• 1 Jackson Network Models of Manufacturing Systems.- 1.1 Introduction.- 1.2 Jackson Networks.- 1.3 The Throughput Function and Computation.- 1.4 Monotonicity of the Throughput Function.- 1.5 Concavity and Convexity.- 1.6 Multiple Servers.- 1.7 Resource Sharing.- 1.8 Arrangement and Majorization.- 1.9 Conclusions.- 1.10 Notes.- 1.11 References.- 2 Hierarchical Modeling of Stochastic Networks, Part I: Fluid Models.- 2.1 Introduction.- 2.2 A Flow Network in Discrete Time.- 2.3 Flow Networks in Continuous Time.- 2.4 Linear Fluid Network and Bottleneck Analysis.- 2.5 Functional Strong Law of Large Numbers.- 2.6 Applications and Hints at Prospects of Fluid Models.- 2.7 References and Comments.- 2.8 References.- 3 Hierarchical Modeling of Stochastic Networks, Part II: Strong Approximations.- 3.1 Introduction.- 3.2 The Model.- 3.3 Preliminaries.- 3.4 The Main Results.- 3.5 Fitting Parametes.- 3.6 Proof of the Main Results.- 3.7 References, Possible Extensions and Future Research.- 3.8 References.- 4 A GSMP Framework for the Analysis of Production Lines.- 4.1 Introduction.- 4.2 GSMP and Its Scheme.- 4.3 Structural Properties of the Scheme.- 4.4 The (a, 6, k) Tandem Queue.- 4.5 Properties with Respect to (a, b, k).- 4.6 Line Reversal.- 4.7 Subadditivity and Ergodicity.- 4.8 Cycle Time Limits.- 4.9 Notes.- 4.10 References.- 5 Stochastic Convexity and Stochastic Majorization.- 5.1 Introduction.- 5.2 Stochastic Order Relations: Functional Characterizations.- 5.3 Second-Order Stochastic Properties.- 5.4 Arrangement and Likelihood Ratio Orderings.- 5.5 Stochastic Rearrangement and Majorization.- 5.6 Notes.- 5.7 References.- 6 Perturbation Analysis of Production Networks.- 6.1 Introduction.- 6.2 Overview Through the Single-Machine Model.- 6.3 Differentiation.- 6.4 Analysis of the Single-Machine Model.- 6.5 Production Networks.- 6.6 Steady-State Derivative Estimation.- 6.7 Concluding Remarks.- 6.8 Notes.- 6.9 References.- 7 Scheduling Networks of Queues: Heavy Traffic Analysis of a Bi-Criteria Problem.- 7.1 Introduction.- 7.2 A Single Server Queue.- 7.3 A Closed Network.- 7.4 A Network with Controllable Inputs.- 7.5 An Example.- 7.6 A Review of Related Results.- 7.7 References.- 8 Scheduling Manufacturing Systems of Re-Entrant Lines.- 8.1 Introduction.- 8.2 Re-Entrant Lines: The Models.- 8.3 Fluctuation Smoothing Scheduling Policies to Reduce Variance of Lateness, Variance of Cycle-Time, and Mean Cycle-Time.- 8.4 Stability of LBFS, SRPTS, EA, EDD and All Least Slack Scheduling Policies.- 8.5 Dynamic Scheduling of a Single Machine with Set-Up Times: A Push Model.- 8.6 Clear-A-Praction Policies.- 8.7 A Lower Bound on Optimal Cost.- 8.8 A Good CAF Policy.- 8.9 Non-Acyclic Manufacturing Systems with Set-Up Times.- 8.10 Concluding Remarks.- 8.11 Notes.- 8.12 References.

"This is a very well-written book, providing a good balance between modeling and mathematical rigor...I enjoyed reading this book and will undoubtedly use it myself; I would also highly recommend it to my graduate students." - Technometrics

• 1 Jackson Network Models of Manufacturing Systems.- 1.1 Introduction.- 1.2 Jackson Networks.- 1.3 The Throughput Function and Computation.- 1.4 Monotonicity of the Throughput Function.- 1.5 Concavity and Convexity.- 1.6 Multiple Servers.- 1.7 Resource Sharing.- 1.8 Arrangement and Majorization.- 1.9 Conclusions.- 1.10 Notes.- 1.11 References.- 2 Hierarchical Modeling of Stochastic Networks, Part I: Fluid Models.- 2.1 Introduction.- 2.2 A Flow Network in Discrete Time.- 2.3 Flow Networks in Continuous Time.- 2.4 Linear Fluid Network and Bottleneck Analysis.- 2.5 Functional Strong Law of Large Numbers.- 2.6 Applications and Hints at Prospects of Fluid Models.- 2.7 References and Comments.- 2.8 References.- 3 Hierarchical Modeling of Stochastic Networks, Part II: Strong Approximations.- 3.1 Introduction.- 3.2 The Model.- 3.3 Preliminaries.- 3.4 The Main Results.- 3.5 Fitting Parametes.- 3.6 Proof of the Main Results.- 3.7 References, Possible Extensions and Future Research.- 3.8 References.- 4 A GSMP Framework for the Analysis of Production Lines.- 4.1 Introduction.- 4.2 GSMP and Its Scheme.- 4.3 Structural Properties of the Scheme.- 4.4 The (a, 6, k) Tandem Queue.- 4.5 Properties with Respect to (a, b, k).- 4.6 Line Reversal.- 4.7 Subadditivity and Ergodicity.- 4.8 Cycle Time Limits.- 4.9 Notes.- 4.10 References.- 5 Stochastic Convexity and Stochastic Majorization.- 5.1 Introduction.- 5.2 Stochastic Order Relations: Functional Characterizations.- 5.3 Second-Order Stochastic Properties.- 5.4 Arrangement and Likelihood Ratio Orderings.- 5.5 Stochastic Rearrangement and Majorization.- 5.6 Notes.- 5.7 References.- 6 Perturbation Analysis of Production Networks.- 6.1 Introduction.- 6.2 Overview Through the Single-Machine Model.- 6.3 Differentiation.- 6.4 Analysis of the Single-Machine Model.- 6.5 Production Networks.- 6.6 Steady-State Derivative Estimation.- 6.7 Concluding Remarks.- 6.8 Notes.- 6.9 References.- 7 Scheduling Networks of Queues: Heavy Traffic Analysis of a Bi-Criteria Problem.- 7.1 Introduction.- 7.2 A Single Server Queue.- 7.3 A Closed Network.- 7.4 A Network with Controllable Inputs.- 7.5 An Example.- 7.6 A Review of Related Results.- 7.7 References.- 8 Scheduling Manufacturing Systems of Re-Entrant Lines.- 8.1 Introduction.- 8.2 Re-Entrant Lines: The Models.- 8.3 Fluctuation Smoothing Scheduling Policies to Reduce Variance of Lateness, Variance of Cycle-Time, and Mean Cycle-Time.- 8.4 Stability of LBFS, SRPTS, EA, EDD and All Least Slack Scheduling Policies.- 8.5 Dynamic Scheduling of a Single Machine with Set-Up Times: A Push Model.- 8.6 Clear-A-Praction Policies.- 8.7 A Lower Bound on Optimal Cost.- 8.8 A Good CAF Policy.- 8.9 Non-Acyclic Manufacturing Systems with Set-Up Times.- 8.10 Concluding Remarks.- 8.11 Notes.- 8.12 References.

"This is a very well-written book, providing a good balance between modeling and mathematical rigor...I enjoyed reading this book and will undoubtedly use it myself; I would also highly recommend it to my graduate students." - Technometrics

• 1 Jackson Network Models of Manufacturing Systems.- 1.1 Introduction.- 1.2 Jackson Networks.- 1.3 The Throughput Function and Computation.- 1.4 Monotonicity of the Throughput Function.- 1.5 Concavity and Convexity.- 1.6 Multiple Servers.- 1.7 Resource Sharing.- 1.8 Arrangement and Majorization.- 1.9 Conclusions.- 1.10 Notes.- 1.11 References.- 2 Hierarchical Modeling of Stochastic Networks, Part I: Fluid Models.- 2.1 Introduction.- 2.2 A Flow Network in Discrete Time.- 2.3 Flow Networks in Continuous Time.- 2.4 Linear Fluid Network and Bottleneck Analysis.- 2.5 Functional Strong Law of Large Numbers.- 2.6 Applications and Hints at Prospects of Fluid Models.- 2.7 References and Comments.- 2.8 References.- 3 Hierarchical Modeling of Stochastic Networks, Part II: Strong Approximations.- 3.1 Introduction.- 3.2 The Model.- 3.3 Preliminaries.- 3.4 The Main Results.- 3.5 Fitting Parametes.- 3.6 Proof of the Main Results.- 3.7 References, Possible Extensions and Future Research.- 3.8 References.- 4 A GSMP Framework for the Analysis of Production Lines.- 4.1 Introduction.- 4.2 GSMP and Its Scheme.- 4.3 Structural Properties of the Scheme.- 4.4 The (a, 6, k) Tandem Queue.- 4.5 Properties with Respect to (a, b, k).- 4.6 Line Reversal.- 4.7 Subadditivity and Ergodicity.- 4.8 Cycle Time Limits.- 4.9 Notes.- 4.10 References.- 5 Stochastic Convexity and Stochastic Majorization.- 5.1 Introduction.- 5.2 Stochastic Order Relations: Functional Characterizations.- 5.3 Second-Order Stochastic Properties.- 5.4 Arrangement and Likelihood Ratio Orderings.- 5.5 Stochastic Rearrangement and Majorization.- 5.6 Notes.- 5.7 References.- 6 Perturbation Analysis of Production Networks.- 6.1 Introduction.- 6.2 Overview Through the Single-Machine Model.- 6.3 Differentiation.- 6.4 Analysis of the Single-Machine Model.- 6.5 Production Networks.- 6.6 Steady-State Derivative Estimation.- 6.7 Concluding Remarks.- 6.8 Notes.- 6.9 References.- 7 Scheduling Networks of Queues: Heavy Traffic Analysis of a Bi-Criteria Problem.- 7.1 Introduction.- 7.2 A Single Server Queue.- 7.3 A Closed Network.- 7.4 A Network with Controllable Inputs.- 7.5 An Example.- 7.6 A Review of Related Results.- 7.7 References.- 8 Scheduling Manufacturing Systems of Re-Entrant Lines.- 8.1 Introduction.- 8.2 Re-Entrant Lines: The Models.- 8.3 Fluctuation Smoothing Scheduling Policies to Reduce Variance of Lateness, Variance of Cycle-Time, and Mean Cycle-Time.- 8.4 Stability of LBFS, SRPTS, EA, EDD and All Least Slack Scheduling Policies.- 8.5 Dynamic Scheduling of a Single Machine with Set-Up Times: A Push Model.- 8.6 Clear-A-Praction Policies.- 8.7 A Lower Bound on Optimal Cost.- 8.8 A Good CAF Policy.- 8.9 Non-Acyclic Manufacturing Systems with Set-Up Times.- 8.10 Concluding Remarks.- 8.11 Notes.- 8.12 References.

"This is a very well-written book, providing a good balance between modeling and mathematical rigor...I enjoyed reading this book and will undoubtedly use it myself; I would also highly recommend it to my graduate students." - Technometrics