Introduction to queueing networks: theory ∩ practice
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| Format: | Book |
| Language: | English |
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Springer
[2018]
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| Series: | Springer series in operations research and financial engineering
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xxv, 562 Seiten Illustrationen, Diagramme (farbig) |
| ISBN: | 9783319788210 |
| ISSN: | 1431-8598 |
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| 245 | 1 | 0 | |a Introduction to queueing networks |b theory ∩ practice |c Smith, J. MacGregor |
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| adam_text | Contents 1 2 Volume Focus and Outline......................................................... Software Tools............................................................................ ix xi 1 Introduction G(V,E)....... .................................................................. 1.1 Prologue..................................................................................... 1.1.1 Queueing Properties....................................................... 1.1.2 Types of Blocking........................................ 1.2 Kendall Notation (A/B/C/D/E/F)........................ 1.3 Topological Network Design (TND) Problems......................... 1.3.1 Design Variables..................................................... 1.3.2 Example Context.............................................. 1.3.3 Performance Variables.................................................... 1.3.4 Contextual Variables.......................... 1.3.5 Performance and Optimization Models ....................... 1.4 Principles of Modeling Queueing Networks............................. 1.4.1 Representation G(V,E).............. 1.4.2 Analysis ƒ [(G(V,£)]................. 1.4.3 Synthesis G{V,E)*........................................................... 1.4.4 Case Study .................................................................... 1.4.5 Steady-State vs. Transient Approach............................. 1.5 TND Optimization Problems .................................................... 1.5.1 OTOP Problem............................ 1.5.2 Layout and Resource Planning (ORAP).......................
1.5.3 Optimal Routing Problem (ORTE).............. 1.5.4 Transportation Assignment Problem....................... 1.5.5 Other Books and Theoretical Research Issues.............. 1.6 Summary and Conclusions....................................................... 1 2 5 7 7 10 10 10 12 12 13 13 13 14 15 16 20 20 20 25 29 31 33 35 2 Problem Overview í2(G(V,ê ))......................................................... 2.1 Introduction................................................................................ 2.1.1 System State Space Orientation......... ............................ 2.1.2 Stochastic Processes....................................................... 2.2 Little s Law ................................................................................ 37 38 39 41 42 XV
xvi Contents 2.3 Single Queue History................................................................ 2.3.1 A. K. Erlang...................................................................... 2.3.2 The Early Pioneer Years.................................................. 2.3.3 Mid-Century.................................................................... 2.4 Queueing Network History........................................................ 2.4.1 Open Queueing Networks......................................... 2.4.2 Closed Queueing Networks........................................... 2.4.3 Mixed Queueing Networks ............................................ 2.4.4 Product-Form Networks................................................ 2.4.5 Non-product-Form Networks......................... 2.4.6 Blocking Networks......................................................... 2.4.7 Transportation and Loss Networks ............................... 2.5 Optimization History................................................................. 2.5.1 Static Optimal Control.................................................... 2.5.2 Optimization Focus......................................................... 2.5.3 Optimal Dynamic Control............................................... 3 46 46 48 50 50 51 52 53 54 57 57 60 62 62 63 64 Mathematical Models and Properties of Queues G(V).................. 65 3.1 Introduction and Motivation..................... 66 3.2 Assumptions, Definitions, Notation.......................................... 68 3.2.1 Definitions................. 69 3.3 Birth-and-Death
Process (BD)................................................... 70 3.3.1 BD Example Hair Salon.................................................. 74 3.4 Product Form: Birth-and-Death Queueing Formulas.............. 77 3.4.1 M/M/X Representation.................................................... 78 3.4.2 Sample Path.................................................................... 78 3.4.3 Steady-State Equations .................................................. 80 3.4.4 Algorithm.................................................................... 82 3.4.5 Example Routing Problem....... ..................................... 83 3.4.6 M/M/c Representation....... ............................................. 85 3.4.7 M/M/c Sample Path........................................................ 85 3.4.8 Birth-Death Equations.................................................... 86 3.4.9 M/M/c Algorithm........................................... 88 3.4.10 M/M/c Examples and Optimization ............................. 88 3.4.11 M/G/oо Queue................................................................. 93 3.5 Non-product-Form Queues: М/G/1/°° and Related Queues.. 95 3.5.1 Embedded Markov Process Approach ......................... 96 3.5.2 M/G/l Generating Function Approach........................ 97 3.5.3 Embedded DTMC Matrix ................................... 98 3.5.4 M/G/c Approximation Formula..................................... 104 3.5.5 M/G/c Approximation Formula Example and Optimization ..................................... 104 3.5.6 G/M/X and G/М/с
Queues.......................... 106 3.5.7 Gl/G/c: Approximation Formula....................................106
Contents xvii 3.6 Blocking Queues: Finite Buffer Queue Models.........................108 3.6.1 M/M/l/K Models............................................................ 108 3.6.2 M/M/l/K Performance Measures................................... 109 3.6.3 M/M/l/K Optimization Example....................................Ill 3.6.4 M/М/с/K Models............................................................ 112 3.6.5 M/M/c/K/N Finite Population Model.......................... 114 3.6.6 M/G/l/К M/G/c/K Models.............................. 120 3.6.7 Two-Moment Approach ................................................. 120 3.6.8 Derivation of if................................................................. 120 3.6.9 M/G/l/K Approximations.............................................. 121 3.6.10 Derivation of рк................................................................122 3.6.11 Increasing the Number of Servers c 1 ............ 124 3.6.12 M/G/l к Performance Analysis Results.........................124 3.6.13 M/G/l к Results .............................................................. 124 3.7 Transportation and Loss Queues................................................128 3.7.1 M/M/c/c M/G/c/c Models....................... 128 3.7.2 Summary and Conclusions................... 131 4 Transportation and Loss Queues G{E).............................. 133 4.1 Introduction.................................................................. 134 4.2 Transportation and Material Handling Systems....................... 135 4.2.1 Literature
Review............................................................ 136 4.2.2 Material Systems.............................................................. 138 4.2.3 Material Handling and Transportation Systems............ 139 4.3 Principles of Traffic Flow Theory....... ........................................ 140 4.3.1 Traffic Flow or Volume and Throughput.......................140 4.3.2 Speed-Density Curves..................................................... 142 4.3.3 Two-Phase Traffic Models................................................143 4.3.4 Three-Phase Traffic Models.............................................. 144 4.4 M/G/c/c State-Dependent Models ...........................................147 4.4.1 State-Dependent Queues.......................... 151 4.4.2 Doublet and Triplet Networks.........................................156 4.4.3 Steady-State Model Focus............................ 159 4.5 M/G/c/c Performance and Optimization ......................... 160 4.5.1 Throughput Curves .......................... 162 4.5.2 Optimal Ψ ...................................................................... 164 4.5.3 Optimal Jžř ....................................................................... 165 4.5.4 Optimal A .........................................................................166 4.6 M/G/c/c State-Dependent Transient Simulation Models .... 166 4.6.1 Four-Story Building Network.........................................167 4.6.2 Classroom Building Network...........................................168 4.7 Open Transportation Loss Networks Javíts
Center................... 170 4.7.1 Purpose of the Case Study............................................. 172 4.7.2 Approach and Experiment.............................................. 175 4.7.3 Modeling of the Gift Fair Evacuation Process................175
xviii Contents 4.8 Web Site for Transient M/G/c/c Queueing Networks.............. 176 4.9 Summary and Conclusions.........................................................179 5 Open Queueing Network Algorithms ƒ (G(V,E))...........................181 5.1 Introduction .............................................................................. 182 5.1.1 Complexity of Open and Closed Queueing Network Algorithms ..................................................................... 184 5.1.2 Complexity Classes...........................................................184 5.1.3 Product Form Open Jackson Networks...........................186 5.1.4 General Decomposition Principles of Modeling with Open Networks................................................................187 5.1.5 Assumptions..................................................................... 187 5.1.6 Definitions and Notation..................................................188 5.2 JacksoriNetwork General Principles...........................................188 5.2.1 Merging or Superposition of Processes...........................189 5.2.2 Equivalence/Reversibility/Transparency Property.... 189 5.2.3 Splitting Processes.............................................................190 5.2.4 Jackson Networks Product Form....................................191 5.2.5 Jackson Network Equations and Maple Program.......... 193 5.2.6 Multi-Server Systems....................................................... 195 5.2.7 Flexible Manufacturing Example................................... 196 5.2.8 Jackson Network
Example.............................................. 198 5.2.9 Health-Care Example..................................... ................ 199 5.2.10 Jackson Network Optimization.......................................201 5.2.11 Generalized Jackson Queueing Networks (GQnet) .... 203 5.2.12 GQnet Basic Assumptions......................... 203 5.2.13 Complex Mixing of Arrival and DepartureProcesses .. 204 5.2.14 Deterministic Routing Vector.......................................... 204 5.2.15 G(Z, E) Dual Graph................ .................. ............... 205 5.2.16 Dichotomous Nodal Types.............................................. 207 5.2.17 Non-instantaneous Transitions.......................................209 5.2.18 GQNET Performance Analysis.............................. 210 5.3 Non-product-Form Networks................................ 212 5.3.1 Queueing Network Analyzer.......................................... 212 5.3.2 QNA Algorithm......................................... 214 5.3.3 QNA Algorithm Example................................................215 5.3.4 QNA Algorithm Optimization.........................................216 5.3.5 QNA Multi-Server Algorithm.......................... 218 5.3.6 QNA Multi-Server Maple Algorithm............... 218 5.3.7 QNA Multi-Server Maple Algorithm Example..............219 5.4 Blocking Networks ..................................................................... 220 5.4.1 Simple Two-Node Blocking Network............................ 220 5.4.2 Concavity of Throughput Function....... ........................224 5.4.3
Exponential Expansion Method ..................................... 229 5.4.4 Performance Algorithm................................................... 230
Contents xix 5.4.5 Basic Stages.............................................. 230 5.4.6 Stage I: Network Reconfiguration................................... 231 5.4.7 Stage II: Parameter Estimation........................................ 231 5.4.8 Stage III: Feedback Elimination.......................................233 5.4.9 Two-Stage Series Topologies............................................235 5.4.10 Comparison with Exact Results................. 236 5.4.11 Generalized Expansion Method (GEM)................ 236 5.4.12 Detailed Performance Results........................................ 239 5.4.13 Six-Node Complex Network.......................................... 241 5.5 Transportation and Material Handling Networks................... 242 5.5.1 Spatial Queueing Networks............................................ 244 5.5.2 Infinite Queueing Networks................................. 244 5.5.3 M/G/c/c Networks........................................................ 244 5.5.4 Type I: Constant Time .....................................................245 5.5.5 Type II: Linear Decreasing ..............................................249 5.5.6 Type III: Nonlinear Decreasing.......................................252 5.5.7 Tandem Freeway Systems....................... 253 5.5.8 Complex Freeway System Example................................253 5.5.9 Analysis of First Complex Freeway System-------:.... 258 5.5.10 Analysis of Second Complex Freeway System..............258 5.5.11 Summary and Conclusions..............................................259 6 Closed Queueing Network
Performance Models f(G(V,E,N)) ...261 6.1 Introduction............... 262 6.2 Background of Closed Networks....... ....................................... 263 6.2.1 Scheer = Gordon and Newell = BCMP = Reiser MVA Networks............................................................... 265 6.2.2 Gordon and Newell, 1967................................................265 6.3 General Principles for Modeling Closed Queueing Networks . 266 6.3.1 Arrival Theorem PASTA/MUSTA/ASTA ..................... 266 6.3.2 Aggregation or Norton s Theorem................................. 267 6.3.3 Diffusion Process Approaches........................................ 267 6.3.4 Concave Throughput Functions................. 267 6.4 Closed Network Algorithms and Models.......................... 269 6.4.1 Product-Form Exact Methods .......... 269 6.4.2 Definitions and Notation................................................. 269 6.4.3 Computer Programs........................................................ 275 6.4.4 MVA Algorithms..............................................................277 6.4.5 Multi-Class MVA Algorithm.......................................... 281 6.5 Algorithm............... 282 6.5.1 Experiments with Multi-Class Algorithm.......................283 6.5.2 Egress for a Small-Scale Facility ..................................... 283 6.5.3 Large-Scale Facility Model............ ................................. 287 6.6 Non-product-Form Networks.....................................................288 6.6.1 Literature Review............................................................
288
xx Contents 6.6.2 6.6.3 6.6.4 6.6.5 6.6.6 Non-product Form Two-Moment Algorithm................. 289 General Service Approximations ................................... 290 Non-product-Form Algorithms....................................... 292 Performance Model: MVA .............................................. 292 Series Two-Moment Algorithm Example in Manufacturing..................................................................293 6.6.7 Maple General Service MVA Code..................................295 6.6.8 Split-Merge Two-Moment Algorithm for Computer Networks...........................................................................296 6.7 Blocking Networks ................................................ 297 6.7.1 Expansion Methods ......................................................... 297 6.7.2 Queue Decomposition..................................................... 299 6.7.3 .Two-Stage Series Systems................ ............................. 300 6.7.4 Three- and Five-Stage Performance Series Systems .... 304 6.7.5 Split and Merge Performance.......................................... 307 6.7.6 Multichain Layout............................................................ 309 6.8 Transportation and Loss Networks................. 312 6.8.1 Type I Systems: Constant Time ....................................... 313 6.8.2 Type II Systems: AGVS Delay Network.........................323 6.8.3 Type III Systems: Nonlinear Decreasing CrossDock System..................................................................... 327 6.9 Summary and
Conclusions....................................................... 329 7 Optimal Resource Allocation Problems (ORAP) G(V*) in TND .. 331 7.1 Introduction..................................................................................332 7.1.1 Iterative Nature of the Methodological Approaches ... 333 7.1.2 TND Example for ORAP Chapter................................... 334 7.1.3 ORAP Optimization Formulations ................................ 336 7.1.4 Assumptions.......................... 336 7.1.5 Notation............................................................................ 337 7.2 Open Network Buffer ß AP Allocation Problems.......................340 7.2.1 Problem...........................................................................340 7.2.2 Mini-Experiments with j8AP Optimization.............. 341 7.2.3 General Mathematical Model.......................................... 344 7.2.4 Powell s Algorithm................................ 345 7.2.5 Experimental Results.................................................. 345 7.2.6 Closed Network Buffer /ЗАР Allocation.........................352 7.2.7 Experimental Results..................................... 353 7.3 Open Network μΑΡ Problems..................... 356 7.3.1 μΑΡ Optimization................ 357 7.4 General Open μΑΡ Blocking Networks..................................... 361 7.4.1 Algorithms................................. 361 7.4.2 Example.................................................. 362 7.4.3 ѓ?9 := {c,p} Simultaneous Optimization.......................364
XXI 7.5 7.6 7.7 7.8 7.4.4 Optimal μΑΡ in Transportation Loss Networks....... 368 7.4.5 M/G/c/c Service Rate Experiments............................... 371 Optimal Number of Servers σΑΡ Problems..............................375 7.5.1 Mini-experiments with σΑΡ Optimization................... 376 7.5.2 General Threshold Algorithm........................................ 378 7.5.3 Open Network Multi-Server σΑΡ Allocation............... 379 7.5.4 З-Node Series Topologies..................................... 379 7.5.5 Splitting Topologies........................................................ 381 7.5.6 Merging Topologies........................................................ 382 7.5.7 Complex Topologies........................................................ 383 7.5.8 Closed Network Multi-Server σΑΡ Allocation..............385 7.5.9 Mathematical Model....................... 385 7.5.10 Experimental Design.......................................................386 7.5.11 3 and 5-Stage Performance Series Systems..................... 386 Composite Problems {λ,μ,ο,Κ} Optimization ........................ 388 7.6.1 ^*5 Simultaneous Optimization of K,c.......................... 389 ¿»ю Composite Problem................................... 393 Summary and Conclusions........................................................ 396 Optimal Routing Problems (ORTE) G(E*) in TND .................... 397 8.1 Introduction.......................... 398 8.1.1 Overview of Optimal Routing Optimization (ORTE) Problems.......................................................................... 398 8.2 ORTE
Background Routing Problems.......................................399 8.2.1 ORTE Problem........................ 401 8.2.2 Series-Parallel Tree Topologies........................................ 401 8.2.3 Background Literature....................... 402 8.2.4 ^4 Optimal Я Control.....................................................404 8.3 Optimal Open ouji Blocking Network Routing Problems....... 407 8.3.1 Assumptions.............................. 407 8.3.2 Mathematical Optimization Problem..............................407 8.3.3 Algorithm .........................................................................408 8.3.4 Experimental Results................. 408 8.3.5 General PDF Assumptions............................ 409 8.4 Optimal Closed аџ Blocking Network Routing Problems .... 410 8.4.1 Concave Programming Problem............................ 412 8.4.2 Sequential Quadratic Programming (SQP) Algorithm . 413 8.4.3 Experimental Results.......................................................414 8.4.4 Single-Chain Networks................................................... 414 8.4.5 Burst Networks............................................................... 414 8.5 Optimal Evacuation Routing in Transportation Networks .... 417 8.5.1 Evacuation Process.......................................................... 419 8.5.2 Mathematical Model................. 419 8.5.3 Experimental Results.......................................................421
xxii Contents 8.6 Closed Transportation Loss Networks aij ...............................423 8.6.1 Representation ......................................... 424 8.6.2 Analysis....................... 425 8.6.3 Synthesis.......................................................................... 428 8.7 Open Blocking Networks Hierarchal Systems ā..................... 429 8.7.1 К-Shortest Example .........................................................429 8.7.2 Algorithms.......................................................................430 8.7.3 К-Shortest Paths .............................................................. 431 8.7.4 Example Demonstration..................................................433 8.7.5 Other Algorithms.............................................. 434 8.8 Closed Blocking Networks Multichains ā................................ 434 8.8.1 Multichain Routing Problems (ORTE)............................ 435 8.9 Open and Closed Transportation Loss Networks Braess a.... 437 8.9.1 Braess Paradox......................................... 438 8.9.2 Vehicular Traffic Assignment ORTE Problems ..............440 8.9.3 Traffic Assignment Case Study..................................... 442 8.10 Closed a¡j¿ Traveling Salesman Routing (TSP) Problems....... 446 8.10.1 Mathematical Model..................................... 447 8.10.2 Algorithm................................ 448 8.10.3 Experimental Results.............................................. 448 8.10.4 TSP ORTE Problem Large Scale.......................................450 8.11 Combined Optimization
Problems............................................ 451 8.11.1 ^6 := {λ,μ} Continuous Optimization .........................451 8.11.2 £?η := {Κ,μ} Mixed Integer Optimization..................... 453 8.11.3 Material Handling Networks...........................................454 8.11.4 Series Topology................................................ 454 8.11.5 Split Topology ..................................................................455 8.11.6 Merge Topology.......................................... 455 8.11.7 ^8 := {λ, AT} Mixed Integer Optimization................... 456 8.11.8 Introduction................... 457 8.11.9 Optimization Problem..................................................... 457 8.11.10 Algorithm........................................................................ 458 8.11.11 Experimental Results....................................... 459 8.11.12Summary and Conclusions............................................ 459 9 Optimal Topology Problems (OTOP) G(V,E)* in TND ................. 461 9.1 Overview of OTOP G(V,E) Problems....................................... 462 9.2 Fixed Topology Open Network OTOP Problems.............. 463 9.2.1 Manufacturing Facility.............................................. 464 9.2.2 Manufacturing Network Topology ................. 465 9.2.3 GQnet Algorithm............................................................ 466 9.2.4 GQnet Network Results..................................................470 9.3 Closed Network Fixed Topology OTOP Problems ...................476 9.3.1 Pedestrian Traffic Closed Loss
Study..............................476
Contents 9.4 9.5 9.6 9.7 9.8 XXÜi 9.3.2 Representation Stage.......................................................478 9.3.3 Analysis Stage................................................................. 479 9.3.4 Synthesis Stage................................................................. 480 G{V) Location Network Design Problems................................. 482 9.4.1 Problem Formulation.......................................................484 9.4.2 Algorithm........................................................................ 486 9.4.3 Examples.................................................................. 486 9.4.4 Steiner/Weber Location Problem, OTOP.......................488 G(E) Tree and Path Network Design Problems........................ 491 9.5.1 Rectilinear Steiner Minimal Tree/MHS Design..............492 9.5.2 Shortest Path Tree Topology............................................496 9.5.3 Concave Optimization Problem............................ 497 9.5.4 Shortest Path Tree Topology............................................498 9.5.5 Optimal Routes............................................................... 498 G(V,E) Quadratic Assignment Layout Generation Two-Moment Methodology........................................ 504 9.6.1 Introduction.............................................. 504 9.6.2 Objective.......................................................................... 506 9.6.3 Definitions and Notation................................................. 506 9.6.4 Assumptions....................................................... 508
9.6.5 Stochastic QAP Models................................................... 508 9.6.6 M/G/°° Model ..................................... 509 9.6.7 M/G/C/C Models............................................................ 511 9.6.8 M/G/C/C Network Model.............................................. 511 9.6.9 Composite Algorithm .....................................................513 9.6.10 Computational Results............... 515 9.6.11 Deterministic Problems................................................... 515 9.6.12 Stochastic Problems........................................................ 516 Open Network Topological Arrangements Problem (TAP).... 518 Closed Network Topological Arrangements Problem (TAP) .. 522 9.8.1 Optimization Problem.............. 523 9.8.2 Algorithm........................................................................ 523 9.8.3 Performance Algorithm................................. 524 9.8.4 Experimental Results................................................. 525 9.8.5 Summary and Conclusions................. 526 10 Final Coda..................................................................................... 527 10.1 Introduction................................................................................. 528 10.1.1 Summary of the Volume................................................. 528 10.1.2 Software Summary.......................................................... 531 10.1.3 Future Research Issues.....................................................532 References................ 535 Index 557
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| id | DE-604.BV045113681 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:09:03Z |
| institution | BVB |
| isbn | 9783319788210 |
| issn | 1431-8598 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030503951 |
| oclc_num | 1053800632 |
| open_access_boolean | |
| owner | DE-11 DE-83 DE-188 DE-355 DE-BY-UBR |
| owner_facet | DE-11 DE-83 DE-188 DE-355 DE-BY-UBR |
| physical | xxv, 562 Seiten Illustrationen, Diagramme (farbig) |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer series in operations research and financial engineering |
| spelling | Smith, J. M. Verfasser (DE-588)17043818X aut Introduction to queueing networks theory ∩ practice Smith, J. MacGregor Cham Springer [2018] © 2018 xxv, 562 Seiten Illustrationen, Diagramme (farbig) txt rdacontent n rdamedia nc rdacarrier Springer series in operations research and financial engineering 1431-8598 Datenverarbeitungssystem (DE-588)4125229-9 gnd rswk-swf Warteschlangentheorie (DE-588)4255044-0 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 gnd rswk-swf Warteschlangennetz (DE-588)4225823-6 s Warteschlangentheorie (DE-588)4255044-0 s DE-604 Datenverarbeitungssystem (DE-588)4125229-9 s Erscheint auch als Online-Ausgabe 978-3-319-78822-7 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030503951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, J. M. Introduction to queueing networks theory ∩ practice Datenverarbeitungssystem (DE-588)4125229-9 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| subject_GND | (DE-588)4125229-9 (DE-588)4255044-0 (DE-588)4225823-6 |
| title | Introduction to queueing networks theory ∩ practice |
| title_auth | Introduction to queueing networks theory ∩ practice |
| title_exact_search | Introduction to queueing networks theory ∩ practice |
| title_full | Introduction to queueing networks theory ∩ practice Smith, J. MacGregor |
| title_fullStr | Introduction to queueing networks theory ∩ practice Smith, J. MacGregor |
| title_full_unstemmed | Introduction to queueing networks theory ∩ practice Smith, J. MacGregor |
| title_short | Introduction to queueing networks |
| title_sort | introduction to queueing networks theory ∩ practice |
| title_sub | theory ∩ practice |
| topic | Datenverarbeitungssystem (DE-588)4125229-9 gnd Warteschlangentheorie (DE-588)4255044-0 gnd Warteschlangennetz (DE-588)4225823-6 gnd |
| topic_facet | Datenverarbeitungssystem Warteschlangentheorie Warteschlangennetz |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030503951&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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