Contents
. -- Preface
. -- Acronyms
. -- Part I Models For Service Systems
. -- Introduction
. -- Network Traffic Engineering: What, Why, How
. -- The Art Of Modeling
. -- An Example: delay Equalization
. -- Model Setting
. -- Analysis By Equations
. -- Analysis By Simulation
. -- Takeaways
. -- Outline Of The Book
. -- Plan
. -- Use
. -- Notation
. -- Further Readings
. -- Problems
. -- Service Systems And Queues
. -- Service System Structure
. -- Arrival And Service Processes
. -- The Queue As a Service System Model
. -- Queues In Equilibrium
. -- Queues And Stationary Processes
. -- Little’S Law
. -- Palm’S Distributions For a Queue
. -- The Traffic Process
. -- Performance Metrics
. -- Throughput
. -- Utilization
. -- Loss
. -- Delay
. -- Age Of Information
. -- Summary And Takeaways
. -- Problems Stochastic Models For Network Traffic Introduction The Poisson Process Light Versus Heavy Tails Inhomogeneous Poisson Process Poisson Process In Multidimensional Spaces Displacement Mapping Thinning Distances Sums And Products On Point Processes Hard Core Processes Testing For Poisson The Markovian Arrival Process Renewal Processes Residual Inter-Event Time And Renewal Paradox Superposition Of Renewal Processes Alternating Renewal Processes Renewal Reward Processes Birth-Death Processes Branching Processes Summary And Takeaways Problems Part Ii Queues Single-Server Queues Introduction And Notation The Embedded Markov Chain Analysis Of The M/G/1 Queue Queue Length Waiting Time Busy Period And Idle Time Remaining Service Time Output Process Evaluation Of The Probabilities {Ak}K?Z The M/G/1/K Queue Exact Solution Asymptotic Approximation For Large K Numerical Evaluation Of The Queue Length Pdf a Special Case: The M/M/1 Queue Optimization Of a Single-Server Queue Maximization Of Net Profit Minimization Of Age Of Information General Expression Of The Average Age Of Information Minimization Of The Age Of Information For An M/M/1 Model The G/M/1 Queue Matrix-Geometric Queues Quasi Birth-Death (Qbd) Processes M/G/1 And G/M/1 Structured Processes General Result On Single-Server Queues
. -- Summary And Takeaways Problems Multi-Server Queues Introduction The Erlang Loss System Insensitivity Property Of The Erlang Loss System a Finite Population Model Non-Poisson Input Traffic Wilkinson’S Method Fredericks’ Method Multi-Class Erlang Loss System Application Of The Erlang Loss Model To Cellular Radio Access Network Cell Dimensioning Under Quality Of Service Constraints Number Of Handoffs In a Connection Lifetime Blocking In a Cell With User Mobility Trade-Off Between Location Updating And Paging Dimensioning Of a Cell With Two Service Classes The M/M/M Queue Finite Queue Size Model Resource Sharing Versus Isolation Infinite Server Queues Analysis Of Message Propagation In a Linear Network Summary And Takeaways Problems Priorities And Scheduling Introduction Conservation Law M/G/1 Priority Queueing Non-Fcfs Queueing Disciplines Head-Of-Line (Hol) Priorities Preempt-Resume Priorities Shortest Job First Shortest Remaining Processing Time The ??c Rule Processor Sharing The M/G/1 Processor Sharing Model Generalized Processor Sharing Weighted Fair Queueing Credit-Based Scheduling Deficit Round Robin Scheduling Least Attained Service Scheduling Miscellaneous Scheduling Scheduling On a Radio Link Proportional Fairness Multi-Rate Orthogonal Multiplexing Job Dispatching Optimal Scheduling Anticipative Systems Server-Sharing, Nonanticipative Systems Non-Server-Sharing, Nonanticipative Systems
. -- Summary And Takeaways Problems Queueing Networks Structure Of a Queueing Network And Notation Open Queueing Networks Optimization Of Network Capacities Optimal Routing Braess Paradox Closed Queueing Networks Arrivals See Time Averages (Asta) Buzen’S Algorithm For The Computation Of The Normalization Constant Mean Value Analysis Loss Networks Erlang Fixed-Point Approximation Alternate Routing Stability Of Queueing Networks Definition Of Stability Turning a Stochastic Discrete Queueing Network Into a Deterministic Fluid Network Further Readings Appendix Summary And Takeaways Problems Bounds And Approximations Introduction Bounds For The G/G/1 Queue 401 Mean Value Analysis 404 Output Process 406 Upper And Lower Bounds Of The Mean Waiting Time 407 Upper Bound Of The Waiting Time Probability Distribution 409 Bounds For The G/G/M Queue 412 Approximate Analysis Of Isolated G/G Queues 416 Approximations From Bounds 416 Approximation Of The Arrival Or Service Process 417 Reflected Brownian Motion Approximation 418 Heavy-Traffic Approximation 423 Approximate Analysis Of a Network Of G/G/1 Queues 426 Superposition Of Flows 427 Flow Through a Queue 428 Bernoulli Splitting Of a Flow 428 Putting Pieces Together: The Decomposition Method 429 Bottleneck Approximation For Closed Queueing Networks 442 Fluid Models 443 Deterministic Fluid Model 444 From Fluid To Diffusion Model 452 Stochastic Fluid Model 456 Steady-State Analysis 459 Infinite Buffer Size (K = 8) 462 Loss Probability 463 First Passage Times 466 Application Of The Stochastic Fluid Model To a Multiplexer With On-Off Traffic Sources
. -- Summary And Takeaways Problems Part Iii Networked Systems And Protocols Multiple Access Introduction Slotted Aloha Analysis Of The Naïve Slotted Aloha Finite Population Slotted Aloha Stabilized Slotted Aloha Pure Aloha With Variable Packet Times Carrier Sense Multiple Access (Csma) Features Of The Csma Protocol Clear Channel Assessment Persistence Policy Retransmission Policy Finite Population Model Of Csma Multi-Packet Reception Csma Multi-Packet Reception 1-Persistent Csma With Poisson Traffic Multi-Packet Reception Nonpersistent Csma With Poisson Traffic Stability Of Csma delay Analysis Of Stabilized Csma Analysis Of The Wifi Mac Protocol Outline Of The Ieee 802.11 Dcf Protocol Model Of Csma/Ca The Back-Off Process Virtual Slot Time Saturation Throughput Service Times Of Ieee 802.11 Dcf Correlation Between Service Times Optimization Of Back-Off Parameters Maximization Of Throughput Minimization Of Service Time Jitter Fairness Of Csma/Ca Further Readings Appendix Summary And Takeaways Problems Congestion Control Introduction Congestion Control Architecture In The Internet Evolution Of Congestion Control In The Internet Tcp Reno Tcp Congestion Control Operations Newreno Tcp Congestion Control With Sack Congestion Window Validation Tcp Cubic Tcp Vegas Data Center Tcp (Dctcp) Marking At The Switch
. -- Ecn-Echo At The Receiver Controller At The Sender Bottleneck Bandwidth And Rtt (Bbr) delivery Rate Estimate Startup And Drain Probebw Probertt Pseudo-Code Of Bbr Algorithm Traffic Engineering With Tcp Fluid Model Of a Single Tcp Connection Congestion Control Classic Tcp With Fixed Capacity Bottleneck Link Classic Tcp With Variable Capacity Bottleneck Link Discretization Of The Evolution Equations Accuracy Of The Fluid Approximation Of Tcp Application To Wireless Links Random Capacity Tcp Over Cellular Link Fluid Model Of Multiple Tcp Connections Congestion Control Negligible Buffering At The Bottleneck Classic Tcp With Drop Tail Buffer At The Bottleneck Classic Tcp With Aqm At The Bottleneck Data Center Tcp With Fifo Buffer At The Bottleneck Fairness And Congestion Control Network Utility Maximization (Num) Challenges To Tcp Fat-Long Pipes Wireless Channels Bufferbloat Interaction With Applications Appendix Summary And Takeaways Problems Quality-Of-Service Guarantees Introduction Deterministic Service Guarantees Arrival Curves Service Curves Performance Bounds Regulators Network Calculus Single Node Analysis End-To-End Analysis Stochastic Service Guarantees Multiplexing With Marginal Buffer Size Multiplexing With Non-Negligible Buffer Size Effective Bandwidth Definition Of The Effective Bandwidth Properties Of The Effective Bandwidth Effective Bandwidth Of a Markov Source Netwo
. -- Urther Readings Appendix Summary And Takeaways Problems a Refresher Of Probability, Random Variables, And Stochastic Processes Probability Random Variables Transforms Of Probability Distribution Functions Inequalities And Limit Theorems Markov Inequality Chebychev Inequality Jensen Inequality Chernov Bound Union Bound Central Limit Theorem (Clt) Stochastic Processes Markov Chains Classification Of States Recurrence Visits To a State Asymptotic Behavior And Steady State Absorbing Markov Chains Continuous-Time Markov Processes Sojourn Times In Process States Reversibility Uniformization Wiener Process (Brownian Motion) Wiener Process With An Absorbing Barrier Wiener Process With a Reflecting Barrier References Index