Kelly F.P. — Reversibility and Stochastic Networks :: Электронная библиотека попечительского совета мехмата МГУ

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Kelly F.P. — Reversibility and Stochastic Networks

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Название: Reversibility and Stochastic Networks

Автор: Kelly F.P.

Аннотация:

Examines the behavior in equilibrium of vector stochastic processes or stochastic networks, considering a wide range of applications by discussing stochastic models that arise in fields such as operational research, biology, and polymer science. Reviews the concept of reversibility, including material necessary to establish terminology and notation. Explains such uses as the study of the output from a queue, the flow of current in a conductor, the age of an allele, and the equilibrium distribution of a polymerization process. Also examines the extent to which the assumption of reversibility can be relaxed without destroying the associated tractability. Requires an understanding of Markov processes.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 230

Добавлена в каталог: 18.12.2004

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Предметный указатель

Age of an allele      151—156 215 221
Allele      145
Allele, age of an      151—156 215 221
Allele, oldest      153—156 222
Allele, time to extinction of an      152—154 156
Allocation, optimal      54 97—99 213
Aperiodic      2 24
Arrival process      11
Arrival process at a quasi-reversible queue      66
Arrival process, more general      89—94
Arrival process, non-Poisson      50 55 63
Arrival rate      11
Arrival rate, mean      13 42 47 54 55 61 87
Arrival rate, more general      89—94
Balance, detailed      5
Balance, full      5
Balance, partial      27
Balking      36 71
Birth and death process      10—17 24 35 44 100 221
Birth and death process, spatial      191 192 197—199 220
Birth, death, and immigration process, simple      14 16
Birth, death, and immigration process, with arbitrarily distributed lifetimes      115—117
Birth, death, and immigration process, with clustering      182
Birth, death, and immigration process, with family sizes      53 56 115 146 149 150 213
Birth-illness-death process      113 114 116 214
Blocking      47 106 107 125 135 140 144
Calculation of the normalizing constant for a closed clustering process      163 165 166
Calculation of the normalizing constant, migration process      47 48
Calculation of the normalizing constant, queueing network      87 212 213
Capacity constraint      47 106 107
Closed migration process      40—49 55 84 86 135—145 193 195 203 212 213 222
Closed network of queues      82—90 92 99—113 120—124 183 207 217
Clustering process      161—183 215 222
Communication network      95—99 131 214
Compartmental model      113—117 214
Competition model      209 210
Components in a complex device      88 105
Components in a power supply model      191—193
Components in a renewal process      79
Components, provision of spare      43—45 47
Computer      96 105—108 214 218
Conveyor belt inspection      118 119 123
Counter, electronic      119 120 123 214
Customer, class      65
Customer, route      57
Customer, type      57
Customer, typical      11 12 16
Cyclic queue      43—47 218 220
Decision making      134 190
Defection      36 59
Departure process      34—39 51 52 55 62 66 70 71 88 89 92 120 124 219 220—221
Description of a random sample      147—150
Detailed balance      5
Determining mutation      158—160
Disposition      85—88 93
Dynamic reversibility      31 32 39 75 144 182 212
Ehrenfest model      17—21 212
Electrical network      20 125—134 157 212 214
Electronic counter      119 120 123 214
entropy      17 19 220
Equilibrium      3
Equilibrium distribution      2 3
Equilibrium equations      2 3
Ergodic      2 3
Erlang's formula      13 79 111 123 219—222
Exit process      51 52
Family size process      53 56 115 146 149 150 213
Fixation times      156—160 215
Flip-flop variable      35 37 71 73 120
Flow model      125 128—134 140—144 199 214 215
Flow model, one-dimensional      132 142—144
Forward equations      18
Fruit trees      184
Full balance conditions      5
Garage      120—124 183
Generating function method      47 48 87
Genetic type      53 145
Geometric distribution      11
Grimmett's formula      188 215
Group decision making      134 190
Haulage firm      88
Heterozygosity      148
Hierarchy, organizational      114 142 143
Infinite alleles model      146—160 162 169
Infinite-server queue      73 74 92 100 106 107 109 112 113 183
Insensitivity      79 87 120 124 184 198 200 203—211 213 216 221
Invasion model      125 132—134 145 158 189 192 214
Irreducible      1
Job-shop      57 58 91—93 97 218
Jump chain      3
Kac's formula      21
Kirchhoff's equations      20 126
Kolmogorov's criteria      21—25 31 92 137 165 190 212
Labelled process      152 153 156
Lifetimes in a clustering process      182
Lifetimes in a migration process      137
Lifetimes in a population genetics model      149
Lifetimes in a spatial process      196—199 203 205—211
Lifetimes, arbitrarily distributed      137 149 196—199
Lifetimes, nominal      137 196
Limiting distribution      2 3 212
Linear migration process      41 52 53
Little's result      13 16 54 64 82 116 123 140 212
M/M/s      14 35 39 41 52 63 64
M/M/s with no waiting room      73 74 79 80 81
M/M/s, priority      59 71 94 96 104
M/M/s, server-sharing      73 74 80 81 96 105 107 137
M/M/s, simple (M/M/l)      11—16 26 34—40 44—49 54 55 57 64 67 71 95—98 100 212
M/M/s, symmetric      72—82 86 87 96 98 99 101—103 105 109 112 121 122 213 216
Machine interference      99—105 108 214
Manpower system      113 114 142 143 214
Markov chain      3 212
Markov field      184—194 200 202 216 217

Markov process      1 212
Mean arrival rate      13 42 47 54 55 61 87
Method of stages      72—82 182 196 197 205 206 213 217
Migration process, closed      40—49 55 84 86 135—145 193 195 203 212 213 222
Migration process, linear      41 52 53
Migration process, open      48—58 64 135—145 199 212 213 222
Migration process, reversible      125 135—145 148 158 161 162 183 195 198 209 214 215
Mining operation      44—47 88 143 144
Mutation      145
Mutation, determining      158—160
Negative binomial distribution      14 16 56 140
Neutral allele model      145—151 215 221
Nominal lifetime      137 196
Normalizing constant, calculation of      47 48 87 163 165 166 212 213
Nucleotide      157—159
Oldest allele      153—156 222
One-dimensional flow model      132 142—144
Open migration process      48—58 64 135—145 199 212 213 222
Open network of queues      54 57—72 95—99 107 110—125 130 213 214 217 218 220 221
Optimal allocation      54 97—99 213
Orchard      184
Organizational hierarchy      114 142 143
Output from a simple queue      34—37
Partial balance      27 33 42 50 67 93 182 184 193—195 200—212 216
Partial balance, conditions      27
Partial balance, equations      42
periodicity      2 24 79
Plant, birth and death model      197—199
Plant, infection model      191 192 198
Point process      37
Pollaczek — Khinchin formula      81
Polymerization      173—180 215 222
Population genetics      53 145—160 215 218
power supply      191—193 198
Priority system      59 71 94 96 104
Probability flux      8 10 12 13 15 16 33 42 46 52 55 63 67 68 70 85 87 140 195
Quality control      118
Quasi-fixation      156—158
Quasi-reversibility      65—124 138 142 144 200
Queue, cyclic      43—47 218 220
Queue, infinite-server $(M/G/\infty)$       73 74 92 100 106 107 109 112 113 183
Queue, M/G/1      81 213
Queue, M/G/s      39
Queue, many-server      23—25 29 30 33 35 36
Queueing times      15
Queueing times in a series of queues      40
Random field      184—186 192 221
Random sample      147—151 154—156 215
Random walk      8 41 125—134 153 157 159 214 220
Random walk, symmetric      126 129 131—134
Renewal process      37 79
Repair shop      91—93 111 214
Reversed process      27—39 46 51 52 61—63 66—70 74 75 78 79 83- 91 121 122 132 144 153 198 200—203 212 215
Reversibility      5 125 212
Reversibility, dynamic      31 32 39 75 144 182 212
Reversibility, quasi-      65—124 138 142 144 200
Road traffic      98 116—118 122 123 214 220
Series of queues      37—40 46 49 117- 212 214
Server-sharing queue      73 74 80 81 96 105 107 137
Service in random order      59 64 95 100
Service, effort      58 72
Service, rate      11 35 54
Service, requirement      59 72 86
Service, time      11 59
Simple birth, death, and immigration process      14 16
Simple queues      11—16 26 71
Simple queues, network of      44—48 54 55 57 64 67 95—98
Simple queues, output from      34—37
Simple queues, series of      37—40 46 49 212
Social grouping behaviour      135 138- 161 214 215
Spare components      43—45 47
Spatial process      184—211 215 216
Spatial process, definition of a      189
Spatial process, general      193—200
Spatial process, reversible      189—193
Species, competition between      209 210
Species, number trapped      150
STACK      16 39 73 81 82 94 96
Stages of a route      57
Stages of service      74
Stages, method of      72—82 182 196 197 205 206 213 217
Stationarity      1 21 28 156
Stationary distribution      2 3
Stirling's formula      178
Stochastic process      1
Sufficient statistic      149 162 204
Switching system      110—112 198 214 217
Symmetric queque      72—82 86 87 96 98 99 101—103 105 109 112 121 122 213 216
Symmetric random walk      126 129 131—134
Telegraph system      95 96
Telephone exchange with a finite source population      15 112 113 182 183
Telephone exchange with unreliable lines      108 109 111 214
Telephone exchange, as a symmetric queue      73 79
Telephone exchange, basic model      13 71 103 108 111
Telephone exchange, calls lost or completed at      35 37 82 212
Teletraffic model      108—113 213 214
Time homogeneous      1 28
Time to extinction      152—154 156
Time to fixation      156—160 215
Timesharing computer      105—108
Traffic intensity      15
Traffic, road      98 116—118 122 123 214 220
Traffic, tele-      108—113 213 214
Transition probability      2
Transition rate      3
Truncation      25—27 33 147 200—207 210 211
Typical customer      11 12 16
Waiting room, joint      26
Waiting room, overflow      27
Waiting room, queue with no      73 74 79 80 81
Waiting times, at a simple queue      11—13
Waiting times, in a network of queues      52 55 63
Waiting times, in a series of queues      38—40 220
Waiting times, virtual      81 21

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