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Saaty T.L. — Elements of Queueing theory with applications
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...


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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$_{k}$/D/1      169
E$_{k}$/M/l      166
E$_{k}$/M/l, waiting time      169
E$_{s}$/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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