.

0 (hodnocen0 x )

BK

New York : John Wiley & Sons, 1976

xx,549 s.

ISBN 0-471-49111-X (váz.)

Rejstř.

Řady matematické - analýza matematická - počítače - aplikace - učebnice vysokošk.

000087578

CONTENTS // VOLUME II // Chapter 1 A Queueing Theory Primer 1 // 1.1. Notation...2 // 1.2. ’ General Results...5 // 1.3. Markov, Birth-Death, and Poisson Processes . . 7 // 1.4. The M/M/1 Queue...10 // 1.5. The M/M/m Queueing System...13 // 1.6. Markovian Queueing Networks...14 // 1.7. The M/G/l Queue...15 // 1.8. The G/M/l Queue...20 // 1.9. The G/M/m Queue...20 // 1.10. The G/G/l Queue...22 // Chapter 2 Bounds, Inequalities and Approximations 27 // 2.1. The Heavy-Traffic Approximation ... 29 // 2.2. An Upper Bound for the Average Wait ... 32 // 2.3. Lower Bounds for the Average Wait ... 34 // 2.4. Bounds on the Tail of the Waiting Time Distribution. 44 // 2.5. Some Remarks for G/G/m...46 // 2.6. A Discrete Approximation...51 // 2.7. The Fluid Approximation for Queues. ... 56 // 2.8. Diffusion Processes...62 // 2.9. Diffusion Approximation for M/G/l ... 79 // 2.10. The Rush-Hour Approximation...87 // Chapter 3 Priority Queueing 106 // 3.1. The Model...106 // 3.2. An Approach for Calculating Average Waiting Times 106 // 3.3. The Delay Cycle, Generalized Busy Periods, and Waiting Time Distributions...110 // xv // XVI // CONTENTS // 3.4. Conservation Laws...113 // 3.5. The Last-Come-First-Serve Queueing Discipline . 118 // 3.6. Head-of-the-Line Priorities...119 // 3.7. Time-Dependent Priorities...126 // 3.8. Optimal Bribing for Queue Position . . . .135 // 3.9. Service-Time-Dependent Disciplines ... 144 // Chapter 4 Computer Time-Sharing and Multiaccess Systems 156 // 4.1. Definitions

and Models...159 // 4.2. Distribution of Attained Service...162 // 4.3. The Batch Processing Algorithm...164 // 4.4. The Round-Robin Scheduling Algorithm . . . 166 // 4.5. The Last-Come-First-Serve Scheduling Algorithm . 170 // 4.6. The FB Scheduling Algorithm...172 // 4.7. The Multilevel Processor Sharing Scheduling Algorithm ...177 // 4.8. Selfish Scheduling Algorithms...188 // 4.9. A Conservation Law for Time-Shared Systems . . 197 // 4.10. Tight Bounds on the Mean Response Time . . 199 // 4.11. Finite Population Models...206 // 4.12. Multiple-Resource Models...212 // 4.13. Models for Multiprogramming...230 // 4.14. Remote Terminal Access to Computers . . . 236 // Chapter 5 Computer-Communication Networks: Analysis and // Design 270 // 5.1. Resource Sharing...272 // 5.2. Some Contrasts and Trade-Offs...290 // 5.3. Network Structures and Packet Switching . . . 292 // 5.4. The ARPANET—An Operational Description of an // Existing Network...304 // 5.5. Definitions, Model, and Problem Statements 314 // 5.6. Delay Analysis...320 // 5.7. The Capacity Assignment Problem ... 329 // 5.8. The Traffic Flow Assignment Problem . . . 340 // 5.9. The Capacity and Flow Assignment Problem . . 348 // 5.10. Some Topological Considerations—Applications to the // ARPANET...351 // 5.11. Satellite Packet Switching...360 // 5.12. Ground Radio Packet Switching...393 // CONTENTS Xvii // Chapter 6 Computer-Communication Networks: Measurement, // Flow Control, and ARPANET Traps 422 // 6.1. Simulation

and Routing...423 // 6.2. Early ARPANET Measurements...429 // 6.3. Flow Control...438 // 6.4. Lockups, Degradations, and Traps ... 446 // 6.5. Network Throughput...451 // 6.6. One Week of ARPANET Data...458 // 6.7. Line Overhead in the ARPANET ... 484 // 6.8. Recent Changes to the Flow Control Procedure . 501 // 6.9. The Challenge of the Future...508 // Glossary of Notation...516 // Summary of Important Results...523 // Index...537 // VOLUME I // PART I: PRELIMINARIES // Chapter 1 Queueing Systems 3 // 1.1. Systems of Flow...3 // 1.2. The Specification and Measure of Queueing Systems 8 // Chapter 2 Some Important Random Processes 10 // 2.1. Notation and Structure for Basic Queueing Systems 10 // 2.2. Definition and Classification of Stochastic Processes . 19 // 2.3. Discrete-Time Markov Chains...26 // 2.4. Continuous-Time Markov Chains ... 44 // 2.5. Birth-Death Processes...53 // PART II: ELEMENTARY QUEUEING THEORY // Chapter 3 Birth-Death Queueing Systems in Equilibrium 89 // 3.1. General Equilibrium Solution...90 // 3.2. M/M/1: The Classical Queueing System ... 94 // xviii CONTENTS // 3.3. Discouraged Arrivals...99 // 3.4. Responsive Servers (Infinite Number of Servers) 101 // 3.5. M/M/m: The m-Server Case...102 // 3.6. M/M/l/K: Finite Storage...103 // 3.7. M/M/m/m: m-Server Loss Systems...105 // 3.8. M/M/1//M: Finite Customer Population—Single Server...106 // 3.9. M/M/CO//M: Finite Customer Population—“Infinite” // Number of Servers...107 // 3.10. M/M/m/K/M: Finite

Population, m-Server Case, Finite // Storage...108 // Chapter 4 Markovian Queues in Equilibrium 115 // 4.1. The Equilibrium Equations...115 // 4.2. The Method of Stages—Erlangian Distribution E, .119 // 4.3. The Queue ?/??...126 // 4.4. The Queue E,/M/l...130 // 4.5. Bulk Arrival Systems...134 // 4.6. Bulk Service Systems...137 // 4.7. Series-Parallel Stages: Generalizations . . . .139 // 4.8. Networks of Markovian Queues...147 // PART III: INTERMEDIATE QUEUEING THEORY // Chapter 5 The Queue M/G/l 167 // 5.1. The M/G/l System...168 // 5.2. The Paradox of Residual Life: A Bit of Renewal // Theory...169 // 5.3. The Imbedded Markov Chain...174 // 5.4. The Transition Probabilities...177 // 5.5. The Mean Queue Length...180 // 5.6. Distribution of Number in System ... 191 // 5.7. Distribution of Waiting Time...196 // 5.8. The Busy Period and Its Duration ... 206 // 5.9. The Number Served in a Busy Period . . . .216 // 5.10. From Busy Periods to Waiting Times ... 219 // 5.11. Combinatorial Methods...223 // 5.12. The Takács Integrodifferential Equation . . . 226 // CONTENTS // XIX // Chapter 6 The Queue G/M/m 241 // 6.1. Transition Probabilities for the Imbedded Markov // Chain (G/M/m)...241 // 6.2. Conditional Distribution of Queue Size . . . 246 // 6.3. Conditional Distribution of Waiting Time . . . 250 // 6.4. The Queue G/M/l...251 // 6.5. The Queue G/M/m...253 // 6.6. The Queue G/M/2...256 // Chapter 7 The Method of Collective Marks 261 // 7.1. The Marking of Customers...261

7.2. The Catastrophe Process...267 // part IV: ADVANCED MATERIAL // Chapter 8 The Queue G/G/l 275 // 8.1. Lindley’s Integral Equation...275 // 8.2. Spectral Solution to Lindley’s Integral Equation . . 283 // 8.3. Kingman’s Algebra for Queues...299 // 8.4. The Idle Time and Duality...304 // Epilogue 319 // Appendix I: Transform Theory Refresher: z-Transform and Laplace Transform // 1.1. Why Transforms?...321 // 1.2. The z-Transform...327 // 1.3. The Laplace Transform...338 // 1.4. Use of Transforms in the Solution of Difference and // Differential Equations...355 // Appendix II: Probability Theory Refresher // ILL Rules of the Game...363 // 11.2. Random Variables...368 // 11.3. Expectation...377 // 11.4. Transforms, Generating Functions, and Characteristic // Functions...381 // 11.5. Inequalities and Limit Theorems...388 // 11.6. Stochastic Processes...393 // XX // CONTENTS // Glossary of Notation 396 // Summary of Important Results 400 // Index 411