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Whitt W. — Stochastic-process limits and application to queues
Whitt W. — Stochastic-process limits and application to queues



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Название: Stochastic-process limits and application to queues

Автор: Whitt W.

Язык: en

Рубрика: Математика/Вероятность/Стохастические процессы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2001

Количество страниц: 617

Добавлена в каталог: 15.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Bremaud      71
Brownian motion, fluctuations of      28
Brownian motion, modulus of continuity for paths      28
Brownian motion, nondifferentiability of paths      28
C(S), cont. bdd. real-val. fcts. on S      1
Carson      75 91
Centering for convergence preservation linear      188
Centering in other direction      180
Central-server model      110
Characterizations of $SM_1$ convergence in D, by linear maps      136
Characterizations of $SM_1$ convergence in D, by visits to strips      138
Characterizations of $SM_1$ convergence in D, main theorem      128
Characterizations of $SM_2$ convergence in D, by linear maps      159
Characterizations of $SM_2$ convergence in D, by local extrema      160
Characterizations of $SM_2$ convergence in D, main theorem      149
Characterizations of $WM_1$ convergence in D      131
Characterizations of $WM_2$ convergence in D      155
Characterizations of feasible regulator set      199
Characterizations of local uniform convergence      126
Characterizations of multidimensional reflection map by complementarity      199
Characterizations of multidimensional reflection map by fixed-point property      199
Characterizations of parametric reps.      122
Chen      27
Choudhury      22
Chow      87
Closed queueing network      110
CLT equivalence for cting. fcts.      62
Comparison of $SJ_1$ and $SM_1$ metrics      121
Comparison of $SM_1$ and $WM_1$ topologies      121
Complementarity and reflection      199
Complete metric space      139
Composition map      68 164
Composition map, continuity of      165
Composition map, not continuous everywhere      165
Composition map, with centering      173
Conditional prob. measure      14
Confidence set      74 76
conjugate      see “Adjoint”
Conservation laws      52
Continuity of addition for $M_1$      135 136
Continuity of addition for $M_2$      159
Continuity of composition      165
Continuity of multidimension reflect, in uniform topology      202
Continuity of multidimension reflect, on (D, $SJ_1$)      203
Continuity of multidimension reflect, with $M_1$ topologies      210
Continuity of the inverse map      184
Continuity, right      114
Continuous-mapping approach      17 51 73
Continuous-mapping theorem      17 19
Convergence preservation, $WM_2$ within bnding fcts.      161
Convergence preservation, with centering inverse map      188
Convergence preservation, with centering reflection map      182
Convergence preservation, with centering supremum map      174 180
Convergence, characterization of $SM_1$      128 138
Convergence, characterization of $SM_2$      149 160
Convergence, characterization of $WM_1$      131
Convergence, characterization of $WM_2$      155
Convergence, extending to product spaces for $SM_1$      134
Convergence, extending to product spaces for $SM_2$      158
Convergence, local uniform      124
Convergence, of prob. measures      1
Convergence, of restrictions      143
Convergence, of sets      246
Convergence, strengthening the mode for $WM_1$      134
Convergence, strengthening the mode for $WM_2$      158
Convergence, to Levy processes      45
Coordinate mapping      10
Corrections      v
Counterexample for weak consistency      94
Counting fcts.      190—194
Counting fcts., asym. equiv., inv. fcts.      192 193
Counting functions      55
Counting functions, CLT equivalence      62
Counting functions, with centering      62
Counting process      190
Couplings      27
Covariance function      34
Crane      88
Csorgo      25 27—29
Cumulative process      37
Cylinder set      15
D, the space      161
D, the space, $SM_2$ and $WM_2$ topologies      144
D, the space, characterization of $M_1$ convergence      128
D, the space, characterization of $M_2$ convergence      148
D, the space, regularity properties      114
Damerdji      90
Derivative      v
Derivative and convergence preservation      237
Derivative of inverse map      267
Derivative of supremum map      243
Derivative of the reflection map      259
Difference operator, fractional      48
Differences      47
Dirac measure      10
Disc(x), set of disc, pts.      19 115
Discontinuity points      115
Discontinuity points, jumps common sign      136 159
Distance, in-probability      17
Distance, order-consistent      119 131
Donsker’s theorem, rate of convergence in      25
Double sequences      41
Dudley      6
Dunford      16
Edgeworth expansion      24
Egoroff’s theorem      12
Einmahl      27
El-Taha      52 54 71 72 164
Equicontinuous      2
Errors      v
Estimating a steady-state mean      89
Estimation process      74
Ethier      29 40
Extending, convergence to product spaces for $SM_1$      134
Extending, convergence to product spaces for $SM_2$      158
Extending, graphs for M' topologies      186
F(t), cdf      6
FARIMA      47
FCLT for a CTMC      34
FCLT for a DTMC      31
FCLT for regenerative processes      38
FCLT with weak dependence      30
FCLT, martingale      40
Feasible regulator, definition      197
Feller      22 24 41 44 45 140 230
Fishman      75 91
Fixed-point char, of ref. map      199
Fox      75 87 91
Fractional AR integrated MA, FARIMA      47
Fractional difference operator      48
Function, oscillation      125
Function, piecewise-constant      115
Functions of sample means      88
Fundamental matrix for a CTMC      33
Fundamental matrix of a DTMC      31
Gamma process      100
Generalized cont.-map. thm.      20
Generalized Pollaczek — Khintchine transform      22 98 99
Glazebrook      87
Gleser      87
Glynn      iv 27 36 38 53 71—95
Gnedenko      41
Goldie      81
Govindarajulu      87
Granger      48
Graph, extended for M' topologies      186
Graph, thick      117
Graph, thin      117
Gut      71 72
Halmos      12
Hausdorff metric on compact subsets of $\mathbb{R}_+$      246
Hausdorff metric on graphs for D      144
Heavy-traffic limit for nonstationary queues      262
Heavy-traffic limits for finite-capacity queues      217
Heavy-traffic limits for queueing networks      217
Heavy-traffic limits for stochastic fluid networks      217
Heidelberger      75 89
Helly selection theorem      140
Hill estimator      92
Horvath      25 27
Hosking      48
Hsu      27
Iglehart      90
In-probability distance      17
Infinitely divisible distribution      41
Infinitesimal generator matrix for CTMC      33
Inheritance of jumps from $WM_2$ convergence      157
Innovation process      47
Innovation process, heavy-tailed      50
Instantaneous reflection map      204
Internet Supplement      164 167 210 220
Inverse map      183—194
Inverse map, continuity of      184
Inverse map, convergence pres. with centering      188
Inverse map, derivative of      267
Inverse relation for cting. fcts.      55 190
J, max-jump fct.      157
Jacknife      88
Jacod      40—42 45 46 142 178
Jenkins      47 48
Joint convergence of random elements for sup with centering      178
Joyeux      48
Kella      v 98 218 224
Kelton      75 87 91
Kemeny      31 33
Kennedy      26
Kiefer — Wolfowitz stochastic approx.      91
Koenig      87
Kogan      111
Kolmogorov      41
Komlos      27
Kurtz      29 40
Laplace exponent      99
Lavenberg      75 88 110
Law      75 87 91
Left limits      114
Lemoine      88
Levy, exponent      42
Levy, measure      42
Levy, metric      18 140
Levy, process, convergence to      41
Levy, process, decomposition      43
Levy, process, model for input      223
Levy, process, reflected      98
Levy, process, strong approx. for      29
Levy, process, without negative jumps      98
Limiting stationary version, criterion for a      221—223
Limiting stationary version, of a reflected process      218
Linc(x), left inc. pts. of a;      248
Lindvall      27 142
Linear fcts. of coord, fcts.      136 159
Linear models      46
Linear process representation      46 50
Lipschitz, function      181
Lipschitz, lin. fct. of coord, fcts.      135 158
Lipschitz, mapping theorem      17 26
Lipschitz, property of multidim. ref. map      202 203 215 217
Liptser      111
Little’s law      52
Local uniform convergence      124
Local-maximum function for $M_2$ topology on D      160
Lucantoni      22 39
M/G/l queue      99
M/M/l queue      35 262
Maigret      36
Major      27
Mandelbaum      v 27 112 235 276
Markov chains      30
Martingale      40
Martingale, difference      40
Martingale, in Levy pr. decomp.      43
Massey      v 71 72 112 235 276
Matrix, norm      200
Matrix, reflection      197
Maximum norm on $\mathbb{R}^k$      114
McLeish      92
Measurability of addition on $D \times D$      136
Measurability of C in (D, $M_1$)      164
Measurability of Disc(x)      19
Measurability of subsets of D      184
Measurability of the inverse map      184
Metric, $M_1$      118
Metric, $SM_1$      118
Metric, $SM_2$      145
Metric, $WM_2$      145
Metric, Hausdorff      144
Metric, Levy      140
Metric, product      145
Metric, uniform on D      114
Meyn      36
Miller      89
Mixture      11
Modulus of continuity of BM      28
Modulus of continuity, over a set      116
Multidimensional reflection      233
Multidimensional reflection as function of the ref. matrix Q      203
Multidimensional reflection, characterization of, by complementarity      199
Multidimensional reflection, characterization of, by fixed-point property      199
Multidimensional reflection, continuity of, as fct of x and Q      216
Multidimensional reflection, continuity of, in $M_1$      210
Multidimensional reflection, counterexamples for $M_1$      217
Multidimensional reflection, definition of      197
Multidimensional reflection, existence of      198
Multidimensional reflection, instantaneous      204
Multidimensional reflection, Lipschitz property for $D([0, \infty), \mathbb{R}^k)$      217
Multidimensional reflection, Lipschitz property for $M_1$      215
Multidimensional reflection, Lipschitz property for $SJ_1$      203
Multidimensional reflection, Lipschitz property for uniform norm      20
Multidimensional reflection, one-sided bounds      202
Multidimensional reflection, properties of      202
Multiprogrammed computer system, input-output devices      110
Nadas      87
Nested family of countable partitions      7
Neuts      39
Neveu      15
Non-compact domains      142
Nonlinear centering      237
Nonstationary queues      262
Norm, matrix      200
Norm, maximum on $\mathbb{R}^k$      114
Number of visits to a strip      137
Numerical transform inversion      22 48 100
Order on completed graph      117
Order, total      117
Order-consistent distance      119 131
Oscillation function      125
Parametric representation, $M_1$, definitions      118
Parametric representation, $M_2$      148
Parametric representation, limits for      209
Parametric representation, reflection of      204
Partition      5
Partition of a set      7
Philipp      27
Piecewise-constant fct.      115
Piecewise-linear fct.      208
Planning queueing simulations      73
Poisson equation      31
Poisson equation for a CTMC      34
Poisson equation for a DTMC      32
Poisson random measure      43
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