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Modeling and dimensioning of mobile wireless networks
ID: 55195
Piotr Zwierzykowski, Mariusz Głąbowski, Maciej Stasiak
The presented book is the first in Poland such a comprehensive study on traffic engineering and dimensioning of wireless networks. The book discusses both the basic issues, ie introduction to the theory of motion and single-channel systems with traffic overflow, as well as more advanced issues, i.e. models of systems with integrated traffic and queuing models. The book also contains algorithms that enable practical dimensioning and optimization of selected interfaces in 2 / 3G mobile phone networks.
Recipients: researchers, scientists, engineers and students interested in designing and modeling UMTS networks, as well as a wide range of customers interested in 2 and 3 generation mobile networks.
Table of Contents:
From the authors of X
1. Introduction 1
2. Basic definitions and terminology 3
2.1. Introduction 3
2.2. Report stream 3
2.2.1. Poisson stream and its properties 3
2.2.2. Parameters of the Poisson stream description 4
2.3. Service stream 7
2.3.1. Definition 7
2.3.2. Parameters describing the service stream 7
2.4. Markov processes 9
2.4.1. Stochastic processes 9
2.4.2. Markov Process as a process of handling requests in a full-access bundle
2.5. The concept of movement 15
2.5.1. Introductory information 15
2.5.2. Traffic and traffic 15
2.5.3. Definitions of average traffic volume 16
2.5.4. Definition of the average traffic offered 18
2.6. Service quality in telecommunications systems 18
2.6.1. Basic GoS parameters in systems with losses 19
2.6.2. Load and load capacity of systems 20
3. Basic elements of traffic engineering in mobile networks 21
3.1. Introduction 21
3.2. The Erlang 21 model
3.2.1. Assumptions of the 21 model
3.2.2. Diagram of the service process 21
3.2.3. Equations of state 22
3.2.4. The probability of occupancy of any and the channels in the beam - Erlang's schedule 22
3.2.5. Lockout probability - Erlang 23 pattern
3.2.6. Loss probability 23
3.2.7. Probability of occupancy x strictly defined channels in the beam - Palma-Jacobaeus pattern 23
3.2.8. Erlang boards 24
3.2.9. The right of the beam 24
3.2.10. Recursive properties of the Erlang pattern 25
3.2.11. Movement dealt by a full-access beam 25
3.2.12. The movement is handled by one full-access beam channel 26
3.3. The Engseta 26 model
3.3.1. Assumptions of the 26 model
3.3.2. Diagram of the service process 27
3.3.3. Equations of state 27
3.3.4. Probability of occupancy of any and the channels in the beam - Engseta's schedule 27
3.3.5. Lockout probability 28
3.3.6. Loss probability 28
3.3.7. An alternative record of the Engseta pattern 29
3.3.8. The relationship of the distributions of Erlang and Engseta 29
3.3.9. Probability of occupancy x strictly defined beam channels 30
3.3.10. Traffic intensity 30
3.3.11. Recursive properties of the Engseta 30 pattern
3.3.12. Comment on averaged traffic values 31
4. Modeling of systems with a traffic transfer 33
4.1. Introduction 33
4.2. Basic information about overflow systems 33
4.2.1. Simplified classification of beams in telecommunications networks 33
4.2.2. Alternative roads 33
4.2.3. Overflow traffic 34
4.3. Models of alternative bundles 35
4.3.1. Analytical model of the system with traffic transfer 36
4.3.2. Equations of state 36
4.3.3. Determination of overflow traffic parameters - Riordan 37 designs
4.4. Equivalent beams 40
4.4.1. Equivalent replacement method (ERT method) 40
4.4.2. Notes on the ERT 41 method
4.4.3. Chapter of the ear 42
4.4.4. The Fredericks-Hayward Method 43
5. Models of bundles links with the integrated movement 44
5.1. Introduction 44
5.2. Multidimensional distribution of Erlang 44
5.2.1. Assumptions of the multidimensional Erlang 45 model
5.2.2. Process diagram at the level of microstates 45
5.2.3. Reversibility of the multidimensional Erlang process 45
5.2.4. Multidimensional distribution of Erlang at the level of microstates - the multiplicative form of the record of the multidimensional distribution of Erlang 47
5.2.5. Probability of macrostan 48
5.2.6. Interpretation of distribution at the level of microstates 48
5.2.7. Likelihood of blockage and losses in the multidimensional distribution of Erlang 48
5.2.8. A recursive record of the multidimensional distribution of Erlang 49
5.2.9. Service streams at the macro level level 49
5.3. Perfect beam with integrated movement 50
5.3.1. Assumptions of the 50 model
5.3.2. Process diagram at the microstane level 50
5.3.3. Reversibility of the process at the level of microstates 51
5.3.4. Probability of macrostate 51
5.3.5. Recursive record of the distribution of occupancy of the perfect beam with the integrated movement - Kaufman-Roberts equation (RKR distribution) 52
5.3.6. Likelihood of blockage and loss probability 53
5.3.7. Recursive properties of the RKR 53 distribution
5.3.8. Delbrouck equations 54
5.3.9. Service streams in a full-field beam with an integrated movement 55
5.3.10. Parallel algorithm 56
5.4. Systems dependent on state 58
5.4.1. General assumptions of the system dependent on state 58
5.4.2. Diagram of process dependent on states at the level of microstates 58
5.4.3. Reversibility of multivariate process dependent on state 59
5.4.4. Approximation of the process dependent on the state of the reversible process 60
5.4.5. Generalized Kaufman-Roberts formula (URKR timetable) 61
5.4.6. Lockout probability 62
5.4.7. Interpretation of URKR distribution 62
5.5. Beam with limited availability 62
5.5.1. Assumptions of the model 63
5.5.2. Locations of free basic band units 63
5.5.3. Conditional probabilities of takeover 64
5.5.4. Distribution of occupancy in the beam (distribution of RWODs) 65
5.6. Generalized beam model with limited availability 5
5.6.1. Assumptions of the 65 model
5.6.2. Busy schedule 66
5.6.3. Conditional probability of acquisition 67
5.6.4. Likelihood of blockage and loss probability 67
5.7. Perfect beam with booking 67
5.7.1. Static reservation 68
5.7.2. Dynamic booking 69
5.7.3. The principle of compensating losses 69
5.7.4. Distribution of occupancy in the beam (RD / R distribution) 70
5.7.5. Comment regarding the RWD / R distribution 70
5.7.6. Modified beam model (ZRWD / R distribution) 71
5.8. Systems with finite and infinite number of traffic sources 74
5.8.1. The assumptions of the multiservice Erlang-Engseta 74 model
5.8.2. Comment on modeling systems with integrated traffic type PCT1 and PCT2 75
5.8.3. The concept of the multiservice model of the Erlang-Engseta distribution
5.8.4. Calculation algorithm 76
5.9. Full threshold systems 78
5.9.1. One-threshold models STM 78
5.9.2. MTM 81 multi-way models
6. Modeling of systems with integrated traffic and traffic transfer 86
6.1. Introduction 86
6.2. One-service model Kaufman-Roberts for perfect beam with overflow 86
6.2.1. Assumptions of the 87 model
6.2.2. Parameters of downward travel 87
6.2.3. Distribution of occupancy and the probability of blocking in an alternative bundle 88
6.3. Determining the collective factor Z 89
6.4. Dimensioning of alternative bundles with integrated traffic 89
6.5. The Kaufman-Roberts multiservice model for a perfect beam with an overflow movement 91
7. Models of packet transmission nodes 94
7.1. Introduction 94
7.2. Basic information about queuing systems 94
7.2.1. Parameters of the queuing system 94
7.2.2. Classification of queuing systems 94
7.2.3. Kendall's 95th notation
7.3. Little's principle 96
7.4. Model M / M / 1 system with one service station and unlimited queue 98
7.4.1. Assumptions of the 98 model
7.4.2. Diagram of the service process 99
7.4.3. State equations 99
7.4.4. System characteristics 100
7.5. System model M / M / 1 / N with one service station and limited queue 103
7.5.1. Assumptions of the 103 model
7.5.2. Diagram of the service process 103
7.5.3. Equations of state 104
7.5.4. System characteristics 104
7.6. System model M / M / m with m service stations and unlimited queue 105
7.6.1. Assumptions of the 105 model
7.6.2. Diagram of the service process 105
7.6.3. Equations of state 106
7.6.4. System characteristics 107
7.7. System model M / M / m / n with limited queue and limited number of service stations 107
7.7.1. Model assumptions 107
7.7.2. System characteristics M / M / m / n 108
7.8. Model M / G / 1 system with one service station and unlimited queue 108
7.8.1. The Pollaczka-Chinczyna 110 pattern
7.8.2. System characteristics 113
7.9. System M / D / 1 114
7.10. Queuing systems with one position and priorities 115
7.11.Model M / G / R PS 118
7.11.1. Model assumptions 118
7.11.2. System characteristics 119
7.12. Comment on self-similar movement 120
8. Modeling and dimensioning of the cellular radio interface 123
8.1. Modeling of resource allocation in the radio interface of cellular systems 123
8.1.1. Hard and soft capacity of the cellular system 13
8.1.2. Allocation of resources in cellular systems with hard capacity 123
8.1.3. Allocation of resources in cellular systems with a soft capacity of 124
8.2 Modeling of the radio interface of cellular systems with one-service traffic 129
8.2.1. The Erlang model for a single cell 129
8.2.2. Engset model for a single cell 131
8.2.3. The intercellular transfer model 133
8.2.4. Intracellular transfer model 135
8.2.5. A simplified model of the cellular network 137
8.3. Modeling of the UMTS cellular radio interface with integrated traffic 139
8.3.1. Cell model with PCT1 integrated traffic 139
8.3.2. Cell model with integrated motion type PCT2 141
8.3.3. Cell model with integrated motion type PCT1 and PCT2 143
8.3.4. A model of a set of cells with an integrated movement type PCT1 and PCT2 147
8.3.5. Cell model with integrated motion type PCT1 and PCT2 155
8.3.6. The intercellular transfer model in a system with integrated motion
PCT1 and PCT2 types 163
8.3.7. Modeling systems with connection transfer 168
8.3.8. Dimensioning of the UMTS HSDPA / HSUPA 173 system
8.4. List of methods for modeling and dimensioning the radio interface 177
9. Modeling and dimensioning of the Iub 181 interface
9.1. Introduction 181
9.2. Equivalent band 181
9.2.1. Equivalent band concept 182
9.2.2. Methods of determining the equivalent band 182
9.2.3. Comment 186
9.3. Iub 187 interface dimensioning algorithm
List of drawings 189
List of tables 191
Bibliography 192
Index 199
Recipients: researchers, scientists, engineers and students interested in designing and modeling UMTS networks, as well as a wide range of customers interested in 2 and 3 generation mobile networks.
Table of Contents:
From the authors of X
1. Introduction 1
2. Basic definitions and terminology 3
2.1. Introduction 3
2.2. Report stream 3
2.2.1. Poisson stream and its properties 3
2.2.2. Parameters of the Poisson stream description 4
2.3. Service stream 7
2.3.1. Definition 7
2.3.2. Parameters describing the service stream 7
2.4. Markov processes 9
2.4.1. Stochastic processes 9
2.4.2. Markov Process as a process of handling requests in a full-access bundle
2.5. The concept of movement 15
2.5.1. Introductory information 15
2.5.2. Traffic and traffic 15
2.5.3. Definitions of average traffic volume 16
2.5.4. Definition of the average traffic offered 18
2.6. Service quality in telecommunications systems 18
2.6.1. Basic GoS parameters in systems with losses 19
2.6.2. Load and load capacity of systems 20
3. Basic elements of traffic engineering in mobile networks 21
3.1. Introduction 21
3.2. The Erlang 21 model
3.2.1. Assumptions of the 21 model
3.2.2. Diagram of the service process 21
3.2.3. Equations of state 22
3.2.4. The probability of occupancy of any and the channels in the beam - Erlang's schedule 22
3.2.5. Lockout probability - Erlang 23 pattern
3.2.6. Loss probability 23
3.2.7. Probability of occupancy x strictly defined channels in the beam - Palma-Jacobaeus pattern 23
3.2.8. Erlang boards 24
3.2.9. The right of the beam 24
3.2.10. Recursive properties of the Erlang pattern 25
3.2.11. Movement dealt by a full-access beam 25
3.2.12. The movement is handled by one full-access beam channel 26
3.3. The Engseta 26 model
3.3.1. Assumptions of the 26 model
3.3.2. Diagram of the service process 27
3.3.3. Equations of state 27
3.3.4. Probability of occupancy of any and the channels in the beam - Engseta's schedule 27
3.3.5. Lockout probability 28
3.3.6. Loss probability 28
3.3.7. An alternative record of the Engseta pattern 29
3.3.8. The relationship of the distributions of Erlang and Engseta 29
3.3.9. Probability of occupancy x strictly defined beam channels 30
3.3.10. Traffic intensity 30
3.3.11. Recursive properties of the Engseta 30 pattern
3.3.12. Comment on averaged traffic values 31
4. Modeling of systems with a traffic transfer 33
4.1. Introduction 33
4.2. Basic information about overflow systems 33
4.2.1. Simplified classification of beams in telecommunications networks 33
4.2.2. Alternative roads 33
4.2.3. Overflow traffic 34
4.3. Models of alternative bundles 35
4.3.1. Analytical model of the system with traffic transfer 36
4.3.2. Equations of state 36
4.3.3. Determination of overflow traffic parameters - Riordan 37 designs
4.4. Equivalent beams 40
4.4.1. Equivalent replacement method (ERT method) 40
4.4.2. Notes on the ERT 41 method
4.4.3. Chapter of the ear 42
4.4.4. The Fredericks-Hayward Method 43
5. Models of bundles links with the integrated movement 44
5.1. Introduction 44
5.2. Multidimensional distribution of Erlang 44
5.2.1. Assumptions of the multidimensional Erlang 45 model
5.2.2. Process diagram at the level of microstates 45
5.2.3. Reversibility of the multidimensional Erlang process 45
5.2.4. Multidimensional distribution of Erlang at the level of microstates - the multiplicative form of the record of the multidimensional distribution of Erlang 47
5.2.5. Probability of macrostan 48
5.2.6. Interpretation of distribution at the level of microstates 48
5.2.7. Likelihood of blockage and losses in the multidimensional distribution of Erlang 48
5.2.8. A recursive record of the multidimensional distribution of Erlang 49
5.2.9. Service streams at the macro level level 49
5.3. Perfect beam with integrated movement 50
5.3.1. Assumptions of the 50 model
5.3.2. Process diagram at the microstane level 50
5.3.3. Reversibility of the process at the level of microstates 51
5.3.4. Probability of macrostate 51
5.3.5. Recursive record of the distribution of occupancy of the perfect beam with the integrated movement - Kaufman-Roberts equation (RKR distribution) 52
5.3.6. Likelihood of blockage and loss probability 53
5.3.7. Recursive properties of the RKR 53 distribution
5.3.8. Delbrouck equations 54
5.3.9. Service streams in a full-field beam with an integrated movement 55
5.3.10. Parallel algorithm 56
5.4. Systems dependent on state 58
5.4.1. General assumptions of the system dependent on state 58
5.4.2. Diagram of process dependent on states at the level of microstates 58
5.4.3. Reversibility of multivariate process dependent on state 59
5.4.4. Approximation of the process dependent on the state of the reversible process 60
5.4.5. Generalized Kaufman-Roberts formula (URKR timetable) 61
5.4.6. Lockout probability 62
5.4.7. Interpretation of URKR distribution 62
5.5. Beam with limited availability 62
5.5.1. Assumptions of the model 63
5.5.2. Locations of free basic band units 63
5.5.3. Conditional probabilities of takeover 64
5.5.4. Distribution of occupancy in the beam (distribution of RWODs) 65
5.6. Generalized beam model with limited availability 5
5.6.1. Assumptions of the 65 model
5.6.2. Busy schedule 66
5.6.3. Conditional probability of acquisition 67
5.6.4. Likelihood of blockage and loss probability 67
5.7. Perfect beam with booking 67
5.7.1. Static reservation 68
5.7.2. Dynamic booking 69
5.7.3. The principle of compensating losses 69
5.7.4. Distribution of occupancy in the beam (RD / R distribution) 70
5.7.5. Comment regarding the RWD / R distribution 70
5.7.6. Modified beam model (ZRWD / R distribution) 71
5.8. Systems with finite and infinite number of traffic sources 74
5.8.1. The assumptions of the multiservice Erlang-Engseta 74 model
5.8.2. Comment on modeling systems with integrated traffic type PCT1 and PCT2 75
5.8.3. The concept of the multiservice model of the Erlang-Engseta distribution
5.8.4. Calculation algorithm 76
5.9. Full threshold systems 78
5.9.1. One-threshold models STM 78
5.9.2. MTM 81 multi-way models
6. Modeling of systems with integrated traffic and traffic transfer 86
6.1. Introduction 86
6.2. One-service model Kaufman-Roberts for perfect beam with overflow 86
6.2.1. Assumptions of the 87 model
6.2.2. Parameters of downward travel 87
6.2.3. Distribution of occupancy and the probability of blocking in an alternative bundle 88
6.3. Determining the collective factor Z 89
6.4. Dimensioning of alternative bundles with integrated traffic 89
6.5. The Kaufman-Roberts multiservice model for a perfect beam with an overflow movement 91
7. Models of packet transmission nodes 94
7.1. Introduction 94
7.2. Basic information about queuing systems 94
7.2.1. Parameters of the queuing system 94
7.2.2. Classification of queuing systems 94
7.2.3. Kendall's 95th notation
7.3. Little's principle 96
7.4. Model M / M / 1 system with one service station and unlimited queue 98
7.4.1. Assumptions of the 98 model
7.4.2. Diagram of the service process 99
7.4.3. State equations 99
7.4.4. System characteristics 100
7.5. System model M / M / 1 / N with one service station and limited queue 103
7.5.1. Assumptions of the 103 model
7.5.2. Diagram of the service process 103
7.5.3. Equations of state 104
7.5.4. System characteristics 104
7.6. System model M / M / m with m service stations and unlimited queue 105
7.6.1. Assumptions of the 105 model
7.6.2. Diagram of the service process 105
7.6.3. Equations of state 106
7.6.4. System characteristics 107
7.7. System model M / M / m / n with limited queue and limited number of service stations 107
7.7.1. Model assumptions 107
7.7.2. System characteristics M / M / m / n 108
7.8. Model M / G / 1 system with one service station and unlimited queue 108
7.8.1. The Pollaczka-Chinczyna 110 pattern
7.8.2. System characteristics 113
7.9. System M / D / 1 114
7.10. Queuing systems with one position and priorities 115
7.11.Model M / G / R PS 118
7.11.1. Model assumptions 118
7.11.2. System characteristics 119
7.12. Comment on self-similar movement 120
8. Modeling and dimensioning of the cellular radio interface 123
8.1. Modeling of resource allocation in the radio interface of cellular systems 123
8.1.1. Hard and soft capacity of the cellular system 13
8.1.2. Allocation of resources in cellular systems with hard capacity 123
8.1.3. Allocation of resources in cellular systems with a soft capacity of 124
8.2 Modeling of the radio interface of cellular systems with one-service traffic 129
8.2.1. The Erlang model for a single cell 129
8.2.2. Engset model for a single cell 131
8.2.3. The intercellular transfer model 133
8.2.4. Intracellular transfer model 135
8.2.5. A simplified model of the cellular network 137
8.3. Modeling of the UMTS cellular radio interface with integrated traffic 139
8.3.1. Cell model with PCT1 integrated traffic 139
8.3.2. Cell model with integrated motion type PCT2 141
8.3.3. Cell model with integrated motion type PCT1 and PCT2 143
8.3.4. A model of a set of cells with an integrated movement type PCT1 and PCT2 147
8.3.5. Cell model with integrated motion type PCT1 and PCT2 155
8.3.6. The intercellular transfer model in a system with integrated motion
PCT1 and PCT2 types 163
8.3.7. Modeling systems with connection transfer 168
8.3.8. Dimensioning of the UMTS HSDPA / HSUPA 173 system
8.4. List of methods for modeling and dimensioning the radio interface 177
9. Modeling and dimensioning of the Iub 181 interface
9.1. Introduction 181
9.2. Equivalent band 181
9.2.1. Equivalent band concept 182
9.2.2. Methods of determining the equivalent band 182
9.2.3. Comment 186
9.3. Iub 187 interface dimensioning algorithm
List of drawings 189
List of tables 191
Bibliography 192
Index 199
55195
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