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Ganesh A., O'Connell N., Wischik D. — Big Queues
Ganesh A., O'Connell N., Wischik D. — Big Queues

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Название: Big Queues

Авторы: Ganesh A., O'Connell N., Wischik D.

Аннотация:

Big Queues aims to give a simple and elegant account of how large deviations theory can be applied to queueing problems. Large deviations theory is a collection of powerful results and general techniques for studying rare events, and has been applied to queueing problems in a variety of ways. The strengths of large deviations theory are these: it is powerful enough that one can answer many questions which are hard to answer otherwise, and it is general enough that one can draw broad conclusions without relying on special case calculations.


Язык: en

Рубрика: Математика/Вероятность/Статистика и приложения/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 254

Добавлена в каталог: 03.06.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolutely continuous      82
Admission control      213 216
Autoregressive process      43 50 222 224
Autoregressive process, path to overflow      175
Bahadur — Rao improvement      See Refined estimates
Basis      58
Borell's inequality      187
Brownian bridge      118 238
Brownian motion      63 124
Brownian motion, sample path LDP      See Schilder's theorem
Buffer level      6
Buffer size      6
Cauchy random variable      29 65
Cauchy sequence      58
Cell burst process      236
Cell loss      See Lost work
Chernoff bound      8
Closed convex      30
Closed set      57
Closure      58
Coarser topology      58
Compact      58
Complete metric space      58
Continuity, definition      59
Contraction principle      63—67
Contraction principle, approximate      66
Contraction principle, extended      66
Contraction principle, inverse      See Inverse contraction principle
Convergence      58
Convex conjugate      7 29
Cramer's theorem      9 32—38
Cramer's theorem, generalized      42
Cumulant generating function      7 27
Dawson — Gaertner theorem      75
Decoupling      181
Delay      92
Delay, LDP      126
Dense      58
departures      98
Departures, continuity      100
Departures, definition      98 99
Departures, effective bandwidth      See under Effective bandwidth
Departures, Hurstiness      194
Departures, LDP      128—144 177
Departures, LDP for mean rate      130
Departures, MDP      205 207
Departures, nonlinear geodesics      130
Drain time      See Delay
Effective bandwidth      212 216
Effective bandwidth of departure process      214 215 217
Effective bandwidth, estimation      See Inference
Effective domain      27
Epigraph      30
Essential smoothness      42
Exponential equivalence      68
Exponential tightness      69
Exponential tilting      See Tilted distribution
Extended notation      83—84
Extended real numbers      7 27
Fenchel — Legendre transform      See Convex conjugate
Finer topology      58 70
Finite buffer      6
Finite-buffer queue size      88
Finite-buffer queue size, continuity      92
Finite-buffer queue size, definition      88 89 92
Finite-buffer queue size, LDP      125 170 173
Fluid equations      97 103
Fractional Brownian motion      54 184 237
Fractional Brownian motion, LDP for queue size      166 186
Fractional Brownian motion, origin of      195
Fractional Brownian motion, path to overflow      174 189
Fractional Brownian motion, sample path LDP      163 187
Gaertner — Ellis theorem      See Cramer's theorem generalized
Gaussian process as an approximation      196 203 205
Gaussian process, examples      236. See also Brownian motion Fractional etc.
Gaussian process, path to overflow      174
Gaussian process, refined estimates      187 221
Gaussian process, sample path LDP      162 188
Gaussian process, with independent increments      123
Generalized Cramer's theorem      See Cramer's theorem generalized
Global approximation      226
Good rate function      27 59
Hausdorff topological space      58
Heavy tails      10 195
Heavy traffic      124 199 205
Horizon      103 104
Hurst parameter      184. See also Hurstiness
Hurstiness      190
Hurstiness, LDP for queue size      193
Independent increments process sample path LDP      164
Induced topology      58
Inference      6 146—150 216 231
Instantaneous rate function      107
Interior      58
Inverse contraction principle      70
Kullback — Leibler divergence      See Relative entropy
Large buffer limit      9 47 105—150 227
Large buffer limit, effective bandwidth      212
Large deviations principle      27 59
Large deviations principle, useful tools      32 63 67—76
LDLB      219
LDLBH      219
LDMF      219
Ldp      see Large deviations principle
Legendre transform      See convex conjugate
Level set      59
Lindley recursion      2
Linear geodesics      See sample path
Linear geodesics, LDP with linear geodesics      117
Log moment generating function      See Cumulant generating function
Long range dependence      52 55 183—198
Long range dependence, causes of      195
Long range dependence, in traffic traces      224
Long range dependence, LDP for queue size      185 227
Long range dependence, scaling properties      190
Lost work      173 220
Lower semicontinuous      27 59
Loynes construction      4
LRD      See Long range dependence
M/G/$\infty$ queue      196 235
M/M/1 queue      5
Many flows limit      15 52 151—181 228
Many flows limit, effective bandwidth      215
Markov jump process      232
Markov modulated process      5 21 43 45 71 163 175 183 222 224 234
MDLB      219
MDMF      219
MDP      See Moderate deviations principle
Mean arrival rate      81
Mean service rate      81
Metric      57
Moderate deviations limit      199—209 228
Moderate deviations principle      200 202
Most likely way      61 65
Neighbourhood      58
networks      144 177 195 231.
On-off process      5 21 51 71 163 175 222 224 234.
Open cover      58
Open neighbourhood      58
Open set      57
Overflow      6
Packet loss      See lost work
Path to overflow      80 123 173
Polish space      58 82 155
Polygonalization      78 106
Power law scaling      52. See also Long range dependence
Principle of the largest term      19 25
Priority queue      94 176 209
Processor sharing      95
Projective limit      See Dawson — Gaertner theorem
Quasi-reversibility      137
Queue size (infinite buffer), continuity      84
Queue size (infinite buffer), definition      4 79
Queue size (infinite buffer), LDP      10 16 47 52 120 166
Queue size, MDP      203
Rate function      27 59
Refined estimates      219
Refined estimates for Gaussian processes      221
Regular over finite horizons      155
Regular over infinite horizon      156
Regular topological space      58
Relative entropy      24 38 149
Reproducing Hilbert space      188
Risk adjustment coefficient      146
Sample path LDP      60
Sample path LDP for many flows limit      156 162
Sample path LDP for partial sums process      109
Sample path LDP with linear geodesics      107
Sample path LDP, examples      see under Gaussian Markov etc.
Sample path MDP      202
Sanov's theorem      38 71
Scaled uniform norm      81
Scaled uniform norm, extended      154
Scaling function      52 156
Scaling properties      144 190 230
Schilder's theorem      63
Schilder's theorem, generalized      See Gaussian process sample
Self similarity      184 237
Separable      58
Sequentially compact      59
Skorohod problem      98
Speed of LDP      189
Stationary increments      54 156
Steady state      4 104
Steep      42
Stirling’s formula      24
Strengthen an LDP      70
Supremum norm      82
Tilted distribution      32 35
Tilting      See Tilted distribution
Time to overflow      14 21 123 167 187
Time-change formula      51
Timescale, critical      See Time to overflow
Topological space      57
topology      57
Traffic models      232
Transient analysis      104
Uniform convergence      82
Uniqueness of rate function      68
Varadhan's lemma      70 71
Wald's approximation      149
Watermark plot      221
Weak queue topology      180
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