Beschreibung
Autorenporträt
Inhaltsangabe1 Jackson Network Models of Manufacturing Systems.- 1.1 Introduction.- 1.2 Jackson Networks.- 1.2.1 The Open Model.- 1.2.2 The Closed Model.- 1.2.3 The Semi-Open Model.- 1.3 The Throughput Function and Computation.- 1.4 Monotonicity of the Throughput Function.- 1.4.1 Equilibrium Rate.- 1.4.2 PF2 Property.- 1.4.3 Likelihood Ratio Ordering.- 1.4.4 Shifted Likelihood Ratio Ordering.- 1.5 Concavity and Convexity.- 1.6 Multiple Servers.- 1.7 Resource Sharing.- 1.7.1 Aggregation of Servers.- 1.7.2 Aggregation of Nodes.- 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.- 2.1.1 Macro, Meso and Microscopic Models for an i.i.d. Sequence.- 2.1.2 Strong Approximations - A Unifying Framework.- 2.1.3 Summary.- 2.2 A Flow Network in Discrete Time.- 2.2.1 The Microscopic Model and Its Dynamics.- 2.2.2 Reformulation in Terms of Cumulants and Oblique Reflection.- 2.2.3 Mesoscopic Models and Strong Approximations.- 2.2.4 Macroscopic Models: FSLLN's.- 2.2.5 Deviations Between Micro and Macro Models: FCLT.- 2.3 Flow Networks in Continuous Time.- 2.3.1 Flow Networks with Time Inhomogeneous Dynamics.- 2.3.2 State-Dependent Dynamics.- 2.4 Linear Fluid Network and Bottleneck Analysis.- 2.4.1 Traffic Equations and Bottleneck Definitions.- 2.4.2 Bottleneck Analysis.- 2.5 Functional Strong Law of Large Numbers.- 2.5.1 FSLLN's for Nonlinear Fluid Networks.- 2.5.2 FSLLN's for Nonparametric Jackson Queueing Networks.- 2.5.3 FSLLN's for State-Dependent Networks.- 2.6 Applications and Hints at Prospects of Fluid Models.- 2.6.1 Stochastic Fluid Models for Manufacturing and Communication Systems.- 2.6.2 Heterogeneous Fluid Networks: Bottleneck Analysis and Scheduling Control.- 2.6.3 Transient Analysis of the Mt/Mt/1 Queue.- 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.- 3.2.1 Primitives and Dynamics.- 3.2.2 Underlying Assumptions and Parameters.- 3.2.3 Nonparametric Jackson Networks.- 3.3 Preliminaries.- 3.3.1 Traffic Equations and Bottlenecks.- 3.3.2 The Oblique Reflection Mapping.- 3.3.3 Reflected Brownian Motion on the Orthant.- 3.4 The Main Results.- 3.4.1 Functional Strong Approximations.- 3.4.2 Functional Laws of the Iterated Logarithm.- 3.4.3 FSLLN's and Fluid Approximations.- 3.4.4 FCLT's and Diffusion Approximations.- 3.5 Fitting Parametes.- 3.5.1 Nonparametric Jackson Networks.- 3.5.2 Product Form and Single Station.- 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.- 4.2.1 The Scheme: GSMS.- 4.2.2 Language and Score Space.- 4.3 Structural Properties of the Scheme.- 4.3.1 Some Useful Properties.- 4.3.2 Condition (M).- 4.3.3 Condition (CX).- 4.3.4 Minimal Elements.- 4.3.5 Monotonicity and Convexity.- 4.3.6 Characteristic Function.- 4.3.7 Subschemes.- 4.3.8 Synchronized Schemes.- 4.4 The (a, 6, k) Tandem Queue.- 4.4.1 Production Lines Under Kanban Control.- 4.4.2 Properties with Respect to Service Times.- 4.5 Properties with Respect to (a, b, k).- 4.5.1 Monotonicity with Respect to (a, b, k).- 4.5.2 Concavity with Respect to (a, b, k).- 4.6 Line Reversal.- 4.6.1 Reversibility of Departure Epochs.- 4.6.2 Full Reversibility.- 4.7 Subadditivity and Ergodicity.- 4.7.1 Event-Epoch Vectorization.- 4.7.2 The Subadditive Ergodic Theorem.- 4.7.3 More General Matrices.- 4.8 Cycle Time Limits.- 4.8.1 Existence of the Limits.- 4.8.2 Rate of Convergence.- 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.- 5.3.1 Stochastic Convexity.- 5.3.2 Stochastic Supermodularity and Submodularity.- 5.3.3 Markov Chain Applications.- 5.3.
