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