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Simulation of Traffic
Simulation of Traffic
Discrete Modeling
Traffic Flow Models
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Numerics of PDE
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Discrete Modeling
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Index
A
abstract model
accuracy
Adams–Moulton method
admissible schedule
admissible schedule (job-shop)
alternative-caution strategy (min-max regret)
analytic solution
approximate-numerical method
arbitrary machines
arc length
arms race of two superpowers
arrival process
arrival rate
Arrow's impossibility theorem
asymmetric (relation)
attractive equilibrium
augmented precedence graph
B
backward recurrence time
best response function
bijective function
binary relation
boundary
boundary point
boundary value problem (BVP)
bounded set
C
canal
capacity
carrying capacity
Cartesian coordinates
caution strategy (max-min payoff)
central difference
central limit theorem
change of variables
characteristic polynomial
chi-square test
Cᵏ class
Cᵏ-curve
closed curve
closed queuing network
closed set
closed subset
closure
coefficient of variation
collective choice function
compact set
condition of a problem
conditional probability
congestion phase
conjugate (A-orthogonal) vectors
conjugate gradient method
conjunctive edge
connex
consistency (numerical method)
continuity (multivariate function)
continuous model
continuously partially differentiable
convergence (numerical method)
convergence (vector sequence)
convex set
coordinate transformation
coordinate transformation matrix
correction scheme
crisp set
critical path
Critical Path Method (CPM)
critical vertex
cross product
cross-product matrix
cubic model
curse of dimensionality
curve
cut fuzzy set
cylindrical coordinates
D
DAG (directed acyclic graph)
data error
decision under certainty
decision under risk
decision under uncertainty
definite integral
definiteness of a symmetric matrix
defuzzification
degree of freedom
density jump (shock)
determinant (2×2)
determinant (3×3)
determinant from eigenvalues
deterministic model
diagonal matrix
difference quotient
differentiable (multivariate)
differentiation rules
direct-numerical method
directional derivative
directional field
Dirichlet boundary condition (ODE)
Dirichlet boundary condition (PDE)
discrete model
discretization
discretization error
discriminant
disjunctive edge
disjunctive edge assignment
divergence
double integral (rectangular domain)
double integral (standard domain)
doubling time
dwelling time
E
eigenvalue and eigenvector
eigenvalues of a diagonal matrix
elementary queuing system
elliptic PDE
embed-test definition
embed-test theorem
equilibrium point
Euclidean norm
Euler description
Euler method
event rate
expected payoff (mixed strategies)
expected value
explicit method
external dictator
F
feedback control
filling
finite difference method
finite element method
floating-point number
forward recurrence time
free-flow phase
Fubini's theorem
full-risk strategy (max-max payoff)
function of a random variable
functional unit
fundamental diagram
fundamental relationship (traffic flow)
fundamental theorem of calculus
fuzzification
fuzzy complement
fuzzy control system
fuzzy inference
fuzzy intersection
fuzzy rule base
fuzzy set
fuzzy union
G
Gauss's divergence theorem
generic decision model
geometric distribution
global discretization error
global extremum
gradient
growth rate
H
harmonic number
hazard rate
heat equation
Hessian matrix
Heun method
heuristic
homogeneous birth–death process
homogeneous Markov process
hyperbolic PDE
I
ideal arithmetic
identical machines
identity matrix
ill-posed problem
image (trace) of a curve
implicit Euler method
implicit method
independence of irrelevant alternatives
independent process
initial condition
initial value problem (IVP)
injective function
inner point
inner product
inner product (geometric form)
instationary (PDE)
integration by parts
integration rules
interior
internal dictator
interpolation polynomial (multistep)
inverse problem
inverse transform sampling
irreducible chain
isoline
iteration matrix
J
Jacobian determinant
Jacobian matrix
job
job-shop model
K
k-times continuously partially differentiable
Kendall notation
Kolmogorov–Smirnov test
L
Lagrange description
Laplace equation
Laplace operator
lead time
linear 1st-order PDE (in 2D)
linear birth and death rates
linear congruential generator
linear feedback control
linear PDE
linear PDE of 2nd order
linguistic variable
Little's law
load
local convergence of Newton's method
local discretization error
local extremum
logistic growth model
M
majority decision
makespan
Malthus model
Markov process
mathematical modeling
maximum throughput
memorylessness
method of steepest descent
midpoint rule
minimax theorem
mixed strategy
model
model hierarchy
multigrid method
multiscale problem
multistep method
multivariate function
N
nabla operator
negative exponential distribution
Neumann boundary condition (ODE)
Neumann boundary condition (PDE)
Newton iteration (multivariate)
no-dictator condition
non-feedback control
normal distribution
null hypothesis
nullcline
number of visits
O
one-step method
open queuing network
open set
order (of a method)
ordinary differential equation (ODE)
P
P controller
parabolic model
parabolic PDE
Pareto condition
partial derivative
partial differential equation (PDE)
partially differentiable
periodic boundary condition
periodic state
pessimism–optimism strategy (Hurwicz)
phase portrait
PID controller
piecewise C¹-curve
plane curve
Poisson distribution
Poisson equation
Poisson process
polar coordinates
Pollaczek–Khinchine formula
positively recurrent state
practical model
precedence condition
precedence graph
preconditioning
predictor–corrector method
preference relation
principle of insufficient reason (Laplace)
priority-list scheduling
process layer
prolongation
pseudo-random numbers
Q
q-th moment
quadratic formula
qualitatively identical machines
quasi-order
quasi-stationary (traffic flow)
quasilinear 1st-order PDE (in 2D)
queuing network
queuing system
R
random variable
random walk
rank addition
rank mapping
recurrence probability
recurrent state
reduction to a first-order system
reflexive (relation)
regret
regular surface
relaxation method
remaining time
repulsive equilibrium
residual
resolution (floating-point)
restriction
root
rotation
round-off error
rounding
Runge–Kutta method (RK4)
runs test
S
saddle point (calculus)
saddle point (game theory)
saddle point (ODE system)
saturation number of jobs
scalar field
scalar projection
scalar surface integral
scale
schedule
scheduling problem
second difference quotient
second-order partial derivative
separable ODE
separation of variables
service process
service rate
service strategy
service time
service unit
set of connex preorders
set of preference relations
shooting method
signal velocity
simulation
simulation pipeline
single machine
skew-symmetric matrix
slack
smooth function
smoothing property
space curve
spectral condition number
spectral radius
spherical coordinates
stability (numerical method)
stable and unstable equilibrium
standard basis
standard domain (R²)
standard domain (R³)
start and completion time
state probability
state space
stationary (PDE)
stationary limit distribution
stationary point
stationary point (ODE system)
stationary process
stencil
stiffness
stiffness matrix
stochastic model
stochastic process
strictly diagonally dominant matrix
support (fuzzy set)
surface
surface area
surface normal
surjective function
symmetric (relation)
symmetric matrix
system
system layer
T
tangent vectors
task stream
Taylor polynomial
theorem of underestimation (Fulkerson 1962)
throughput
topological sort
trace
trace from eigenvalues
traffic bottleneck
traffic density
traffic equation
traffic flow
traffic velocity
trajectory
transition probability
transition rate
transitive (relation)
translation invariance (differentiation)
transpose
trial function
trigonometric derivatives
trigonometric integrals
triple integral (box domain)
triple integral (standard domain)
truncation error
two-player zero-sum game
two-species model
U
uniform distribution
upwind discretization
utilization
V
V-cycle
validation
variance
vector field
vector projection
vector surface integral
Verhulst saturation model
Vieta's formulas
voting paradox
W
well-posed problem
#
1st-order linear PDE with constant coefficients
α-cut
ε-ball
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