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Saaty T.L. — Elements of Queueing theory with applications
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Название: Elements of Queueing theory with applications
Автор: Saaty T.L.
Аннотация: A "queue" is a waiting line. Queues are commonly observed to form before ticket offices, cafeterias, and bus stops. Thus, to have a queue, one must have arrivals at a service facility where they often wait; for example, at a doctor's office to see the doctor in the order of their appointments. Telegrams are classified according to the order of their arrival with priority assigned to regular telegrams over night letters.
Queueing theory is a branch of applied mathematics utilizing concepts from the field of stochastic processes. It has been developed in an attempt to predict fluctuating demands from observational data and to enable an enterprise to provide adequate service for its customers with tolerable waiting. However, the theory also basically improves understanding of a queueing situation, enabling better control. For example, loss of customers at a grocery store because of slow check-out-counter service may be remedied by rapid service at a larger number of counters. To put this into effect does not require a theory. But to organize airport take-off and landing operations at a minimum inconvenience does, because of the many factors entering the problem and the large size of the operation. Thus, the theory provides one with predictions about waiting times, the number waiting at any time, the length of a busy period and so fcrth...
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Рубрика: Математика /
Серия: Сделано в холле
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 1983
Количество страниц: 436
Добавлена в каталог: 04.12.2010
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Предметный указатель
Absorbing barriers 117 126 136
Absorbing Markoff chain 70
Accidents 13
Action and analysis 9
Air conditioning 15
Aircraft 5 171 318
Aircraft carrier 181 352
AirPort 5 322
Allocation to channels 250
applications 5 302 350
Applications and reservations 2!0
Applications, accidents 13
Applications, air conditioning 15
Applications, aircraft 5 171 318 322
Applications, aircraft carrier 181 352
applications, AirPort 5 322
Applications, appointments, at doctor’s office 4
Applications, apron control 322
Applications, aviation traffic 318-321
Applications, bacteria 1!17
Applications, bakeries 352
Applications, bank 10
Applications, barbers 352
Applications, buses 352
Applications, cafeteria design 346
Applications, car traffic 311
Applications, clerks 350
Applications, coal faces 347
Applications, collusion 10 12 374
Applications, communications 322
Applications, computers 2!98 374
Applications, conveyor belts 352
Applications, courts 352
Applications, dams 336
Applications, elevator 171
Applications, engines 332
Applications, epidemics 117
Applications, feedback 294
Applications, grocery stores 3
Applications, highway 11 44
Applications, hospitals 9 343-345
Applications, influx of papers to editors 216
Applications, inspection line 49
Applications, inventory 334-336
Applications, jockeying 10 23 284 374
Applications, machines 323 331 332
Applications, manufacturing units 252
Applications, medical care 343
Applications, messages 298
Applications, moving server 291
Applications, nervous impulses 352
applications, networks 7 373
Applications, oil pumps 351
Applications, passenger debarkation 344
Applications, perishable goods 18
Applications, post office 10 298 352
Applications, production-line operation 11 49
Applications, repairman 326 329
Applications, reservoirs 336
Applications, restaurants 44 346
Applications, semiconductor noise 338
Applications, ships 10 12 352
Applications, stoppages 317 329
Applications, Suez Canal 10 12
Applications, supermarkets 11 25 352
Applications, taxis 78 352
Applications, telegraphy 352
Applications, telephony 10 20 171 302
Applications, toll collection 350
Applications, traffic lights 313
Applications, truck docks 351
applications, tunnels 317
Applications, waitress 352
Appointments and reservations 20
Appointments and reservations at doctor’s office 4
Approach time 6
Approximation 299 328
Apron control 322
Arbitrary input 198 209 219 275
arrivals 14
Arrivals, batches 5 9 12
Arrivals, bulk 184
Arrivals, constant intervals 10 49 210
Arrivals, distribution 5 9
Arrivals, input 5 9 198 209 219 275
Arrivals, interval 7
Arrivals, oriented 280
Arrivals, periodic 321
Arrivals, Poisson 63 172 193 194
Arrivals, regular 27
Arrivals, retarded 280
Arrivals, scheduled 282
Arrivals, single 12
Asymptotic behavior 359
Asymptotic distribution 341
Autocorrelation function 130
Average number, of renewals 361
Average number, of waiting individuals 18
Average waiting time 42
Average waiting time, for all customers 7
Average waiting time, for those who wait 7
Aviation traffic 318 321
Backward equation 74
bacteria 117
Bakeries 352
Balking 6 10 12 23 270
Balking distribution 270
Balking sequence 275
Bank 10
Barbers 352
Batches 5 9 171 342
Bessel function, modified 91
beta function 267
Binomial distribution 65 181 272
Binomial input, arbitrary service 181
Birth-death process 76
Birth-death process, backward equations 84
Birth-death process, existence and uniqueness of solution 84
Birth-death process, forward equations 83
Birth-death process, spectral solution of equations 145
Birth-death process, steady-state solution 87
Blackwell’s theorem 366
Blocked call 308
Blocking 354
Boolean algebra 55
Boolean sigma algebra 56
Breakdown causes 19
Bulk arrivals and arbitrary service times 184
Bulk queues 171
Bulk service and arrivals 180
Bulk waiting time 177
Bus queues 4
buses 352
Busy channels 353
Busy period 129 194 223 227
Busy period, average length 18
Busy period, distribution of 99 107 128 218
Cafeteria design 346
Call congestion 356 357
Canceled channels 285
Capacity of reservoir 337
Car traffic 311
Centavos 352-353
Central-limit theorem 66 67
Chance variable 32
Channels, busy 46 353
Channels, canceled 285
Channels, communication 6
Channels, cooperating 11 288
Channels, fault finding 48
Channels, full availability 10 20 303
Channels, idle number 125
Channels, infinite number of 99 127
Channels, limited availability 10
Channels, loss system 353
Channels, multiqueues 219
Channels, series and parallel 13 261
Channels, single 95 96 161 198 211
Channels, special and general 11 13 290
Channels, total idle time 7
Channels, variable number 13 285
Chapman — Kolmogorov equation 74 76 185
Characteristic equation 139
Characteristic function 57 65
Characteristic roots 138
Chi square 45 65 211
Circling aircraft 6
Classification (Kendall’s) 25
Clerks, optimum number 350
Coal faces 347
Coefficient of loss 19 125
coin tossing 66
Collusion 10 12 374
Combinatorial approach 308
Common control 355
Common-control loss system 309
Common-control waiting system 310
Communication 322
Communication, channels of 6
Competing enterprises 13
Completely monotone function 78
Compound distribution 64
Computer 298 374
Conditional distribution 47
Conditional probability 56
Conduction band 349
Congested traffic 10
Congestion delays and loss of creativity 25
Conservative process 85
Constant arrivals 210
Constant input and exponential service 49
Constant service time 176
Continuous parameter 199
Continuous probability 32
Contour representation of queues 21
Control of air traffic 318 321
Conveyor belts 352
Convolution 58 77 113 218 299
Cooperating channels 11 288
Correlation 12
Cosine transform 130 348
cost analysis 19
Cost analysis, comparisons 125
Cost analysis, of additional channel 7
Courts 352
Cubic equation, solution of 144
Cumulant 59
Cumulant generating function 175
Cumulative probability 32
Cumulative process 370
customers 14
Customers, adaptation 10
Customers, behavior 10
Customers, departing 41
Customers, habits 32
Customers, wait 7
CYCLE 334 398
Cyclic queues 294
Cycling 6 11 13 23 294
Dams 336
DATA 44
Decision process 48
Delay distribution 320
Delayed aircraft 319
Delayed calls 10 12 305
Density function 57
Departing customer 41
Departure 255
Departure, epochs of 171
Dependence 68 214
Deterministic example 31
Dice Rolling 31
Difference methods 52
Different rates of service 290
Differential-difference equation 35
Dirac delta function 61 108 110 118 320
Discipline, allocation to channels 250
Discipline, dynamic 241
Discipline, first-come first-served 11 38
Discipline, last-come first-served 11 252
Discipline, nonpreemptive 12 30 231 232
Discipline, ordered 7 11 12 22 219
Discipline, preemptive 12 231 237
Discipline, priorities 23 231 234 236 241 304
Discipline, random selections 11 12 23 243-250 278
Discrete probabilities 31 66
Discrete time 336 337
Distribution function 57
Distribution, balking 270
Distribution, beta function 267
Distribution, binomial 65 181 272
Distribution, busy period 99 107 128
Distribution, chi-square 45 65
Distribution, compound 64
Distribution, conditional 47
Distribution, Engset 304
Distribution, Erlangian 65 66 68 167 227 288
Distribution, extreme value 132
Distribution, Fisher — Tippett 132
Distribution, flat 78
Distribution, gamma 65
Distribution, Gaussian or normal 65 254
Distribution, geometric 40 183
Distribution, hyperexponential 77 371
Distribution, hypergeometric 65
Distribution, initial number 101 418
Distribution, log normal 65
Distribution, negative 273
Distribution, negative binomial or Pascal 65 273
Distribution, O’Dell 304 356
Distribution, Pearson Type-III 65
Distribution, Poisson 65
Distribution, probability 14
Distribution, steep 78
Distribution, sum of independent variables 58 80
Distribution, uniform or rectangular 65
Dynamic priorities 241
E /D/1 169
E /M/l 166
E /M/l, waiting time 169
E /G/1 189
Efficiency 125
Elementary renewal theorem 366
Elevator 171
Emergency 6
Engines 332
Engset distribution 304
Epidemic model 117
Epochs of departure 171
Equilibrium 15
Ergodic analysis 38
Ergodic equivalence class, periodic 70
Ergodic equivalence class, regular 70
Ergodic property 69
Ergodic system 72
Erlang loss formula 282 303
Erlang, A. K. 21
Erlangian distribution 65 164 288
Erlangian distribution, approximation with 66
Erlangian distribution, as filtered Poisson distribution 66
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