This paper presents a novel method for optimal control of timed Petri nets, introducing a novel temporal logic based constraint called a generalized mutual exclusion temporal constraint (GMETC). The GMETC is described by a metric temporal logic (MTL) formula where each atomic proposition represents a generalized mutual exclusion constraint (GMEC). We formulate an optimal control problem of the timed Petri nets under a given GMETC and solve the problem by transforming it into an integer linear programming problem where the MTL formula is encoded by linear inequalities. We show the effectiveness of the proposed approach by a numerical simulation.

Effective emergency resource allocation is essential to guarantee a successful emergency disposal, and it has become a research focus in the area of emergency management. Emergency event logs are accumulated in modern emergency management systems and can be analyzed to support effective resource allocation. This paper proposes a novel approach for efficient emergency resource allocation by mining emergency event logs. More specifically, an emergency event log with various attributes, e.g., emergency task name, emergency resource type (reusable and consumable ones), required resource amount, and timestamps, is first formalized. Then, a novel algorithm is presented to discover emergency response process models, represented as an extension of Petri net with resource and time elements, from emergency event logs. Next, based on the discovered emergency response process models, the minimum resource requirements for both reusable and consumable resources are obtained, and two resource allocation strategies, i.e., the Shortest Execution Time (SET) strategy and the Least Resource Consumption (LRC) strategy, are proposed to support efficient emergency resource allocation decision-making. Finally, a chlorine tank explosion emergency case study is used to demonstrate the applicability and effectiveness of the proposed resource allocation approach.

Safety critical systems are often modeled using Time Petri Nets (TPN) for analyzing their reliability with formal verification methods. This paper proposed an efficient verification method for TPN introducing bounded model checking based on satisfiability solving. The proposed method expresses time constraints of TPN by Difference Logic (DL) and uses SMT solvers for verification. Its effectiveness was also demonstrated with an experiment.

Business process similarity measure is required by many applications, such as business process query, improvement, redesign, and etc. Many process behavior similarity measures have been proposed in the past two decades. However, to the best of our knowledge, most existing work only focuses on the direct causality transition relations and totally neglect the concurrent and transitive transition relations that are proved to be equally important when measuring process behavior similarity. In this paper, we take the weakness of existing process behavior similarity measures as a starting point, and propose a comprehensive approach to measure the business process behavior similarity based on the so-called Extended Transition Relation set, ETR-set for short. Essentially, the ETR-set is an ex-tended transition relation set containing direct causal transition relations, minimum concurrent transition relations and transitive causal transition relations. Based on the ETR-set, a novel process behavior similarity measure is defined. By constructing a concurrent reachability graph, our approach finds an effective technique to obtain the ETR-set. Finally, we evaluate our proposed approach in terms of its property analysis as well as conducting a group of control experiments.

This paper proposes a Petri net based mathematical programming approach to combinatorial optimization, in which we generate integer linear programming problems from Petri net models instead of the direct mathematical formulation. We treat two types of combinatorial optimization problems, ordinary problems and time-dependent problems. Firstly, we present autonomous Petri net modeling for ordinary optimization problems, where we obtain fundamental constraints derived from Petri net properties and additional problem-specific ones. Secondly, we propose a colored timed Petri net modeling approach to time-dependent problems, where we generate variables and constraints for time management and for resolving conflicts. Our Petri net approach can drastically reduce the difficulty of the mathematical formulation in a sense that (1) the Petri net modeling does not require deep knowledge of mathematical programming and technique of integer linear model formulations, (2) our automatic formulation allows us to generate large size of integer linear programming problems, and (3) the Petri net modeling approach is flexible for input parameter changes of the original problem.

Workflow nets (WF-nets for short) are a subclass of Petri nets and are used for modeling and analysis of workflows. Soundness is a criterion of logical correctness defined for WF-nets. A WF-net is said to be sound if it satisfies three conditions: (i) option to complete, (ii) proper completion, and (iii) no dead tasks. In this paper, focusing our analysis on acyclic free choice WF-nets, we revealed that (1) Conditions (i) and (ii) of soundness are respectively equivalent to the liveness and the boundedness of its short-circuited net; (2) The decision problem for each condition of soundness is co-NP-complete; and (3) If the short-circuited net has no disjoint paths from a transition to a place (or no disjoint paths from a place to a transition), each condition can be checked in polynomial time.

Response property is a kind of liveness property. Response property problem is defined as follows: Given two activities α and β, whenever α is executed, is β always executed after that? In this paper, we tackled the problem in terms of Workflow Petri nets (WF-nets for short). Our results are (i) the response property problem for acyclic WF-nets is decidable, (ii) the problem is intractable for acyclic asymmetric choice (AC) WF-nets, and (iii) the problem for acyclic bridge-less well-structured WF-nets is solvable in polynomial time. We illustrated the usefulness of the procedure with an application example.

This paper proposes a scheme for automatic generation of mixed-integer programming problems for scheduling with multiple resources based on colored timed Petri nets. Our method reads Petri net data modeled by users, extracts the precedence and conflict relations among transitions, information on the available resources, and finally generates a mixed integer linear programming for exactly solving the target scheduling problem. The mathematical programing problems generated by our tool can be easily inputted to well-known optimizers. The results of this research can extend the usability of optimizers since our tool requires just simple rules of Petri nets but not deep mathematical knowledge.

For a service-oriented architecture based system, the problem of synthesizing a concrete model, i.e., behavioral model, for each service configuring the system from an abstract specification, which is referred to as choreography, is known as the choreography realization problem. In this paper, we assume that choreography is given by an acyclic relation. We have already shown that the condition for the behavioral model is given by lower and upper bounds of acyclic relations. Thus, the degree of freedom for behavioral models increases; developing algorithms of synthesizing an intelligible model for users becomes possible. In this paper, we introduce several metrics for intelligibility of state machines, and study the algorithm of synthesizing Pareto efficient state machines.

This paper presents the formal analysis of the feature negotiation and connection management procedures of the Datagram Congestion Control Protocol (DCCP). Using state space analysis we discover an error in the DCCP specification, that result in both ends of the connection having different agreed feature values. The error occurs when the client ignores an unexpected Response packet in the OPEN state that carries a valid Confirm option. This provides an evidence that the connection management procedure and feature negotiation procedures interact. We also propose solutions to rectify the problem.

Workflow nets (WF-nets for short) are a standard way to automate business processes. Well-Structured WF-nets (WS WF-nets for short) are an important subclass of WF-nets because they have a well-balanced capability to expression power and analysis power. In this paper, we revealed structural and behavioral properties of WS WF-nets. Our results on structural properties are: (i) There is no EFC but non-FC WF-net in WS WF-nets; (ii) A WS WF-net is sound iff it is a van Hee et al.'s ST-net. Our results on behavioral properties are: (i) Any WS WF-net is safe; (ii) Any WS WF-net is separable; (iii) A necessary and sufficient condition on reachability of sound WS WF-net (N,[pIk]). Finally we illustrated the usefulness of the proposed properties with an application example of analyzing workflow evolution.

An organization may have two or more similar workflows as a result of workflow evolutions or mergers and acquisitions. We should grasp the common behavior of those workflows to consolidate the management of them and/or to do business process reengineering. Workflows can be modeled as a particular class of Petri nets, called workflow nets. The common behavior of two or more workflow nets can be represented as a superclass under the behavioral inheritance of those workflow nets. In this paper, we tackled a problem of extracting a superclass from two workflow nets, named Superclass Extraction problem. We first gave a definition of the problem. Next we proposed a procedure to solve the problem on the basis of process mining technique. Then we gave an application of the proposed procedure.

In the classical computation theory, the language of a system features the computational behavior of the system but it does not distinguish the determinism and nondeterminism of actions. However, Milner found that the determinism and nondeterminism affect the interactional behavior of interactive systems and thus the notion of language does not features the interactional behavior. Therefore, Milner proposed the notion of (weak) bisimulation to solve this problem. With the development of internet, more and more interactive systems occur in the world, such as electronic trading system. Security is one of the most important topics for these systems. We find that different security policies can also affect the interactional behavior of a system, which exactly is the reason why a good policy can strengthen the security. In other words, two interactive systems with different security policies are not of an equivalent behavior although their functions (or business processes) are identical. However, the classic (weak) bisimulation theory draws an opposite conclusion that their behaviors are equivalent. The notion of (weak) bisimulation is not suitable for these security-oriented interactive systems since it does not consider a security policy. This paper proposes the concept of secure bisimulation in order to solve the above problem.

Time performance optimization and resource conflict resolution are two important challenges in multiple project management contexts. Compared with traditional project management, multi-project management usually suffers limited and insufficient resources, and a tight and urgent deadline to finish all concurrent projects. In this case, time performance optimization of the global project management is badly needed. To our best knowledge, existing work seldom pays attention to the formal modeling and analyzing of multi-project management in an effort to eliminate resource conflicts and optimizing the project execution time. This work proposes such a method based on PRT-Net, which is a Petri net-based formulism tailored for a kind of project constrained by resource and time. The detailed modeling approaches based on PRT-Net are first presented. Then, resource conflict detection method with corresponding algorithm is proposed. Next, the priority criteria including a key-activity priority strategy and a waiting-short priority strategy are presented to resolve resource conflicts. Finally, we show how to construct a conflict-free PRT-Net by designing resource conflict resolution controllers. By experiments, we prove that our proposed priority strategy can ensure the execution time of global multiple projects much shorter than those without using any strategies.

Many actual systems, e.g. computer programs, can be modeled as a subclass of Petri nets, called bridge-less workflow nets. For bridge-less workflow nets, we revealed the following properties: (i) any acyclic bridge-less workflow net is free choice; (ii) an acyclic bridge-less workflow net is sound iff it is well-structured; and (iii) any sound bridge-less workflow net is well-structured. We also proposed a necessary and sufficient condition to decide whether a given workflow net is bridge-less, and then constructed a polynomial-time procedure for it.

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.

A workflow may be extended to adapt to market growth, legal reform, and so on. The extended workflow must be logically correct, and inherit the behavior of the existing workflow. Even if the extended workflow inherits the behavior, it may be not logically correct. Can we modify it so that it satisfies not only behavioral inheritance but also logical correctness? This is named behavioral inheritance preserving soundizability problem. There are two kinds of behavioral inheritance: protocol inheritance and projection inheritance. In this paper, we tackled protocol inheritance preserving soundizability problem using a subclass of Petri nets called workflow nets. Limiting our analysis to acyclic free choice workflow nets, we formalized the problem. And we gave a necessary and sufficient condition on the problem, which is the existence of a key structure of free choice workflow nets called TP-handle. Based on this condition, we also constructed a polynomial time procedure to solve the problem.

A service-oriented architecture builds the entire system using a combination of independent software components. Such an architecture can be applied to a wide variety of computer systems. The problem of synthesizing service implementation models from choreography representing the overall specifications of service interaction is known as the choreography realization problem. In automatic synthesis, software models should be simple enough to be easily understood by software engineers. In this paper, we discuss a semi-formal method for synthesizing hierarchical state machine models for the choreography realization problem. The proposed method is evaluated using metrics for intelligibility.

In this paper, we proposed reduction operators of timed Petri net for efficient model checking. Timed Petri nets are used widely for modeling and analyzing systems which include time concept. Analysis of the system can be done comprehensively with model checking, but there is a state-space explosion problem. Therefore, previous researchers proposed reduction methods and translation methods to timed automata to perform efficient model checking. However, there is no reduction method which consider observability and there is a trade-off between the amount of description and the size of state space. In this paper, first, we have defined a concept of timed behavioral inheritance. Next, we have proposed reduction operators of timed Petri nets based on timed behavioral inheritance. Then, we have applied our proposed operators to an artificial timed Petri net. Moreover, the results show that the reduction operators which consider observability can reduce the size of state space of the original timed Petri nets within the experiment.

Workflow nets are a standard way for modeling and analyzing workflows. There are two aspects in a workflow: definition and instance. In form of workflow nets, a workflow definition and a workflow instance are respectively represented as a net structure and a marking. The correctness of the workflow definition can be checked by using a workflow nets' property, called soundness. On the other hand, the correctness of the workflow instance can be checked by using a Petri nets' well-known property, called reachability. The reachability problem is known to be intractable. In this paper, we have shown that the reachability problem for (i) sound extended free-choice workflow nets with a marking representing one workflow instance or (ii) acyclic well-structured workflow nets with a marking representing one or more workflow instances can be solved in polynomial time.