Systems Manufacturing Systems Traffic Systems 1.4 Summary of System Classifications 1.5 The Goals of System Theory
Chapter 2 Untimed Models of Discrete-Event Systems
2.1 Introduction 2.2 Languages and Automata Theory 2.2.1 Language Notation and Definitions 2.2.2 Finite-State Automata State Transition Diagrams Automata as Language Recognizers Nondeterministic Finite State Automata Equivalence of Finite-State Automata and Regular Expressions 2.2.3 State Aggregation in Automation 2.2.4 Discrete-Event Systems as State Automata 2.2.5 State Automata Models for Queuing Systems 2.2.6 State Automata with Output 2.2.7 Supervisory Control of Discrete-Event Systems 2.3 Petri Nets 2.3.1 Petri Net Notation and Definitions 2.3.2 Petri Net Markings and State Spaces 2.3.3 Petri Net Dynamics 2.3.4 Petri Net Models for Queueing Systems 2.3.5 Comparison of Petri Net and State Automata Models 2.4 Analysis of Untimed Models of Discrete-Event Systems 2.4.1 Problem Classification Boundedness Conservation Liveness and Deadlocks State Reachability State Coverability Persistence Language Recognition 2.4.2 The Coverability Tree 2.4.3 Applications of the Coverability Tree Boundedness Problems Conseration Problems Coverability Problems Coverability Tree Limitations
Chapter 3 Time Models of Discrete-Event Systems
3.1 Introduction 3.2 Timed State Automata 3.2.1 The Clock Structure 3.2.2 Event Timing Dynamics 3.2.3 A State Space Model 3.2.4 Queueing Systems as Timed State Automata 3.2.5 The Event Scheduling Scheme 3.3 Timed Petri Nets 3.3.1 Time Petri Net Dynamics 3.3.2 Queueing Systems as Timed Petri Nets 3.4 Dioid Algebras 3.4.1 Basic Properties of the (max, +) Algebra 3.4.2 Modeling Queueing Systems in the (max, +) Algebra
Chapter 4 Stochastic Timed Models for Discrete-Event Systems
4.1 Introduction 4.2 Definitions, Notations, and Classifications of Stochastic Processes 4.2.1 Continuous-state and Discrete-state Stochastic Processes 4.2.2 Continuous-time and Discrete-time Stochastic Processes 4.2.3 Some Important Classes of Stochastic Processes Stationary Processes Independent Processes Markov Processes Semi-Markov Processes Renewal Processes 4.3 Stochastic Clock Structures 4.4 Stochastic Timed State Automata 4.5 The Generalized Semi-Markov Process (GSMP) 4.5.1 Queueing Systems as Generalized Semi-Markov Processes 4.5.2 GSMP Analysis 4.6 The Poisson Counting Process 4.7 Properties of The Poisson Process 4.7.1 Exponentially Distributed Interevent Times 4.7.2 The Memoryless Property 4.7.3 Superposition of Poisson Processes 4.7.4 The Residual Lifetime Paradox 4.8 The GSMP With a Poisson Clock Structure 4.8.1 Distribution of Interevent Times 4.8.2 Distribution of Events 4.8.3 Markov Chains 4.9 Extensions of The Generalized Semi-Markov Process
Chapter 5 Markov Chains
5.1 Introduction 5.2 Discrete-Time Markov Chains 5.2.1 Model Specification 5.2.2 Transition Probabilities and the Chapman-Kolmogorov Equations 5.2.3 Homogeneous Markov Chains 5.2.4 The Transition Probability Matrix 5.2.5 State Holding Times 5.2.6 State Probabilities 5.2.7 Transient Analysis 5.2.8 Classification of State Null and Positive Recurrent States Periodic and Aperiodic States Summary of State Classifications 5.2.9 Steady State Analysis 5.2.10 Irreducible Markov Chains 5.2.11 Reducible Markov Chains 5.3 Continuous-time Markov Chains 5.3.1 Model Specifications 5.3.2 Transition Function 5.3.3 The Transition Rate Matrix 5.3.4 Homogeneous Markov Chains 5.3.5 State Holding Times 5.3.6 Physical Interpretation and Properties of the Transition Rate Matrix 5.3.7 Transition Probabilities 5.3.8 State Probabilities 5.3.9 Transient Analysis 5.3.10 Steady State Analysis 5.4 Birth-Death Chains 5.4.1 The Pure Birth Chain 5.4.2 The Poisson Process Revisited 5.4.3 Steady State Analysis of Birth-Death Chains 5.5 Uniformzation of Continuous-Time Markov Chains