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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
ed2k: ed2k stats
Год издания: 1983
Количество страниц: 436
Добавлена в каталог: 04.12.2010
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Предметный указатель
Queues, Poisson 83 88
Queues, pooling 11
Queues, properties 12
Queues, ramifications 230
Queues, remedies, staggering working hours 19
Queues, resistance 270
Queues, selection rule 6
Queues, specialized 12
Queues, stacked 5 6
Queues, varieties 9
random selection 7 278
Random selection for service 23
Random selection, constant service times 249
Random selection, exponential service 243
Random variables 14
Random variables, depending on time 32
Random variables, infinitely divisible 79
Ratio, of average waiting time to service time 43
Ratio, of mean queueing time to mean service time 19
Reflecting barriers 136
Regeneration points 171 172
Regeneration process 370
Regular arrivals 27
Regular service 27
Reinitiating calls 10
Remedies 17 19
Reneging 6 10 23 208 270 277
Reneging and balking 277
Renewal function 360 365
Renewal process 359
Renewal process, central-limit theorem for 370
Renewal-density theorem 366
Reorder 334
Repairman 326 329
Repeated calls 357
Repeated rule 237
Replenishment cycle 334
replenishment time 335
Reservoir 336
Residual life 369
Residues 156
Restaurant 171
Restaurant operation 44
Resume rule 237
Retarded arrivals 280
Riemann — Stieltjes integral 57
Risk level 48
Rouch ’s theorem 87 89
Rounding errors 52
Runway 5
Runway, turnoffs 6
Sampling distribution 46
Saturated case 237
Scale-modified distribution 164
Scheduled arrivals 282
Scheduling of outpatient care 346
Schlafli’s integral representation 249 350
Selection rules 231
Semi-Markoff process 189
Semiconductor noise 348
Serially independent random variables 337
Series and parallel channels 11 261
Series and parallel channels, queues 255
Service 5 6 9
Service, constant 176
Service, cyclic 298
Service, different rates 290
Service, exponential 176
Service, extra 269
Service, outlets 349
Service, partially fulfilled 208
Service, procedure 11
Service, rate 18
Ships 10 12 352
Sigma algebra 55
Significance level 46 48
Simulation 17 49 374
Single channel 198 211
Small barriers 135
Spare machines 332
Special and general channels 11 13
Special service 290
Spectral form 137
Spectral function 147
Stacked queue 5 6
Standard deviation 31
State of system 69
State, absorbing 84
State, equivalences classes 70
State, ergodic 71
State, null 71
State, periodic 71
State, recurrent 71
State, reflecting 84
State, transient 71
Stationary process 67 74
Statistical equilibrium 40
Statistical sampling 7
Steady state 15 16 30 164 167 203 357
Steep distribution 78
Steepest descent 372
Stochastic matrix 68
Stochastic matrix, regular 70
Stochastic process 14 33 66
Stoppages 317 329
Storage systems 336
Suez Canal 10 12
Sum of independently distributed random variables 58 80
Supermarket 11 25 352
Superposition theorem 370
Tak c’s equation 198 202
Tandem queues 255 259
Tandem queues, ergodicity 268
Tandem queues, waiting-time distribution 263 267
Tauberian theorem 218
Taxis 78 352
Telegraph communications 352
Telephone 171 302—311
Telephone, busy signal 10
Telephone, common control 22 309 355
Telephone, grading 21 311
Telephone, limited availability 21 311
Telephone, link systems 22 308
Telephone, subscribers 67
Testing hypotheses 44
Theatres 352
Three preemptive priorities 238
Time average 42
Time congestion 353 356
Time, to serve all items which have waited 28
Time, total, in system 30
Time-dependent parameters 101 104
Toll collection 350
Total idle-time computation 7
Total probability 245
Total waiting time 6
Traffic handled 358
Traffic intensity 18 302
Traffic lane 11
Traffic lights 313
Transient equivalence class 70
Transient solution 30
Transient state 18
Transition matrix, infinitesimal 76
Transition matrix, limiting 69
Transition probability 68
Truck docks 351
Truncation errors 52
tunnels 317
Turnaround 322
Two channels in parallel 126
Type-III ordinate 273
Uniform or rectangular distribution 65
Variable number of channels 13 285
Variance 31
Variance, ratio test 44
Vehicular stoppages 317
waiting line 3 12
Waiting space 7
Waiting time 198
Waiting time of nth customer 16
Waiting time, bulk 177
Waiting time, distribution 18 108 198 200 202 205 207 210 215
Waiting time, variance 18
Waitress 352
Walking repairman 332
Walking time 350
Warehouse 351
Wasted time 4
Water storage 337
Wiener — Hopf-type integral equation 210
Work load 215
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