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Breuer L., Baum D. — Introduction to Queueing Theory and Matrix-Analytic Methods
Breuer L., Baum D. — Introduction to Queueing Theory and Matrix-Analytic Methods



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Название: Introduction to Queueing Theory and Matrix-Analytic Methods

Авторы: Breuer L., Baum D.

Аннотация:

The textbook contains the records of a two — semester course on queueing theory, including an introduction to matrix — analytic methods. The course is directed to last year undergraduate and first year graduate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present material that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for their analysis. A prominent part of the book will be devoted to matrix — analytic methods. This is a collection of approaches which extend the applicability of Markov renewal methods to queueing theory by introducing a finite number of auxiliary states. For the embedded Markov chains this leads to transition matrices in block form resembling the structure of classical models. Matrix — analytic methods have become quite popular in queueing theory during the last twenty years. The intention to include these in a students' introduction to queueing theory has been the main motivation for the authors to write the present book. Its aim is a presentation of the most important matrix — analytic concepts like phase — type distributions, Markovian arrival processes, the GI/PH/1 and BMAP/G/1 queues as well as QBDs and discrete time approaches.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 288

Добавлена в каталог: 07.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absorbing      14
Accessible      13
Age      122
Alternating renewal process      144
Arrival process      4 153
Arrival rate      52
Asymptotic distribution      5
Backward process      64
Balance equations      45 50
Batch arrivals      186
Batch Markovian Arrival Process      186
Bernoulli process      10 114
Birth-and-death process      59
Blackwell’s theorem      119
Block Toeplitz structure      196
Blockwise skip-free      232
BMAP      186
Chapman — Kolmogorov equations      12 40
Characterization      227
Characterizing matrices      186
Characterizing matrix      138
Characterizing matrix sequence      186
Closed      14
closed network      62
Closure properties      176
Communicate      13
Communication class      14
Compatible      255
Conditional expectation      252
Conditional memoryless property      184
Conditional probability      253
Convolution      112
Convolutional exponential of a matrix sequence      189
Convolutional power      113
Convolutional powers of a matrix sequence      188
Convolutions of matrix sequences      188
Counting measure      240
Counting process      153
Cox distribution      174
Cyclic closed network      106
Cylinder      254
Delay      111
Delay system      54
Delayed regenerative process      143
Delayed renewal reward process      132
Departure rate      52
Detailed balance equation      64
Directly Riemann integrable      120
Discrete batch Markovian arrival process      230
Discrete BMAP      230
Discrete PH renewal process      231
Discrete phase-type distribution      227
Discrete random walk      10
Doubly stochastic Poisson process      187
Elapsed time representation      229
Elementary renewal theorem      117
Embedded Markov chain      37
Embedded Markov renewal chain      136
Engset distribution      59
Environment process      187
Ergodicity condition      202
Erlang distribution      172
Erlang’s delay formula      56
Erlang’s loss formula      57
Excess life      122
Exit vector      169
Expectation      251
Failure rate      106
Finite-dimensional marginal distributions      44 256
First return time      139
First visit      15
Forward process      64
Foster’s criterion      28
Generalized Erlang distribution      172
Generator matrix      40
Geometric process      130
Gershgorin’s circle theorem      258
GI/M/1 queue      145
GI/M/1 type matrix      197
GI/PH/1 queue      195
Global balance      64
Holding time      37
Homogeneous      9 136
Hyper-exponential distribution      173
Hypo-exponential distribution      172
Indicator function      253
Infinitesimal transition rate      40
Initial distribution      11 44 169
Insensitivity property      84
Intensity      38 145
Inter-arrival time      4
Interrupted Bernoulli process      236
Interrupted PH renewal process      187
Invariant      151
IPP      187
Irreducible      14 44 137
Kendall notation      4
Kernel      254
Key renewal theorem      120
Kolmogorov forward and backward equations      41
Kronecker product      179
Kronecker sum      179
Laplace — Stieltjes transform      174 257
Lattice      119
Level      196 212 230 232
Load      31 51 150
Loss system      168
Lower Hessenberg matrix      155
LST      174
M/G/1 queue      153
M/G/1 type      212
M/G/k queue      133
M/M/c/c+K queue      167
Machine repair problem      59
MAP      185
Markov chain      9
Markov process      37
Markov property      9 39
Markov routing      77
Markov-additive jump process      239
Markov-modulated Poisson process      187
Markovian Arrival Process      185
Markovian queues      49
Matrix convolution      138
Matrix exponential function      169
Matrix-geometric distribution      198
Mean arrival rate      192
Mean recurrence time      140
Memoryless property      29 38
Minimal subinvariant measure      151
Mixed network      62
MMPP      187
moment      171
n-process      193
Non-defective      170
Null recurrent      21
Open network      62
Order      169 227
Ordinary renewal process      111
Path      256
Period      119
PH distribution      169
PH renewal process      183
Phase      169 196 212 227 230 232
Phase equilibrium      191
Phase process      190 196 230
Phase-type distribution      169
Poisson process      37—38
Polish space      239
Pollaczek-Khinchin mean value formula      164
Positive recurrent      21 44
Potential matrix      17
Probability flux      64
Product form (PF-) networks      63
Pure jump process      37
QUEUE      4
Queueing network      61
Queueing system      4
Radon measure      240
Random point field      240
Random variable      251
Rate      114
Rate conservation law      162
Rate matrix      198
Rate of flow      64
Recurrent      17 44 137
Reducible      14
Regeneration cycle      133
Regeneration property      133
Regeneration time      133
Regenerative process      133
Regular      46
Reliability theory      59 107
Remaining time representation      229
Renewal equation      115
Renewal function      114
Renewal interval      111
Renewal process      111
Renewal reward process      128
Renewal time      111
Residual life time      122
Reversed process      64
Reversible      66
Reward      128
Routing matrix      61
Routing probabilities      61
Semi-Markov process      136
Semi-regenerative process      141
Separable networks      63
Service discipline      4
Service times      4
Skip-free Markov chain      232
Skip-free Markov process      52
Skip-free to the left      155 212
Skip-free to the right      147 197
SMAP      241
Spatial arrival process      239
Spatial Markovian arrival process      241
Stability condition      32 150 156 197
Stable      243
State      37
State space      9 37
State transition graph      41
Station balance      73
Stationary      18 44
Stationary distribution      18
Stationary increments      125
Stationary measure      18
Stationary renewal process      125—126
Stochastic chain      9 255
Stochastic matrix      11
Stochastic process      255
Stopping time      12 133
Strong Markov property      12
Sub-stochastic distribution functions      137
Subinvariant      151
Superfluous      174
Superposition      47 188
System capacity      4
System process      5
Taboo probabilities      151 198
Tandem queue      106
Time until absorption      169
Total number of visits      16
Total reward      128
Transient      17 44 137
Transient distributions      138
Transition matrix      9
Transition probabilities      39
Transition probability      9
Transition probability matrix      40
Transitions with arrivals      184
Transitions without arrivals      184
Upper Hessenberg matrix      147
Versatile Markovian point process      193
Version      11 44
Waiting time paradox      127
Wald’s Lemma      117
z-transform      256
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