Fishwick P.A. (editor) Handbook of Dynamic System Modeling
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37-20 Handbook of Dynamic System Modeling
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Index
A
Abstract model, 3-10
Abstraction and scaling, 5-9 to 5-17
choice of, consequences, 5-14 to 5-15
geometric scaling, 5-11 to 5-13
lumped elements and, 5-9 to 5-11
of data presentations, 5-15 to 5-17
scale in equations, size and limits, 5-13 to 5-14
Adams’ method, 17-17
Agent-oriented modeling in simulation, 8-1 to 8-12
agents for modeling, 8-3 to 8-6
agent metaphor for, 8-3 to 8-6
modeling and simulation for agents, 8-6 to 8-10
for multiagent systems, 8-7 to 8-8
multiagent systems, designing, 8-8 to 8-10
Algebraic reasoning and verification, 19-11 to 19-19
bottle filling line example, 19-12 to 19-14
normal form, syntax of, 19-15 to 19-16
parallel composition, elimination of, 19-17
process instantiation, elimination of, 19-15
recursion scope operator, syntax and semantics of,
19-14
substitution of constants and additional
elimination, 19-17 to 19-18
tool-based verification, 19-19
Agriculture and natural resources
ontology-based simulation in,
30-1 to 30-13
building, 30-6 to 30-10: collection of relevant
documents, 30-6; define equations, 30-9 to
30-10; generating program code for
implementing the simulation, 30-10;
identifying classes, individuals, and
properties, 30-7 to 30-9; initial values of
state variables, constants, and database
access, 30-10; model defining in terms of
elements, 30-7; simulation execution,
30-10
connecting models with data sources, 30-4 to
30-5
integrating documentation and training
resources, 30-5
model base, 30-3
reasoning, 30-6 to 30-7
representing equations and symbols, 30-4
system structure (logical and physical), 30-3 to
30-4
tools for, 30-10 to 30-12: EquationEditor, 30-11
to 30-12; ontology editor, 30-10 to 30-11;
SimulationEditor, 30-12
Analogy-making
architectural principles, 2-8 to 2-12, See also
separate entry
as a means of ‘bootstrapping’ cognition, 2-3 to 2-5
as sameness,2-2 to 2-3
bottom-up/top-down interaction, 2-6 to 2-8
computational modeling, dynamics of, 2-1 to 2
-17
context-dependent computational temperature,
2-6
definition, 2-1
mechanisms presented, impact of, 2-16
program, working, 2-12 to 2-13
Copycat, 2-12
Ta bl e to p, 2-12
proportional analogies, 2-2
representation-building in, dynamics of, 2-5 to 2-6
scaling up issue, 2-16
top-down and bottom-up processes, interaction
between,2-6 to 2-8
Architectural principles,
in analogy-making, 2-8 to 2-12
‘slipnet,’ a semantic network, 2-8 to 2-9
codelets, 2-10
coderack, 2-10
computational temperature, dynamic codelet
selection via, 2-10 to 2-12
local, stochastic processing, 2-12
representation-building and
correspondence-finding, integration, 2-12
workspace, 2-9: AAB, 2-9
worldview, 2-10
Artificial Intelligence (AI), 2-11
Asymptotic stability, 18-9 to 18-13
I-1
I-2 Index
Asynchronous input property, 14-16 to 14-17
Automata theory, 19-2
Automatic synchronization, 36-12
B
Balloted product development process (BPDP), 9-7
Blender interface, 14-10 to 14-11
Boiling water example, of multimodeling, 14-20 to
14-26
2D representation, 14-22
code generation, 14-23 to 14-26
FBM, multimodeling for, 14-21
first-level FSM for, 14-22
FSM, multimodeling for, 14-21
model creation, 14-2 to 14-23
geometry and dynamic models, 14-22 to 14-23
interaction model, 14-23
second-level FSM for, 14-22
third-level FBM, 14-22
Bond graphs, 26-5 to 26-21
appearance, 26-6
causality, 26-14 to 26-21
arbitrary causality, 26-16, 26-18 to 26-19
causal analysis, feedback on modeling decisions,
26-16 to 26-17
causal constraints, 26-16
causal port properties, 26-14
elementary behaviors, 26-6 to 26-14
environment, sources, boundary conditions,
constraints, 26-7 to 26-8
fixed causality of second kind, 26-15, 26-18
fixed causality of the first kind, 26-14 to 26-15,
26-17
power continuous structure, 26-8 resistor, 26-8
to 26-9
preferred causality, 26-15 to 26-16, 26-17 to
26-18
storage, 26-6 to 26-7
generalized junction structure (GJS), See also
separate entry
Bottom-up/top-down interaction, 2-6 to 2-8
computational models implementing, 2-8
Boundedness, 20-9
Buckingham Pi theorem, 5-5, 5-7 to 5-9
Bulirsch–Stoer method, 17-17
Burke’s theorem, 25-12, 25-14
C
Cash–Karp formulas, 17-12
Causality-based classification, 3-9
Causal loop diagrams, 33-17 to 33-19
Cellular automata (CA)
characteristics, 21-3
dynamic systems modeling with, 21-1 to 21-16
history, 21-2 to 21-3
lattice gas cellular automata (LGCA) models of
fluid dynamics, 21-5 to 21-16, See also
separate entry
one-dimensional CAS, 21-3 to 21-5
boundary conditions, 21-3
Chemical reactions, dynamics of, 17-2
Classification based on determinism, 3-9
Colored Petri nets (CPNs), 24-10 to 24-12
Commercial off-the-shelf (COTS) simulation
packages
commercial off-the-shelf discrete-event simulation
packages (CSPs), 9-2
CSP-based distributed simulation, 9-5 to 9-6:
current progress, 9-6; problem of, 9-5 to
9-6
modeling with, 9-2 to 9-3
Component-oriented simulation toolkit (COST),
35-3 to 35-7
functor, 35-5
implementation, 35-4
inport and outport class, 35-6
motivation, from object to component, 35-3 to
35-5
simulation time and port index, 35-6 to 35-7
timer, 35
-7
Concurrency theory, 19-2
Connectionist networks (CNs), 22-2 to 22-4
basic approach, 22-2 to 22-3
function approximation, 22-3
learning, 22-3 to 22-4
Conservation laws, 11-16 to 11-18
Consistent-mass formulation, 13-16
Context-dependent computational temperature, 2-6
Continuous systems, discrete-event simulation of,
11-1 to 11-22
conservation laws, 11-16 to 11-18
coupled ordinary differential equations,
simulating, 11-6 to 11-8
DEVS representation of discrete-event integrators,
11-8 to 11-13, See also separate entry
heat equation, 11-13 to 11-16
single ordinary differential equation, simulating,
11-2 to 11-5
two-point integration schemes, 11-19 to 11-21
Continuous-time models, 3-7
Coordinate-wise monotonicity, 18-10 to 18-13
Copycat program, 2-12
Critical damping, 13-17
D
Daisy world model, 27-6 to 27-9
background, 27-6
equilibrium diagram for, 27-7
Index I-3
feedback loop control of Daisy world
temperatures, 27-8
management flight simulator, 27-9 to 27-13
Decision making, models to support, 33-2 to 33-4
Defense Advanced Research Project Agency
(DARPA), 16-2
Defense simulation
interoperability and composability in, 16-1 to 16-9,
See also under Simulation interconnection
Differential-algebraic equations (DAE), 36-19
Determinism, 3-9
DEVS representation of discrete-event integrators,
11-8 to 11-13
atomic models, 11-8
coupled models, 11-8
DEVS simulation algorithm, 11-9
of two coupled ordinary differential equations
simulation of, 11-13
Differential equations, See also Ordinary differential
equations
Dimensional analysis, 5-4
basic method of, 5-5 to 5-7
Buckingham Pi theorem, 5-5, 5-7 to 5-9
Discontinuity sticking, 15-18
Discontinuous systems, 36-10 to 36-13
Discrete dynamical systems, difference equations as,
18-1 to 18-17
basic concepts, 18-2 to 18-4
first-order difference equations, 18-4 to 18-8
asymptotic stability, 18-4 to 18-6
chaos,
18-7 to 18-8
cycles and limit cycles, 18-6 to 18-7
higher order difference equations, 18-8 to 18-17,
See also separate entry
Discrete-event execution, 10-7 to 10-13
ATM multiplexer model, 10-8
cell arrival event handler, 10-9
cell departure event handler, 10-9
state, 10-9
conservative parallel execution, 10-10 to 10-11
execution method, 10-7
optimistic parallel execution, 10-11 to 10-13
mixed-mode parallel execution, 10-13
reverse computation in, 10-12
parallelizing, 10-9 to 10-13
sequential, 10-8
Discrete-event modeling ontology (DeMO), 3-2, 3-7
to 3-8
DeModel class hierarchy, 3-18
model component class hierarchy, 3-16
model concept, 3-14
model mechanism, 3-14
overview, 3-14 to 3-18
Discrete-event models, 3-7 to 3-8
Discrete-event simulation (DES), 9-2, 10-2
conceptual basis for, 3-4 to 3-6
of continuous systems, 11
-1 to 11-22, See also
under Continuous systems
in management science, 33-7 to 33-16, See also
under Management science
in manufacturing systems, 34-7 to 34-8, See also
under Manufacturing systems
overview of, 3-12 to 3-14
Discrete-event systems modeling
DEVS formalism for, 6-1 to 6-12
for discrete-event systems modeling, 6-1 to 6-12
atomic DEVS model, 6-4 to 6-5: composition
of, 6-8 to 6-9; state equation form of, 6-7
composed DEVS model, system analysis by,
6-9 to 6-10
coupled DEVS model, 6-5
DES analysis with, 6-7 to 6-10
ping-pong protocol, DEVS modeling, 6-2, 6-5
to 6-7
RECEIVER, 6-2
SENDER: external views, 6-2; internal views,
6-2
simulation of, 6-10 to 6-12
methodology and environment, 6-10 to 6-12
simulation speedup and simulators
interoperation, 6-12
system-theoretic DES modeling, 6-3
Discrete-state transition
basic forms, 15-11
combinational logic,
15-11
sequential logic, 15-11 to 15-12
Discrete-time models, 3-8
Distributed interactive simulation (DIS), 16-2
Distributed modeling, 9-1 to 9-16, See also under
Commercial off-the-shelf
case study, 9-13 to 9-16
bicycle assembly SOM, 9-15
bicyclefactormodel,9-14
bicycle manufacturing, system FOM, 9-15
frame production line SOM, 9-14
illustrative protocol, 9-13 to 9-16
wheel production line SOM, 9-14
definition, 9-1
distributed simulation, 9-3 to 9-5
standards-based approach, 9-7 to 9-13
emerging standards and the CSPI-PDG, 9-7 to
9-8
entity transfer specification, 9-9 to 9-13:
architecture, 9-10; interaction hierarchy,
9-11; OMT tables used for, 9-12
simulation interoperability standards
organization, 9-7
type I interoperability reference model, 9-8 to
9-9
Distributed simulation, 9-3 to 9-5, 10-2
I-4 Index
Domains, See also under individual entries;
Mesh-based simulation
continuum domains, 12-7 to 12-9
definitions, transformations, and interactions,
12-7 to 12-9
discrete domains, 12-9
discretized geometric domains, 12-13
geometric domain, 12-13
interactions of domains, 12-9
Domain-specific languages (DSL), 7-2
language definition formalism, 7-3 to 7-4
abstract syntax of, 7-3
concrete syntax of, 7-3
Domain-specific modeling (DSM), 7-1 to 7-18
case studies, 7-6 to 7-11
customized Petri net modeling language, 7-6 to
7-11, See also under Petri nets
components of, 7-2 to 7-6, See also
Domain-specific languages
application areas of, 7-5 to 7-6
domain-specific modeling environments
(DSME), 7-4; characteristics, 7-4
model generators, 7-4 to 7-5
conference registration application
design of, 7-14
model, 7-15 to 7-16
S60 simulator, 7-16
modeling language, defining, 7-12 to 7-13
supporting tools,
7-17 to 7-18
metamodeling tools, retrospective of, 7-17
modern metamodeling tools, 7-17 to 7-18
Dymola symbolic processing, 36-22
Dynamic context-dependent
representation-building, 2-4
Dynamic exchange language (DXL), 14-13 to 14-20
between heterogeneous models in DXL, 14-20
between homogeneous models, 14-18 to 14-20
concepts, 14-13
FBM-to-DXL translation, 14-18
multimodel syntax, 14-14
programming semantics, 14-14
semantics of, 14-15 to 14-17
asynchronous input property, 14-16 to 14-17
augmented DXL syntax, 14-15
DXL block notation, 14-15
information stream mechanism, 14-15 to 14-16
notation, 14-15
synchronous input property, 14-16
syntax of, 14-14
Dynamic system modeling,
categorizing models, ways of, 1-2
analysis, 1-2
synthesis, 1-2
theory, 1-2
examples, 1-2 to 1-3; types of, 1-2
finite state machine, 1-2
functional block model, 1-2
ordinary differential equation,
1-2
Petri net, 1-2
language, 1-3 to 1-5, See also separate entry
languages of, 1-1 to 1-11
taxonomic approaches, 1-3
E
Ecological modeling and simulation
from historical development to individual-based
modeling, 29-1 to 29-16
applications, 29-12 to 29-15
as scientific instruments, 29-7 to 29-8
determinism or probability?, 29-5
individual-based models, 29-9 to 29-12
modeling techniques, 29-5 to 29-7
organization levels and methodological choices,
29-8 to 29-9
Effective process times (EPT), 34-8 to 34-10
Elman network, 22-5
Energy systems language, dynamic simulation with,
28-1 to 28-32
reading an, 28-4 to 28-8
diagram layout: and its connection to energy
theory, 28-4 to 28-6; sources arrangement,
28-5 to 28-6; transformity principle of,
28-5, See also under Transformity principle
Forrester’s systems dynamics approach,
comparison with, 28-29 to 28-31
Marshsectormodel,28-27 to 28-29, See also
separate entry
model constants, calibration of, 28-21 to 28-22
simulation, preparation for, 22-27: simulation
software and energy systems language,
28-22 to 28-26
stylistic diagramming features, 28-7 to 28-8:
converging and diverging flow lines, 28-8;
nested symbols,
28-8; sector boundaries,
28-7 to 28-8; vertical and horizontal stacks
of symbols, 28-8
symbols within the system boundary, 28-6 to
28-7, See also under Symbols
timescales and numerical integration, 28-26 to
28-27
translating a diagram to dynamic equations,
28-8 to 28-21: basic equation forms
indicated in, 28-16 to 28-21; equation
naming convention, 28-10 to 28-15;
feedback effect of production processes on
the environmental variables involved,
28-20; flow-limited source, 28-18 to 28-19;
multiple simultaneous interactions in,
28-19 to 28-20; of Marsh Sector, 28-11 to
Index I-5
28-15; passive inputs and environmental
conditions, 28-21; two-way interactions,
28-20 to 28-21
Environmental systems
Daisy world model, 27-6 to 27-9, See also separate
entry
system dynamics modeling of, 27-1 to 27-13
flowers and sales models, comparison of, 27-4 to
27-6: feedback loop structure of flowers
model, 27-5; feedback loop structure of the
sales model, 27-5
Stella diagram, 27-2
Vensim diagram, 27-2
Euler–Cauchy integration, 33-16
Euler’s theorem, 26-22
Event relationship graphs (ERGs)
enrichments to, 23-7 to 23-10
building large and complex models, 23-8 to 23-9
parametric event relationship graphs, 23-7 to
23-8
process interaction flows, 23-13
experimenting with, 23-17 to 23-20
graph analysis, 23-16 to 23-17
modeling causality with, 23-1 to 23-20
background and definitions, 23-2 to 23-7
discrete-event systems and models, 23-2 to 23-3,
23-10 to 23-16: attributes, 23-2; factors,
23-2; mapping Petri nets into event
relationship graphs,
23-11 to 23-13;
parameters, 23-2; stochastic timed Petri net
(STPN), 23-10 to 23-11
discrete-event system simulations, 23-3
graph modeling element, ER in, 23-3 to 23-6
verbal event graphs, 23-6
reading, 23-6 to 23-7
simulation of, 23-16
variations of, 23-9 to 23-10
Execution, model, 10-1 to 10-13
discrete-event execution, 10-7 to 10-13, See also
under Discrete-event execution
elements of, 10-2 to 10-3
executable timelines, 5
physical time, 10-5
simulation time, 10-5
wallclock time, 10-5
execution platforms, 10-3 to 10-4
generating executables from models, 10-4 to 10-5
pacing the execution, 10-5
simulating large-scale models/scenarios,
approaches to, 10-3
systems and models, 10-1 to 10-2
time-stepped execution, 10-5 to 10-7
for parallel execution, 10-7
for sequential execution, 10-6
parallelizing, 10-6 to 10
-7
F
4D face-centered hyper cube (FCHC), 21-10
Faraday’s law of induction, 26-13
Finite elements, 13-1 to 13-21
dynamics, 13-16 to 13-21
finite element theory (FEM), 13-1 to 13-9
shape functions, 13-4
simple FEM theory, 13-1 to 13-4
tapered extensional example, 13-4 to 13-6; axial
loaded tapered problem, 13-4; shape
function models for, 13-5; axial
displacement result, 13-5; axial stress for,
13-6
available elements, 13-8 to 13-9
mapping errors, 13-7 to 13-8
numerical integration, 13-6 to 13-7
shape function accuracy, 13-6
membrane elements, 13-9 to 13-12, See also
separate entry
multiple degree of freedom (MDOF) dynamic
analysis, 13-19 to 13-21
single degree of freedom (SDOF) dynamic
analysis, 13-17 to 13-19
solid elements, 13-15 to 13-16
behavior and DOF, 13-15 to 13-16
Flow models, 34-16 to 34-18
Forrester’s systems dynamics approach, 28-29 to
28
-31
Formalism, 1-4
‘FSM synthesis’, 1-9
FSM Moore machine semantics, 1-9
Function
set-theoretic concepts, 1-9
G
Gaia hypothesis, 27-6
Gauss–Legendre quadrature method, 13-6 to 13-7
Generalized junction structure (GJS)
transduction and interconnection, 26-9 to 26-14
junctions, 26-10
decomposition, 26-12
Generalized semi-Markov Processes (GSMP), 23-13
Generic runtime infrastructure for distributed
simulation (GRIDS), 9-6
Geometric scaling, 5-11 to 5-13
Giles et al network, 22-5
H
Heat equation, 11-13 to 11-16
Higher order difference equations, 18-8 to 18-17
asymptotic stability
coordinate-wise monotonicity, 18-10 to 18-13
weak contractions, 18-9 to 18-10
I-6 Index
Higher order difference equations, (Contd.)
persistent oscillations and chaos, 18-13
to 18-14
semiconjugacy, 18-14 to 18-17
Human behavior representation (HBR), 8-5
Human interaction in organizational systems,
modeling, 31-1 to 31-13
systems and human interaction, 31-2
to 31-3
case study at Ford Motor Company, 31-8
to 31-12
designed abstract systems, 31-2
designed physical systems, 31-2
human activity systems, 31-2
human-to-human interaction, modeling, 31-5
human-to-system interaction, modeling, 31-4
to 31-5
knowledge-based improvement (KBI)
methodology, 31-5 to 31-8, See also
separate entry
natural systems, 31-2
need for, 31-3 to 31-4
research and practice, 31-4 to 31-5
Hybrid dynamic systems, modeling and execution,
15-1 to 15-24
advanced topics in, 15-17 to 15-22
mode changes, 15-19 to 15-22: reinitialization,
15-19 to 15-20; sequences of, 15-20 to
15-22
zero-crossing detection,
15-17 to 15-18:
difficulty in, 15-17
behavior classes of, 15-4, 15-9 to 15-12
continuous-time behavior, 15-9 to 15-10
handling mode transitions, 15-10 to 15-12:
event detection and location, 15-10 to
15-11; mode transition inferencing, 15-11
to 15-12
operational structure, 15-9
reinitialization of state variables, 15-12
description, 15-6
design, 15-7 to 15-9
explicit models, 15-8 to 15-9
implicit models, 15-7 to 15-8
driver control in, 15-4
geometric representation of, 15-6
implementation, 15-12 to 15-16
classes of events, 15-12
classes of temporal behavior, 15-12 to 15-13
event-driven execution, 15-14
time-driven execution, 15-13 to 15-14
types, combining, 15-14 to 15-16
need for, 15-3 to 15-5
pathological behavior classes, 15-22 to 15-23
Hybrid process algebra,
19-3
Hypertext markup language (HTML), 3-2 to 3-3
I
Individual-based models, 29-9 to 29-12
Integrative multimodeling, 14-2 to 14-4
general multimodeling, 14-2 to 14-4
homogeneous and heterogeneous multimodels,
14-3 to 14-4
intralevel and interlevel couplings, 14-2 to 14-3
purpose of, 14-2
Irreflexivity, 20-7 to 20-8
J
Jackson network, 25-14
K
Kadanoff–Swift model, 21-6
Kingman’s equation, 34-5
Kirchoff theory, 13-13 to 13-14, 36-5
Knowledge-based improvement (KBI) methodology,
31-5 to 31-8
data collection through simulation (stage 2), 31-7
to 31-8
determining the consequences of the decision
making strategies (stage 4), 31-8
determining the decision makers’ decision making
strategies (stage 3), 31-8
seeking improvements (stage 5), 31-8
understanding the decision making process
(stage 1), 31-7
L
Languages
natural language, 1-4
of dynamic system modeling, 1-3 to 1-5
pragmatics, 1-4, See also separate entry
semantics, 1-4
syntax, 1-4, See also separate entry
Lattice Boltzmann method (LBM), 21-14 to 21-16
Lattice-BGK (L-BGK) method, 21-15
Lattice gas cellular automata (LGCA) models
of fluid dynamics, 21-5 to 21-16
FHP model, 21-9
HPP model, 21-7
research activity on, 21-10
applications, 21-14
fluid dynamics and, 21-11 to 21-12
lattice Boltzmann method (LBM), 21-14 to
21-16, See also separate entry
simulating an, 21-12 to 21-14
Learning algorithms, 22-3
Lefkovitch models, 29-3
Legendre transforms, 26-22 to 22-25
causality and, 26-24 to 26-25
Index I-7
in electrical circuits, 26-24
in mechanics, 26-24
in thermodynamics, 26-23 to 26-24
Leslie matrix, 29-3
Level-rate diagrams, 33-19 to 33-21
Lindley’s equation, 25-7
Linearity, 20-8 to 20-9
Linearity, 5-19 to 5-20
geometric scaling and, 5-19 to 5-20
Little’s Law, 25-7 to 25-8, 34-6
Lookahead, 10-10
Lotka–Volterra model, 17-2
Lumped elements, 5-9 to 5-11
Lumped-mass formulation, 13-16
M
M/M/1 queueing system, 25-9 to 25-11
average queue length, 25-10
average system time, 25-10
departure process of, 25-12 to 25-13
stability condition for, 25-10
utilization and throughput, 25-10
Management science, dynamic modeling in, 33-1 to
33-22
conceptual modeling skills, 33-5 to 33-6
discrete event simulation, 33-7 to 33-16
activity cycle diagrams in conceptual modeling,
33-10 to 33-13
application areas, 33-8 to 33-9: business process
re-engineering (BPR), 33-8; in business
process improvement, 33-8; in health care,
33-8; in transport and physical logistics,
33-9
DES model implementation in computer
software, 33-13
discrete event simulation using a VIMS, 33-14 to
33-16
suitable problems, 33-7 to 33-8: complicated
characteristic, 33-7; discrete events
characteristic, 33-8; dynamic characteristic,
33-7; individual entities characteristic,
33-8; interactive characteristic, 33-7;
stochastic behavior characteristic, 33-8
terminology, 33-9 to 33-10: simulation
activities, 33-10; simulation clock, 33-10;
simulation entities, 33-9; simulation
events, 33
-10; simulation processes, 33-10;
simulation resources, 33-9
model validation, 33-21 to 33-22
models to support decision making, 33-2 to 33-4
dynamic systems modeling in, 33-4
project management skills, 33-4 to 33-5
initial negotiation and project definition, 33-5
project completion, 33-5
project management and control, 33-5
system dynamics, 33-16 to 33-21
qualitative system and dynamics, 33-17 to 33-19
quantitative system dynamics, 33-19 to 33-21
system structure and system behavior, 33-16 to
33-17
technical skills, 33-6 to 33-7
Manufacturing systems, modeling and analysis of,
34-1 to 34-19
basic quantities for, 34-2
control of, 34-10 to 34-12
discrete-event models, 34-7 to 34-8
effective process times, 34-8 to 34-10
flow models, 34-16 to 34-18
traffic flow model, 34-17 to 34-18
hybrid model, 34-15 to 34-16
preliminaries, 34-2 to 34-3
standard fluid model and extensions, 34-12 to
34-16
common fluid model, 34-12 to 34-14
extended fluid model, 34-14: approximation to,
34-14 to 34-15
steady-state analysis, analytical models for, 34-3 to
34-7
mass conservation (throughput), 34-4
queueing relations (Wip, Flow Time), 34-5 to
34-7
MarkovChains, 29-3
Markovian queueing models/networks, simple, 25-8
to 25-17
closed queueing networks, 25-15 to 25-17
M/M/1 queueing system, 25-9 to 25-11, See also
separate entry
mean value analysis (MVA), 25-16 to 25-17
non-Markovian queueing systems, 25-17 to 25-18
open queueing networks, 25-13 to 25-15
product form networks, 25-17
Marshsectormodel
dynamic output of, 28-27 to 28-29
model output analysis, 28-28 to 28-29
model validation, 28-29
Mathematical modeling
basic elements, 5-1 to 5-20
abstraction and scale, 5-9 to 5-17, See also
separate entry
conservation and balance principles, 5-17 to
5-19
dimensional analysis, 5-5 to 5-7, See also
separate entry
dimensional consistency and analysis, 5-3
to 5-9
dimensional homogeneity, 5-4 to 5-5
linearity, role of, 5-19 to 5-20
types of, 3-6 to 3-8
classification based on state, 3-6 to 3-7