Delayed and Network Queues. (2016)

• Record Type: Book
• Further Information: Note: Aliakbar Montazer Haghighi, Dimitar P. Mishev.
• Authors: Haghighi, Aliakbar Montazer; Mishev, Dimitar P
• Contents: Dedication i Preface i 1. Preliminaries 1 1.1. Basics of Probability 1 1.1.1. Introduction 1 1.1.2. Conditional Probability 2 1.2. Discrete Random Variables and Distributions 4 1.3. Discrete Moments 9 1.4. Continuous Random Variables, Density and Cumulative Distribution Functions 15 1.5. Continuous Random Vector 19 1.6. Functions of Random Variables 22 1.7. Continuous Moments 26 1.8. Difference Equations 28 1.8.1. Introduction 28 1.8.2. Basic Definitions and Properties 29 1.9. Methods of Solving Linear Difference Equations with Constant Coefficients 31 1.9.1. Characteristic Equation Method 31 1.9.2. Recursive Method 33 1.9.3. Generating Function Method 34 1.9.4. Laplace Transform Method 37 Exercises 41 2. Stochastic Processes 1 2.1. Introduction and Basic Definitions 1 2.2. Markov Chain 6 2.2.1. Classification of States 5 2.3. Markov Process 21 2.3.1. Markov Process with Discrete Space State 21 2.4. Random Walk 25 2.5. Up-and-Down Biased Coin Design as a Random Walk 33 Exercises 39 3. Birth and Death Processes 1 3.1. Overviews of the Basis of the Chapter, Birth and Death Processes 1 3.2. Finite Birth and Death Process 10 3.3. Pure Birth Process (Poisson Process) 17 3.4. Pure Death Process (Poisson Death Process) 20 Exercises 23 4 Standard Queues 1 4.1. Introduction of Queues (General Birth and Death Process) 1 4.1.1. Mechanism, Characteristics and Types of Queues 3 4.2. Remarks on Non-Markovian Queues 7 4.2.1. Takács’s Waiting Time Paradox 8 4.2.2. The Virtual Waiting Time and Takács’s Integro-Differential Equation 9 4.2.3. The Unfinished Work 15 4.3. The Stationary M/M/1 Queueing Process 1 4.4. A Parallel M/M/c/K with Baking and Reneging 4 4.5. The Stationary M/M/1/K Queueing Process 6 4.6. Busy Period of a Transient M/M/1/K 7 4.7. The Stationary M/M/1 and M/M/1/K Queueing Processes with Feedback 11 4.7.1. The Stationary Distribution of the Sojourn Time of a Task 11 4.7.2. The Distribution of the Total Time of Service by a Task 14 4.7.3. The Stationary Distribution of the Feedback Queue Size 15 4.7.4. The Stationary Distribution of (the Sojourn Time of the nth task) 16 4.8. Queues with Bulk Arrivals and Batch Service 17 4.9. A Priority Queues with Balking and Reneging 20 4.10. The Discrete-Time M/M/1 Queueing Process, Combinatorics Method (Lattice Paths) 24 4.10.1 The Basic Ballot Problem 25 4.10.2. Ballot Problem [based on Takács (1997)] 27 4.10.3. Transient Solution of the M/M/1 by Lattice Path Method 35 4.11. The Stationary M/M/c Queueing Process 40 4.11.1. A Stationary Multi-server Queue 40 Exercises 43 5 Queues with Delay 1 5.1. Introduction 1 5.2. A Queueing System with Delayed-Service 5 5.3. An M/G/1 Queue with Server Breakdown and with Multiple Working Vacation 11 5.3.1. Mathematical Formulation of the Model 12 5.3.2. The Steady-State Mean Number of Tasks in the System 12 5.3.3. A Special Case 22 5.4. A Bulk Queueing System under N-Policy with Bilevel Service Delay Discipline and Start-up Time 25 5.4.1. Analysis of the Model 26 5.5. The Interrelationship between N-policy M/G/1/K and F-policy G/M/1/K Queues with Startup Time 28 5.5.1. N-policy M/G/1/K Queueing System with Exponential Startup Time 29 5.5.2. F-policy G/E/1/K Queueing System with Exponential Startup Time 37 5.6. A Transient M/M/1 Queue under (M, N)-Policy, Lattice Path Method 42 5.6.1. The Solution in Discrete Time 43 5.6.2. The Solution in Continuos Time 49 5.7. The Stationary M/M/1 Queueing Process with Delayed-Feedback 1 5.7.1. Distribution of the Queue Length 2 5.7.2. Mean Queue Length and Waiting Time 6 5.8. A Single-server Queue with Unreliable Server and Breakdowns with an Optional Second Service 17 5.9. A Bulk Arrival Retrial Queue with Unreliable Server 1 5.9.1. The Model 2 5.9.2. The Model Analysis 4 5.9.3. The Steady-State System Analysis 9 5.9.4. Performance Measures 17 5.9.5. Numerical Illustration 21 5.10. A Multi-Server Queue with Retrial Feedback Queueing System with two Orbits 25 5.11. Steady-state Stability Condition of a Retrial Queueing System with two Orbits, Reneging and Feedback 30 5.11.1. Necessary Stability Condition for the Steady-State System 31 5.12. A Batch Arrival Queue with General Service in Two Fluctuating Modes and Reneging during Vacation and Breakdowns 35 5.12.1. The Model 35 5.12.2. Analysis 38 Exercises 35 6 Networks of Queues with Delay 1 6.1. Introduction of Networks of Queues 1 6.2. Historical Notes on Networks of Queues 4 6.3. Jackson’s Network of Queues 5 6.3.1. Jackson’s Model 6 6.4. Robustness of Networks of Queues 33 6.5. A MAP Single-server Queueing System with Delayed Feedback as a Network of Queues 1 6.5.1. Description of the Model 3 6.5.2. The Service-Station 6 6.5.2.a. Number of Tasks in the Service-Station 6 6.52.b. Busy Period of the Service-Station 8 6.5.2.c. Number of Busy Periods 12 6.5.2.d. Computation of Takács’s Renewal Equation (5.5.35), Mean Number of Busy Periods 16 6.5.3. Stepwise Explicit Joint Distribution of the Number of Tasks in the System: General Case when batch sizes vary between a minimum k and a maximum K 19 6.6. Unreliable Networks of Queueing System Models 1 6.6.1. Unreliable Network Model of Goodman and Massey 1 6.6.2. Unreliable Network of Queues Model of Mylosz and Daduna 5 6.6.3. Unreliable Network of Queues Model of Gautam Choudhury, Jau-Chuan Ke and Lotfi Tadj: A Queueing System with two Network Phases of Services, Unreliable Server, Repair-time Delay under N-policy 13 6.7. Assessment of Reliability of a Network of Queues 29 6.8. Effect of Network Service Breakdown 32 6.8.1. The Model (CoginfoCom system) 33 6.8.2. Analysis 5 6.8.3. Numerical Example 37 Exercises 42 References 1 Index 1
• Edition: 1st
• Publisher Details: Wiley
• Publication Date: 2016
• Extent: 1 online resource (416 pages)
• Subjects: 519.82
• Languages: English
• ISBNs: 9781119022152
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.