Workflow Nets Research Articles

Two Sufficient Conditions on Refactorizability of Acyclic Extended Free Choice Workflow Nets to Acyclic Well-Structured Workflow Nets and Their Application

Two Sufficient Conditions on Refactorizability of Acyclic Extended Free Choice Workflow Nets to Acyclic Well-Structured Workflow Nets and Their Application

State Number Calculation Problem of Workflow Nets

The number of states is a very important matter for model checking approach in Petri net's analysis. We first gave a formal definition of state number calculation problem: For a Petri net with an initial state (marking), how many states does it have? Next we showed the problem cannot be solved in polynomial time for a popular subclass of Petri nets, known as free choice workflow nets, if P≠NP. Then we proposed a polynomial time algorithm to solve the problem by utilizing a representational bias called as process tree. We also showed effectiveness of the algorithm through an application example.

Sufficient and Necessary Condition to Decide Compatibility for a Class of Interorganizational Workflow Nets

Interorganizational Workflow nets (IWF-nets) can well model many concurrent systems such as web service composition, in which multiple processes interact via sending/receiving messages. Compatibility of IWF-nets is a crucial criterion for the correctness of these systems. It guarantees that a system has no deadlock, livelock, or dead tasks. In our previous work we proved that the compatibility problem is PSPACE-complete for safe IWF-nets. This paper defines a subclass of IWF-nets that can model many cases about interactions. Necessary and sufficient condition is presented to decide their compatibility, and it depends on the net structures only. Finally, an algorithm is developed based on the condition.

An analytical method for well-formed workflow/Petri net verification of classical soundness

Abstract In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Փ strictly positive m vector such that AՓ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.

Transformation of Logical Workflow Nets

Interorganizational logical workflow nets (LWNs) are formally proposed to represent the cooperations across organizations in this paper. The LWN transformation means that each organization involved in the agreement converts its agreement-level model to detailed one. The soundness of the interorganizational LWNs is introduced and analyzed. The transformation rules of LWNs are presented. The detailed model of each organization can be investigated based on its agreement-level model and the transformation rules. The concepts and techniques proposed in this paper are illustrated with an example of online shopping in electronic commerce.

Resource Relocation in Workflow Nets With Time, Resource, and Task Priority Constraints

Complex workflows arising from practical applications usually combine time, resource, and task priority constraints. The goal of this paper is to formulate a suitable WF net model with all these three types of constraints, and to investigate the soundness property of the resulting model. Thus, the concept of a multilevel resource constrained workflow net (mlRCWF net) as being a place composition of resource constrained workflow (RCWF) nets is introduced, and its soundness property is investigated. This model is then enriched with time and task priority constraints. It is shown that the soundness property of timed priority mlRCWF nets can be reduced in linear time to the soundness property of (untimed) priority RCWF nets. A resource relocation policy is a policy by which resources already allocated to some task are then relocated to urgent tasks, the current task being thus delayed. When the current tasks support an indefinite delay, the soundness of timed priority mlRCWF nets with resource relocation can be reduced in quadratic time to the soundness property of (untimed) priority RCWF nets.

Partial order reduction for checking soundness of time workflow nets

Due to the critical role of workflows in organizations, their design must be assisted by automatic formal verification approaches. The aim is to prove formally, before implementation, their correctness w.r.t. the required properties such as achieving safely the expected services (soundness property). In this perspective, time workflow nets (TWF-nets for short) are proposed as a framework to specify and verify the soundness of workflows. The verification process is based on state space abstractions and takes into account the time constraints of workflows. However, it suffers from the state explosion problem due the interleaving semantics of TWF-nets. To attenuate this problem, this paper investigates the combination of a state space abstraction with a partial order reduction technique. Firstly, it shows that to verify soundness of a TWF-net, it suffices to explore its non-equivalent firing sequences. Then, it establishes a selection procedure of the subset of transitions to explore from each abstract state and proves that it covers all its non-equivalent firing sequences. Finally, the effectiveness of the proposed approach is assessed by some experimental results.

Some Complexity Results for the Soundness Problem of Workflow Nets

Workflow nets (WF-nets) are widely used to model and verify the business process management systems and composite web services. The (weak) soundness of WF-nets is an important criterion for the correctness of these systems. This paper focuses on the complexity of solving the (weak) soundness problem. Aalst et al. have proven that the (weak) soundness problem is decidable. Our previous work has proven that the soundness problem for bounded WF-nets is PSPACE-complete. This paper shows that the weak soundness problem for bounded WF-nets is also PSPACE-complete. Aalst et al. has proven that the soundness problem is polynomially solvable for free-choice WF-nets (FCWF-nets). This paper discovers that the weak soundness problem is equivalent to the soundness problem for FCWF-nets. Therefore, the weak soundness problem for FCWF-nets is also polynomially solvable. Unfortunately, many composite web services are not modeled by FCWF-nets. Lots of them can be modeled by asymmetric-choice WF-nets (ACWF-nets). This paper proves that the soundness problem is co-NP-hard for ACWF-nets even when they are three-bounded. Additionally, this paper proves that the k-soundness problem is equivalent to the weak soundness problem for WF-nets, which implies that the k-soundness problem for bounded WF-nets is also PSPACE-complete.

Verifying soundness of business processes: A decision process Petri nets approach

This paper presents a trajectory-tracking approach for verifying soundness of workflow/Petri nets represented by a decision-process Petri net. Well-formed business processes correspond to sound workflow nets. The advantage of this approach is its ability to represent the dynamic behavior of the business process. We show that the problem of finding an optimum trajectory for validation of well-formed business processes is solvable. To prove our statement we use the Lyapunov stability theory to tackle the soundness verification problem for decision-process Petri nets. As a result, applying Lyapunov theory, the well-formed verification (soundness) property is solved showing that the workflow net representation using decision process Petri nets is uniformly practically stable. It is important to note that in a complexity-theoretic sense checking the soundness property is computationally tractable, we calculate the computational complexity for solving the problem. We show the connection between workflow nets and partially ordered decision-process Petri net used for business process representation and analysis. Our computational experiment of supply chains demonstrate the viability of the modeling and solution approaches for solving computer science problems.

Complexity of the Soundness Problem of Workflow Nets

Classical workflow nets WF-nets for short are an important subclass of Petri nets that are widely used to model and analyze workflow systems. Soundness is a crucial property of workflow systems and guarantees that these systems are deadlock-free and bounded. Aalst et al. proved that the soundness problem is decidable for WF-nets and can be polynomially solvable for free-choice WF-nets. This paper proves that the soundness problem is PSPACE-hard for WF-nets. Furthermore, it is proven that the soundness problem is PSPACE-complete for bounded WF-nets. Based on the above conclusion, it is derived that the soundness problem is also PSPACE-complete for bounded WF-nets with reset or inhibitor arcs ReWF-nets and InWF-nets for short, resp.. ReWF-and InWF-nets are two extensions to WF-nets and their soundness problems were proven by Aalst et al. to be undecidable. Additionally, we prove that the soundness problem is co-NP-hard for asymmetric-choice WF-nets that are a larger class and can model more cases of interaction and resource allocation than free-choice ones.

Controllable Deadlocks in Parallel Resource-Constrained Workflows

We study the verification of the soundness property for workflow nets extended with resources. A workflow is sound if it terminates properly (no deadlocks and livelocks are possible). A class of resource-constrained workflow nets (RCWF-nets) is considered, where resources can be used by a process instance, but cannot be created or spent. Two sound RCWF-nets using the same set of resources can be put in parallel. This parallel composition may in some cases produce additional deadlocks. A problem of deadlock avoidance in parallel workflows is studied, some methods of deadlock search and control are presented.

Discovery of Cancellation Regions within Process Mining Techniques

Process mining is a relatively new field of computer science which deals with process discovery and analysis based on event logs. In this work we consider the problem of discovering workflow nets with cancellation regions from event logs. Cancellations occur in the majority of real-life event logs. In spite of huge amount of process mining techniques little has been done on cancellation regions discovery. We show that the state-based region algorithm gives labeled Petri nets with overcomplicated control flow structure for logs with cancellations. We propose a novel method to discover cancellation regions from the transition systems built on event logs and show the way to construct equivalent workflow net with reset arcs to simplify the control flow structure.

Protocol Inheritance Preserving Soundizability Problem and Its Polynomial Time Procedure for Acyclic Free Choice Workflow Nets

Protocol Inheritance Preserving Soundizability Problem and Its Polynomial Time Procedure for Acyclic Free Choice Workflow Nets

Polynomial Time Verification of Reachability in Sound Extended Free-Choice Workflow Nets

Polynomial Time Verification of Reachability in Sound Extended Free-Choice Workflow Nets

Safety and Soundness for Priced Resource-Constrained Workflow Nets

We extend workflow Petri nets wf-nets with discrete prices, by associating a price to the execution of a transition and to the storage of tokens. We first define the safety and the soundness problems for priced wf-nets. A priced wf-net is safe if no execution costs more than a given budget. The soundness problem is that of deciding whether the workflow can always terminate properly, where in the priced setting “properly” also means that the execution does not cost more than a given threshold. Then, we study safety and soundness of resource-constrained workflow nets rcwf-nets, an extension of wf-nets for the modeling of concurrent executions of a workflow, sharing some global resources. We develop a framework in which to study safety and soundness for priced rcwf-nets, that is parametric on the cost model. Then, that framework is instantiated, obtaining the cases in which the sum, the maximum, the average and the discounted sum of the prices of all instances are considered. We study the decidability and the complexity of these properties, together with their relation.

Workflow performance analysis and simulation based on multidimensional workflow net

Workflow model performance analysis plays an important role in the research of workflow techniques and efficient implementation of workflow management. Instances dwelling times (IDT) which consist of waiting times and handle times in a workflow model is a key performance analysis goal. In a workflow model the instances which act as customers and the resources which act as servers form a queuing network. Multidimensional workflow net (MWF-net) includes multiple timing workflow nets (TWF-nets) and the organization and resource information. This paper uses queuing theory and MWF-net to discuss mean value and probability distribution density function (PDDF) of IDT. It is assumed that the instances arrive with exponentially distributed inter-arrival times and the resources handle instances within exponentially distributed times or within constant times. First of all, the mean value and PDDF of IDT in each activity is calculated. Then the mean value and PDDF of IDT in each control structure of a workflow model is computed. According to the above results a method is proposed for computing the mean value and PDDF of IDT in a workflow model. Finally an example is used to show that the proposed method can be effectively utilized in practice.

The relationship between workflow graphs and free-choice workflow nets

Workflow graphs represent the main control-flow constructs of industrial process modeling languages such as BPMN, EPC and UML activity diagrams, whereas free-choice workflow nets are a well understood class of Petri nets that possesses many efficient analysis techniques. In this paper, we provide new results on the translation between workflow graphs and free-choice workflow nets.We distinguish workflow graphs with and without inclusive Or-logic. For workflow graphs without inclusive logic, we show that workflow graphs and free-choice workflow nets are essentially the same thing. More precisely, each workflow graph and each free-choice workflow net can be brought into an equivalent normal form such that the normal forms are, in some sense, isomorphic. This result gives rise to a translation from arbitrary free-choice workflow nets to workflow graphs.For workflow graphs with inclusive logic, we provide various techniques to replace inclusive Or-joins by subgraphs without inclusive logic, thus giving rise to translations from workflow graphs to free-choice nets. Additionally, we characterize the applicability of these replacements. Finally, we also display a simple workflow graph with an inclusive Or-join, which, in some sense, cannot be replaced. This shows a limitation of translating inclusive logic into free-choice nets and illustrates also a difficulty of translating inclusive logic into general Petri nets.

Predicting high-speed train operation conflicts using workflow nets and triangular fuzzy numbers

The dispatching system of a high-speed railway system is the basis that guarantees trains that run at high speed, high density, are secure and have a good punctuality. The prediction of train operation conflicts is the main issue of train operation adjustment. In this paper, we propose the use of workflow nets and triangular fuzzy numbers to study the issues associated with predicting train operation conflicts. The linked lists for conflict prediction are built and used as tools to derive the train running states corresponding to the two operating modes of train workflow nets: the sequential mode and the alternative mode. Based on the current train running status and the triangular fuzzy numbers of times for future activities in train operation, the probabilities of all kinds of train operation conflicts that might occur can be obtained by comparing the possible end times of the workflow nets with the fixed deadlines. Hence, the prediction of train operation conflicts is realized.

On generating ⁎-sound nets with substitution

We present a method for hierarchically generating sound workflow nets by substitution of nets with multiple inputs and outputs. We show that this method is correct and generalizes the class of nets generated by other hierarchical approaches. The method involves a new notion of soundness which is preserved by the generalized type of substitution that is presented in this paper. We show that this notion is better suited than ⁎-soundness for use with the presented type of generalized substitution, since ⁎-soundness is not preserved by it. It is moreover shown that it is in some sense the optimal notion of soundness for the purpose of generating sound nets by the presented type of substitution.

RESOURCE ORIENTED WORKFLOW NETS AND WORKFLOW RESOURCE REQUIREMENT ANALYSIS

Petri nets are a powerful formalism in modeling workflows. A workflow determines the flow of work according to pre-defined business process. In many situations, business processes are constrained by scarce resources. The lack of resources can cause contention, the need for some tasks to wait for others to complete, which slows down the accomplishment of larger goals. In our previous work, a resource-constrained workflow model was introduced and a resource requirement analysis approach was developed for emergency response workflows, in which support of on-the-fly workflow change is critical [14]. In this paper, we propose a Petri net based approach for recourse requirements analysis, which can be used for more general purposes. The concept of resource-oriented workflow nets (ROWN) is introduced and the transition firing rules of ROWN are presented. Resource requirements for general workflows can be done through reachability analysis. An efficient resource analysis algorithm is developed for a class of well-structured workflows, in which when a task execution is started it is guaranteed to finish successfully. For a task that may fail in the middle of execution, an equivalent non-failing task model in terms of resource consumption is developed.