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Network traffic engineering : stochastic models and applications / / Andrea Baiocchi, University of Roma, Rome, IT
Network traffic engineering : stochastic models and applications / / Andrea Baiocchi, University of Roma, Rome, IT
Autore Baiocchi Andrea <1962->
Edizione [First edition.]
Pubbl/distr/stampa Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2020
Descrizione fisica 1 PDF
Disciplina 004.601/51982
Soggetto topico Computer networks - Mathematical models
Queuing theory
ISBN 1-119-63251-X
1-119-63250-1
1-119-63249-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface xv -- Acronyms xvii -- Part I Models for Service Systems -- 1 Introduction 3 -- 1.1 Network Traffic Engineering: what, why, how 3 -- 1.2 The art of modeling 7 -- 1.3 An example: delay equalization 11 -- 1.3.1 Model setting 12 -- 1.3.2 Analysis by equations 13 -- 1.3.3 Analysis by simulation 16 -- 1.3.4 Takeaways 18 -- 1.4 Outline of the book 18 -- 1.4.1 Plan 18 -- 1.4.2 Use 21 -- 1.4.3 Notation 23 -- 1.5 Further readings 24 -- Problems 25 -- 2 Service systems and queues 27 -- 2.1 Service system structure 27 -- 2.2 Arrival and service processes 28 -- 2.3 The queue as a service system model 32 -- 2.4 Queues in equilibrium 33 -- 2.4.1 Queues and stationary processes 33 -- 2.4.2 Littlés law 37 -- 2.5 Palḿs distributions for a queue 40 -- 2.6 The traffic process 44 -- 2.7 Performance metrics 46 -- 2.7.1 Throughput 47 -- 2.7.2 Utilization 49 -- 2.7.3 Loss 49 -- 2.7.4 Delay 51 -- 2.7.5 Age of Information 51 -- Problems 54 -- 3 Stochastic models for network traffic 59 -- 3.1 Introduction 59 -- 3.2 The Poisson process 60 -- 3.2.1 Light versus heavy tails 65 -- 3.2.2 Inhomogeneous Poisson process 66 -- 3.2.3 Poisson process in multidimensional spaces 70 -- 3.2.4 Testing for Poisson 80 -- 3.3 The Markovian Arrival Process 83 -- 3.4 Renewal processes 86 -- 3.4.1 Residual interevent time and renewal paradox 91 -- 3.4.2 Superposition of renewal processes 93 -- 3.4.3 Alternating renewal processes 94 -- 3.4.4 Renewal reward processes 95 -- 3.5 Birthdeath processes 97 -- 3.6 Branching processes 102 Problems 107 -- Part II Queues -- 4 Single server queues 113 -- 4.1 Introduction and notation 113 -- 4.2 The Embedded Markov Chain analysis of the M/G/1 queue 114 -- 4.2.1 Queue length 116 -- 4.2.2 Waiting time 120 -- 4.2.3 Busy period and idle time 123 -- 4.2.4 Remaining service time 126 -- 4.2.5 Output process 127 -- 4.2.6 Evaluation of the probabilities 129 -- 4.3 The M/G/1/K queue 130 -- 4.3.1 Exact solution 130 -- 4.3.2 Asymptotic approximation for large K 133 -- 4.4 Numerical evaluation of the queue length PDF 141.
4.5 A special case: the M/M/1 queue 143 -- 4.6 Optimization of a single server queue 145 -- 4.6.1 Maximization of net profit 146 -- 4.6.2 Minimization of age of information 149 -- 4.7 The G/M/1 queue 152 -- 4.8 Matrixgeometric queues 159 -- 4.8.1 Quasi BirthDeath (QBD) processes 159 -- 4.8.2 M/G/1 and G/M/1 structured processes 161 -- 4.9 A general result on single server queues 164 -- Problems 167 -- 5 Multiserver queues 171 -- 5.1 Introduction 171 -- 5.2 The Erlang loss system 173 -- 5.2.1 Insensitivity property of the Erlang loss system 182 -- 5.2.2 A finite population model 183 -- 5.2.3 NonPoisson input traffic 184 -- 5.2.4 Multiclass Erlang loss system 189 -- 5.3 Application of the Erlang loss model to cellular radio access network 192 -- 5.3.1 Cell dimensioning under Quality of Service constraints 193 -- 5.3.2 Number of handoffs in a connection lifetime 198 -- 5.3.3 Blocking in a cell with user mobility 199 -- 5.3.4 Tradeoff between location updating and paging 201 -- 5.3.5 Dimensioning of a cell with two service classes 202 -- 5.4 The M/M/m queue 204 -- 5.4.1 Finite queue size model 209 -- 5.4.2 Resource sharing versus isolation 209 -- 5.5 Infinite server queues 212 -- 5.5.1 Analysis of message propagation in a linear network 216 -- Problems 221 -- 6 Priorities and scheduling 227 -- 6.1 Introduction 227 -- 6.2 Conservation law 230 -- 6.3 M/G/1 priority queueing 233 -- 6.3.1 NonFCFS queueing disciplines 234 -- 6.3.2 HeadOfLine (HOL) priorities 237 -- 6.3.3 Preemptresume priority 243 -- 6.3.4 Shortest Job First 244 -- 6.3.5 Shortest Remaining Processing Time 245 -- 6.3.6 The ơC rule 247 -- 6.4 Processor sharing 248 -- 6.4.1 The M/G/1 Processor Sharing model 248 -- 6.4.2 Generalized Processor Sharing 250 -- 6.4.3 Weighted Fair Queueing 255 -- 6.4.4 Creditbased scheduling 258 -- 6.4.5 Deficit Round Robin scheduling 262 -- 6.4.6 Least Attained Service scheduling 263 -- 6.5 Miscellaneous scheduling 266 -- 6.5.1 Scheduling on a radio link 266 -- 6.5.2 Job dispatching 271.
6.6 Optimal scheduling 276 -- 6.6.1 Anticipative systems 277 -- 6.6.2 Serversharing, nonanticipative systems 277 -- 6.6.3 Nonserversharing, nonanticipative systems 278 -- Problems 279 -- 7 Queueing networks 283 -- 7.1 Structure of a queueing network and notation 283 -- 7.2 Open queueing networks 284 -- 7.2.1 Optimization of network capacities 295 -- 7.2.2 Optimal routing 297 -- 7.2.3 Braess paradox 300 -- 7.3 Closed queueing networks 303 -- 7.3.1 Arrivals See Time Averages (ASTA) 306 -- 7.3.2 Buzeńs algorithm for the computation of the normalization constant 307 -- 7.3.3 Mean Value Analysis 308 -- 7.4 Loss networks 315 -- 7.4.1 Erlang fixedpoint approximation 319 -- 7.4.2 Alternate routing 323 -- 7.5 Stability of queueing networks 326 -- 7.5.1 Definition of stability 329 -- 7.5.2 Turning a stochastic discrete queueing network into a deterministic fluid network 331 -- Appendix 334 -- Problems 337 -- 8 Bounds and approximations 341 -- 8.1 Introduction 341 -- 8.2 Bounds for the G/G/1 queue 343 -- 8.2.1 Mean Value Analysis 345 -- 8.2.2 Output process 347 -- 8.2.3 Upper and lower bounds of the mean waiting time 348 -- 8.2.4 Upper bound of the waiting time probability distribution 350 -- 8.3 Bounds for the G/G/m queue 352 -- 8.4 Approximate analysis of isolated G/G queues 355 -- 8.4.1 Approximations from bounds 356 -- 8.4.2 Approximation of the arrival or service process 356 -- 8.4.3 Reflected Brownian Motion approximation 358 -- 8.4.4 Heavytraffic approximation 361 -- 8.5 Approximate analysis of a network of G/G/1 queues 364 -- 8.5.1 Superposition of flows 365 -- 8.5.2 Flow through a queue 365 -- 8.5.3 Bernoulli splitting of a flow 366 -- 8.5.4 Putting pieces together: the decomposition method 366 -- 8.5.5 Bottleneck approximation for closed queueing networks 378 -- 8.6 Fluid models 379 -- 8.6.1 Deterministic fluid model 379 -- 8.6.2 From fluid to diffusion model 386 -- 8.6.3 Stochastic fluid model 389 -- 8.6.4 Steadystate analysis 392 -- 8.6.5 First passage times 398.
8.6.6 Application of the stochastic fluid model to a multiplexer with ON-OFF traffic sources 400 -- Problems 403 -- Part III Networked Systems and Protocols -- 9 Multiple access 409 -- 9.1 Introduction 409 -- 9.2 Slotted ALOHA 411 -- 9.2.1 Analysis of the na℗ ♯łve Slotted ALOHA 412 -- 9.2.2 Finite population Slotted ALOHA 416 -- 9.2.3 Stabilized Slotted ALOHA 422 -- 9.3 Pure ALOHA with variable packet times 426 -- 9.4 Carrier Sense Multiple Access (CSMA) 431 -- 9.4.1 Finite population model of CSMA 435 -- 9.4.2 Multipacket reception CSMA 438 -- 9.4.3 Stability of CSMA 447 -- 9.4.4 Delay analysis of stabilized CSMA 452 -- 9.5 Analysis of the WiFi MAC protocol 455 -- 9.5.1 Outline of the IEEE 802.11 DCF protocol 456 -- 9.5.2 Model of CSMA/CA 459 -- 9.5.3 Optimization of backoff parameters 473 -- 9.5.4 Fairness of CSMA/CA 481 -- Appendix 487 -- Problems 489 -- 10 Congestion control 493 -- 10.1 Introduction 493 -- 10.2 Congestion control architecture in the Internet 497 -- 10.3 Evolution of congestion control in the Internet 500 -- 10.3.1 TCP Reno 500 -- 10.3.2 TCP CUBIC 507 -- 10.3.3 TCP Vegas 509 -- 10.3.4 Data Center TCP (DCTCP) 512 -- 10.3.5 Bottleneck Bandwidth and RTT (BBR) 514 -- 10.4 Traffic engineering with TCP 520 -- 10.5 Fluid model of a single TCP connection congestion control 522 -- 10.5.1 Classic TCP with fixed capacity bottleneck link 523 -- 10.5.2 Classic TCP with variable capacity bottleneck link 525 -- 10.5.3 Application to wireless links 536 -- 10.6 Fluid model of multiple TCP connections congestion control 540 -- 10.6.1 Negligible buffering at the bottleneck 540 -- 10.6.2 Classic TCP with droptail buffer at the bottleneck 541 -- 10.6.3 Classic TCP with AQM at the bottleneck 542 -- 10.6.4 Data Center TCP 543 -- 10.7 Fairness and congestion control 545 -- 10.8 Network Utility Maximization (NUM) 548 -- 10.9 Challenges to TCP 553 -- 10.9.1 Fatlong pipes 554 -- 10.9.2 Wireless channels 556 -- 10.9.3 Bufferbloat 557 -- 10.9.4 Interaction with applications 558.
Appendix 559 -- Problems 564 -- 11 Quality of Service guarantees 567 -- 11.1 Introduction 567 -- 11.2 Deterministic service guarantees 568 -- 11.2.1 Arrival curves 571 -- 11.2.2 Service curves 575 -- 11.2.3 Performance bounds 578 -- 11.2.4 Regulators 579 -- 11.2.5 Network calculus 584 -- 11.3 Stochastic service guarantees 596 -- 11.3.1 Multiplexing with marginal buffer size 596 -- 11.3.2 Multiplexing with nonnegligible buffer size 603 -- 11.3.3 Effective bandwidth 605 -- 11.3.4 Network analysis and dimensioning 611 -- 11.4 Further readings 616 -- Appendix 617 -- Problems 622 -- A Refresher of probability, random variables and stochastic processes 623 -- A.1 Probability 623 -- A.2 Random variables 625 -- A.3 Transforms of probability distribution functions 627 -- A.4 Inequalities and limit theorems 631 -- A.4.1 Markov inequality 631 -- A.4.2 Chebychev inequality 632 -- A.4.3 Jensen inequality 632 -- A.4.4 Chernov bound 633 -- A.4.5 Union bound 633 -- A.4.6 Central Limit Theorem (CLT) 634 -- A.5 Stochastic processes 634 -- A.6 Markov Chains 635 -- A.6.1 Classification of states 636 -- A.6.2 Recurrence 637 -- A.6.3 Visits to a state 640 -- A.6.4 Asymptotic behavior and steadystate 641 -- A.6.5 Absorbing Markov chains 646 -- A.6.6 Continuoustime Markov processes 647 -- A.6.7 Sojourn times in process states 649 -- A.6.8 Reversibility 650 -- A.6.9 Uniformization 651 -- A.7 Wiener process (Brownian Motion) 652 -- A.7.1 Wiener process with an absorbing barrier 654 -- A.7.2 Wiener process with a reflecting barrier 655 -- References 657 -- Index 669.
Altri titoli varianti Network Traffic Engineering
Record Nr. UNINA-9910555154603321
Baiocchi Andrea <1962->  
Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2020
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Network traffic engineering : stochastic models and applications / / Andrea Baiocchi, University of Roma, Rome, IT
Network traffic engineering : stochastic models and applications / / Andrea Baiocchi, University of Roma, Rome, IT
Autore Baiocchi Andrea <1962->
Edizione [First edition.]
Pubbl/distr/stampa Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2020
Descrizione fisica 1 PDF
Disciplina 004.601/51982
Soggetto topico Computer networks - Mathematical models
Queuing theory
ISBN 1-119-63251-X
1-119-63250-1
1-119-63249-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface xv -- Acronyms xvii -- Part I Models for Service Systems -- 1 Introduction 3 -- 1.1 Network Traffic Engineering: what, why, how 3 -- 1.2 The art of modeling 7 -- 1.3 An example: delay equalization 11 -- 1.3.1 Model setting 12 -- 1.3.2 Analysis by equations 13 -- 1.3.3 Analysis by simulation 16 -- 1.3.4 Takeaways 18 -- 1.4 Outline of the book 18 -- 1.4.1 Plan 18 -- 1.4.2 Use 21 -- 1.4.3 Notation 23 -- 1.5 Further readings 24 -- Problems 25 -- 2 Service systems and queues 27 -- 2.1 Service system structure 27 -- 2.2 Arrival and service processes 28 -- 2.3 The queue as a service system model 32 -- 2.4 Queues in equilibrium 33 -- 2.4.1 Queues and stationary processes 33 -- 2.4.2 Littlés law 37 -- 2.5 Palḿs distributions for a queue 40 -- 2.6 The traffic process 44 -- 2.7 Performance metrics 46 -- 2.7.1 Throughput 47 -- 2.7.2 Utilization 49 -- 2.7.3 Loss 49 -- 2.7.4 Delay 51 -- 2.7.5 Age of Information 51 -- Problems 54 -- 3 Stochastic models for network traffic 59 -- 3.1 Introduction 59 -- 3.2 The Poisson process 60 -- 3.2.1 Light versus heavy tails 65 -- 3.2.2 Inhomogeneous Poisson process 66 -- 3.2.3 Poisson process in multidimensional spaces 70 -- 3.2.4 Testing for Poisson 80 -- 3.3 The Markovian Arrival Process 83 -- 3.4 Renewal processes 86 -- 3.4.1 Residual interevent time and renewal paradox 91 -- 3.4.2 Superposition of renewal processes 93 -- 3.4.3 Alternating renewal processes 94 -- 3.4.4 Renewal reward processes 95 -- 3.5 Birthdeath processes 97 -- 3.6 Branching processes 102 Problems 107 -- Part II Queues -- 4 Single server queues 113 -- 4.1 Introduction and notation 113 -- 4.2 The Embedded Markov Chain analysis of the M/G/1 queue 114 -- 4.2.1 Queue length 116 -- 4.2.2 Waiting time 120 -- 4.2.3 Busy period and idle time 123 -- 4.2.4 Remaining service time 126 -- 4.2.5 Output process 127 -- 4.2.6 Evaluation of the probabilities 129 -- 4.3 The M/G/1/K queue 130 -- 4.3.1 Exact solution 130 -- 4.3.2 Asymptotic approximation for large K 133 -- 4.4 Numerical evaluation of the queue length PDF 141.
4.5 A special case: the M/M/1 queue 143 -- 4.6 Optimization of a single server queue 145 -- 4.6.1 Maximization of net profit 146 -- 4.6.2 Minimization of age of information 149 -- 4.7 The G/M/1 queue 152 -- 4.8 Matrixgeometric queues 159 -- 4.8.1 Quasi BirthDeath (QBD) processes 159 -- 4.8.2 M/G/1 and G/M/1 structured processes 161 -- 4.9 A general result on single server queues 164 -- Problems 167 -- 5 Multiserver queues 171 -- 5.1 Introduction 171 -- 5.2 The Erlang loss system 173 -- 5.2.1 Insensitivity property of the Erlang loss system 182 -- 5.2.2 A finite population model 183 -- 5.2.3 NonPoisson input traffic 184 -- 5.2.4 Multiclass Erlang loss system 189 -- 5.3 Application of the Erlang loss model to cellular radio access network 192 -- 5.3.1 Cell dimensioning under Quality of Service constraints 193 -- 5.3.2 Number of handoffs in a connection lifetime 198 -- 5.3.3 Blocking in a cell with user mobility 199 -- 5.3.4 Tradeoff between location updating and paging 201 -- 5.3.5 Dimensioning of a cell with two service classes 202 -- 5.4 The M/M/m queue 204 -- 5.4.1 Finite queue size model 209 -- 5.4.2 Resource sharing versus isolation 209 -- 5.5 Infinite server queues 212 -- 5.5.1 Analysis of message propagation in a linear network 216 -- Problems 221 -- 6 Priorities and scheduling 227 -- 6.1 Introduction 227 -- 6.2 Conservation law 230 -- 6.3 M/G/1 priority queueing 233 -- 6.3.1 NonFCFS queueing disciplines 234 -- 6.3.2 HeadOfLine (HOL) priorities 237 -- 6.3.3 Preemptresume priority 243 -- 6.3.4 Shortest Job First 244 -- 6.3.5 Shortest Remaining Processing Time 245 -- 6.3.6 The ơC rule 247 -- 6.4 Processor sharing 248 -- 6.4.1 The M/G/1 Processor Sharing model 248 -- 6.4.2 Generalized Processor Sharing 250 -- 6.4.3 Weighted Fair Queueing 255 -- 6.4.4 Creditbased scheduling 258 -- 6.4.5 Deficit Round Robin scheduling 262 -- 6.4.6 Least Attained Service scheduling 263 -- 6.5 Miscellaneous scheduling 266 -- 6.5.1 Scheduling on a radio link 266 -- 6.5.2 Job dispatching 271.
6.6 Optimal scheduling 276 -- 6.6.1 Anticipative systems 277 -- 6.6.2 Serversharing, nonanticipative systems 277 -- 6.6.3 Nonserversharing, nonanticipative systems 278 -- Problems 279 -- 7 Queueing networks 283 -- 7.1 Structure of a queueing network and notation 283 -- 7.2 Open queueing networks 284 -- 7.2.1 Optimization of network capacities 295 -- 7.2.2 Optimal routing 297 -- 7.2.3 Braess paradox 300 -- 7.3 Closed queueing networks 303 -- 7.3.1 Arrivals See Time Averages (ASTA) 306 -- 7.3.2 Buzeńs algorithm for the computation of the normalization constant 307 -- 7.3.3 Mean Value Analysis 308 -- 7.4 Loss networks 315 -- 7.4.1 Erlang fixedpoint approximation 319 -- 7.4.2 Alternate routing 323 -- 7.5 Stability of queueing networks 326 -- 7.5.1 Definition of stability 329 -- 7.5.2 Turning a stochastic discrete queueing network into a deterministic fluid network 331 -- Appendix 334 -- Problems 337 -- 8 Bounds and approximations 341 -- 8.1 Introduction 341 -- 8.2 Bounds for the G/G/1 queue 343 -- 8.2.1 Mean Value Analysis 345 -- 8.2.2 Output process 347 -- 8.2.3 Upper and lower bounds of the mean waiting time 348 -- 8.2.4 Upper bound of the waiting time probability distribution 350 -- 8.3 Bounds for the G/G/m queue 352 -- 8.4 Approximate analysis of isolated G/G queues 355 -- 8.4.1 Approximations from bounds 356 -- 8.4.2 Approximation of the arrival or service process 356 -- 8.4.3 Reflected Brownian Motion approximation 358 -- 8.4.4 Heavytraffic approximation 361 -- 8.5 Approximate analysis of a network of G/G/1 queues 364 -- 8.5.1 Superposition of flows 365 -- 8.5.2 Flow through a queue 365 -- 8.5.3 Bernoulli splitting of a flow 366 -- 8.5.4 Putting pieces together: the decomposition method 366 -- 8.5.5 Bottleneck approximation for closed queueing networks 378 -- 8.6 Fluid models 379 -- 8.6.1 Deterministic fluid model 379 -- 8.6.2 From fluid to diffusion model 386 -- 8.6.3 Stochastic fluid model 389 -- 8.6.4 Steadystate analysis 392 -- 8.6.5 First passage times 398.
8.6.6 Application of the stochastic fluid model to a multiplexer with ON-OFF traffic sources 400 -- Problems 403 -- Part III Networked Systems and Protocols -- 9 Multiple access 409 -- 9.1 Introduction 409 -- 9.2 Slotted ALOHA 411 -- 9.2.1 Analysis of the na℗ ♯łve Slotted ALOHA 412 -- 9.2.2 Finite population Slotted ALOHA 416 -- 9.2.3 Stabilized Slotted ALOHA 422 -- 9.3 Pure ALOHA with variable packet times 426 -- 9.4 Carrier Sense Multiple Access (CSMA) 431 -- 9.4.1 Finite population model of CSMA 435 -- 9.4.2 Multipacket reception CSMA 438 -- 9.4.3 Stability of CSMA 447 -- 9.4.4 Delay analysis of stabilized CSMA 452 -- 9.5 Analysis of the WiFi MAC protocol 455 -- 9.5.1 Outline of the IEEE 802.11 DCF protocol 456 -- 9.5.2 Model of CSMA/CA 459 -- 9.5.3 Optimization of backoff parameters 473 -- 9.5.4 Fairness of CSMA/CA 481 -- Appendix 487 -- Problems 489 -- 10 Congestion control 493 -- 10.1 Introduction 493 -- 10.2 Congestion control architecture in the Internet 497 -- 10.3 Evolution of congestion control in the Internet 500 -- 10.3.1 TCP Reno 500 -- 10.3.2 TCP CUBIC 507 -- 10.3.3 TCP Vegas 509 -- 10.3.4 Data Center TCP (DCTCP) 512 -- 10.3.5 Bottleneck Bandwidth and RTT (BBR) 514 -- 10.4 Traffic engineering with TCP 520 -- 10.5 Fluid model of a single TCP connection congestion control 522 -- 10.5.1 Classic TCP with fixed capacity bottleneck link 523 -- 10.5.2 Classic TCP with variable capacity bottleneck link 525 -- 10.5.3 Application to wireless links 536 -- 10.6 Fluid model of multiple TCP connections congestion control 540 -- 10.6.1 Negligible buffering at the bottleneck 540 -- 10.6.2 Classic TCP with droptail buffer at the bottleneck 541 -- 10.6.3 Classic TCP with AQM at the bottleneck 542 -- 10.6.4 Data Center TCP 543 -- 10.7 Fairness and congestion control 545 -- 10.8 Network Utility Maximization (NUM) 548 -- 10.9 Challenges to TCP 553 -- 10.9.1 Fatlong pipes 554 -- 10.9.2 Wireless channels 556 -- 10.9.3 Bufferbloat 557 -- 10.9.4 Interaction with applications 558.
Appendix 559 -- Problems 564 -- 11 Quality of Service guarantees 567 -- 11.1 Introduction 567 -- 11.2 Deterministic service guarantees 568 -- 11.2.1 Arrival curves 571 -- 11.2.2 Service curves 575 -- 11.2.3 Performance bounds 578 -- 11.2.4 Regulators 579 -- 11.2.5 Network calculus 584 -- 11.3 Stochastic service guarantees 596 -- 11.3.1 Multiplexing with marginal buffer size 596 -- 11.3.2 Multiplexing with nonnegligible buffer size 603 -- 11.3.3 Effective bandwidth 605 -- 11.3.4 Network analysis and dimensioning 611 -- 11.4 Further readings 616 -- Appendix 617 -- Problems 622 -- A Refresher of probability, random variables and stochastic processes 623 -- A.1 Probability 623 -- A.2 Random variables 625 -- A.3 Transforms of probability distribution functions 627 -- A.4 Inequalities and limit theorems 631 -- A.4.1 Markov inequality 631 -- A.4.2 Chebychev inequality 632 -- A.4.3 Jensen inequality 632 -- A.4.4 Chernov bound 633 -- A.4.5 Union bound 633 -- A.4.6 Central Limit Theorem (CLT) 634 -- A.5 Stochastic processes 634 -- A.6 Markov Chains 635 -- A.6.1 Classification of states 636 -- A.6.2 Recurrence 637 -- A.6.3 Visits to a state 640 -- A.6.4 Asymptotic behavior and steadystate 641 -- A.6.5 Absorbing Markov chains 646 -- A.6.6 Continuoustime Markov processes 647 -- A.6.7 Sojourn times in process states 649 -- A.6.8 Reversibility 650 -- A.6.9 Uniformization 651 -- A.7 Wiener process (Brownian Motion) 652 -- A.7.1 Wiener process with an absorbing barrier 654 -- A.7.2 Wiener process with a reflecting barrier 655 -- References 657 -- Index 669.
Altri titoli varianti Network Traffic Engineering
Record Nr. UNINA-9910829983603321
Baiocchi Andrea <1962->  
Hoboken, New Jersey : , : John Wiley & Sons, Inc., , 2020
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui