous. " MAX {x(t)}, MIN {y(t)} =[3,3]. ∀t∈{tAb,t } Bb ∀t∈{t ,tAb} Bb R2 = ({tAe , tBe }, ∅, ({tAe , tBe }, {tAe , tBe }), (0, 0, 2, 2)) 4.4 Cases Study Examples Means that the earliest time to start delivery task can be advanced not more than 2 times In this section, we present two case-studies to units, and can be delayed to no more than 2 highlight how the RTWFN model is suitable to time units. Furthermore, R2 can # fire within model worflow systems with complex synchroniza- " MAX {x(t)}, MIN {y(t)} − 2 =[1,5-2] tion patterns. ∀t∈{tAe ,tBe } ∀t∈{tAe ,tBe } International Conference on Advanced Aspects of Software Engineering Page 81 ICAASE, December, 01-02, 2018 Using the RTPN model for the modelling of complex Workflow systems ICAASE'2018 =[1,3]. This pattern denotes a restricted ren- dezvous. Figure 8: A ”healthcare” example (task T6 )(a second slave task). Otherwise (I1 no supplementary treatment is provided. After all these therapeutic actions, the workflow ends. As discussed in [Car09], we want to express the Figure 7: The RTWFN modelling the ”on line ven- fact that the synchronization of the reperfusion dor” workflow (T4 ) and the oral therapy (T5 ) neither can start more than 2 minutes before nor can start more than 1 minute after the end of the oral therapy (T5 ). To this aim, We consider the following 4.4.2 Example-2 rendezvous in our model: We consider here the example of ST-segment Ele- R1 = ({T 5}, {T 4}, ({T 4, T 5}, {T 5}), (0, 0, 2, 1)) vation Myocardial Infarction (STEMI), published without a nitroglycerin therapy: T6 ; and by the American College of Cardiology/American  1 can fire within: R  Heart Association in 2004 [Car09]. The associated MAX {x(t)}, MIN {y(t) − 2} =[4,6-2]=[4,4]. ∀t∈{T 5,T 4} ∀t∈{T 5} RTWFN is depicted in Fig. 8. The problem is This denotes a critical cobegin rendezvous ), or: as follows: when a patient comes to the Emer-  MAX {x(t)}, MIN {y(t) + 1} = [4,6+1]=[4,7] gency Department (E.D.) (task T1 ), he can wait ∀t∈{T 5,T 4} ∀t∈{T 5} between approximatively [2, 4] minutes before which denotes a cobegin synchronized rendezvous. being handled. Once he is admitted, the patient is examined first (task T2 ), which takes between [5, 20] minutes. If the diagnosis is a (STEMI) 5 Conclusion occurrence ( transition C1), then a well-know In this paper, we have presented a modelling ap- set of therapy and diagnosis tasks has to be proach for timed workflow systems with complex performed. Otherwise, ( transition C2) a further synchronizations. The approach is based on Petri patient evaluation has to be done (choice). Since net formalism, by a subclass of Time Petri Nets the guideline considers only (STEMI) patients, with rendezvous (RTPN), called time workflow we have decided to close the flow issued from C2 nets with rendezvous RTWFN. The latter provides after the task T3 . The flow from C1 is composed a large panel of concise synchronization patterns by three parallel sub-flows. The lowest from that can deal with any complex synchronization place B) refers to the main therapeutic action in scheme in timed workflow systems. Further work presence of a myocardial infarction: reperfusion is will lead us to investigate a methodology for the obtained through a fibrinolytic therapy (transition analysis of the quantitative and the qualitative T4 which is a slave task). The flow from place C properties of the RTWFN model. refers to the complementary therapeutic action consisting of the assumption of beta blocker drugs (task T5 ) (master task). The uppermost flow References (from place A) contains the possible activities related to therapies for ischemic discomfort. If the [Aal05] W.M.P. Van der Aalst, A.H.M. ter Hof- presence of ischemic discomfort (C2) is confirmed stede: YAWL: yet another workflow language. (transition I2), a nitroglycerin therapy is provided Inf. Syst. 30(4): 245-275, 2005. 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