Kunihiko Hiraishi

Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs

We study the problem of nonpreemptively scheduling n jobs on m identical machines in parallel to maximize the weighted number of jobs that are completed exactly at their due dates. We show that this problem is solvable in polynomial time even if positive set-up times are allowed. Moreover, we show that if due date tolerances are permitted, then already the single-machine case is NP-hard even if all set-up times are zero and all weights are the same.

Formal verification of business processes with temporal and resource constraints

The correctness of business process models is critical for IT system development. The properties of business processes need to be analyzed when they are designed. In particular, business processes usually have various constraints on time and resources, which may cause serious problems like bottlenecks and deadlocks. In this paper, we propose an approach based on the model checking technique for verifying business process models with temporal and resource constraints. First, we extend Business Process Modeling Notation (BPMN) to handle these constraints. Then, we provide a mapping of the business process models described with this extended BPMN onto timed automata that can be verified by the UPPAAL model checker. This approach helps to eliminate various problems with time and resources in the early phase of development, and enables the quality assurance of business process models.

Brief paper: An integer programming approach to optimal control problems in context-sensitive probabilistic Boolean networks

A Boolean network is one of the models of biological networks such as gene regulatory networks, and has been extensively studied. In particular, a probabilistic Boolean network (PBN) is well known as an extension of Boolean networks, but in the existing methods to solve the optimal control problem of PBNs, it is necessary to compute the state transition diagram with 2^n nodes for a given PBN with n states. To avoid this computation, an integer programming-based approach is proposed for a context-sensitive PBN (CS-PBN), which is a general form of PBNs. In the proposed method, a CS-PBN is transformed into a linear system with binary variables, and the optimal control problem is reduced to an integer linear programming problem. By a numerical example, the effectiveness of the proposed method is shown.

On Solvability of a Decentralized Supervisory Control Problem With Communication

We study a decentralized control problem of discrete event systems with communication. We first give a general automata-theoretic formalism that enables us to handle various types of communication, including delay. The decentralized control problem is shown to be undecidable under this formalism. Next we propose a semi-decision procedure for computing finite-state controllers to achieve a given specification in the sense of bisimilarity between the controlled system and a given specification. Using this procedure, we prove decidability of the problem for two special cases, one is the case in which the communication behavior is given as k -bounded-delay communication, and the other is the case in which any cycle in the state transition diagram of the system contains an event observable by all controllers. We also show a method for optimizing controllers based on a graph problem.

Performance Evaluation of Workflows Using Continuous Petri Nets with Interval Firing Speeds

In this paper, we study performance evaluation of workflow-based information systems. Because of state space explosion, analysis by stochastic models, such as stochastic Petri nets and queuing models, is not suitable for workflow systems in which a large number of flow instances run concurrently. We use fluid-flow approximation technique to overcome this difficulty. In the proposed method, GSPN (Generalized Stochastic Petri Nets) models representing workflows are approximated by a class of timed continuous Petri nets, called routing timed continuous Petri nets (RTCPN). In RTCPN models, each discrete set is approximated by a continuous region on a real-valued vector space, and variance in probability distribution is replaced with a real-valued interval. Next we derive piecewise linear systems from RTCPN models, and use interval methods to compute guaranteed enclosures for state variables. As a case study, we solve an optimal resource assignment problem for a paper review process.

PN2: An Elementary Model for Design and Analysis of Multi-agent Systems

Agent technology is widely recognized as a new paradigm for design of concurrent software and systems. The aim of this paper is to give a mathematical foundation for design and analysis of multi-agent systems by means of a Petri-net-based model. The proposed model, called PN2, is based on place/transition nets (P/T nets), which is one of the simplest classes of Petri nets. The main difference between PN2s and P/T nets is that each token, representing an agent, is also a P/T net. State equation and invariants are known as standard techniques for the analysis of P/T nets. As the first step of mathematical analysis of PN2s, we define these for PN2s, and show how the invariants are computed in an efficient way.

Optimal control of gene regulatory networks with effectiveness of multiple drugs: a Boolean network approach.

Developing control theory of gene regulatory networks is one of the significant topics in the field of systems biology, and it is expected to apply the obtained results to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of gene regulatory networks, and gene expression is expressed by a binary value (0 or 1). In the control problem, we assume that the concentration level of a part of genes is arbitrarily determined as the control input. However, there are cases that no gene satisfying this assumption exists, and it is important to consider structural control via external stimuli. Furthermore, these controls are realized by multiple drugs, and it is also important to consider multiple effects such as duration of effect and side effects. In this paper, we propose a BN model with two types of the control inputs and an optimal control method with duration of drug effectiveness. First, a BN model and duration of drug effectiveness are discussed. Next, the optimal control problem is formulated and is reduced to an integer linear programming problem. Finally, numerical simulations are shown.

Polynomial-time algorithm for controllability test of a class of Boolean biological networks

In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.

Stabilization of Finite Automata with Application to Hybrid Systems Control

This paper discusses the state feedback stabilization problem of a deterministic finite automaton (DFA), and its application to stabilizing model predictive control (MPC) of hybrid systems. In the modeling of a DFA, a linear state equation representation recently proposed by the authors is used. First, this representation is briefly explained. Next, after the notion of equilibrium points and stabilizability of the DFA are defined, a necessary and sufficient condition for the DFA to be stabilizable is derived. Then a characterization of all stabilizing state feedback controllers is presented. Third, a simple example is given to show how to follow the proposed procedure. Finally, control Lyapunov functions for hybrid systems are introduced based on the above results, and the MPC law is proposed. The effectiveness of this method is shown by a numerical example.

A Wavelet Approach for Solving linear quadratic optimal control problems

In this article a method that is based on the recently developed Chebyshev wavelets is presented to solve the linear quadratic optimal control problem with terminal constraints. The Chebyshev wavelets are reviewed, and a method of approximating the optimal control problem is described. In addition, the formulation of the optimal control problem into mathematical programming one is presented. The method is based on converting the optimal control problem into a quadratic programming problem. To show the effectiveness of the method a numerical example is solved