Analytical and Stochastic Modelling Techniques and Applications: 25th International Conference, ASMTA 2019, Moscow, Russia, October 21–25, 2019, Proceedings ... Notes in Computer Science Book 12023)

This book constitutes the refereed proceedings of the 25th International Conference on Analytical and Stochastic Modelling Techniques and Applications, ASMTA 2019, held in Moscow, Russia, in October 2019. Methods of analytical and stochastic modelling are widely used in engineering to assess and design various complex systems, like computer and communication networks, and manufacturing systems. The 13 full papers presented in this book were carefully reviewed and selected from 22 submissions. The papers detail a diverse range of analysis techniques, including Markov processes, queueing theoretical results, reliability of stochastic systems, stochastic network calculus, and wide variety of applications. Preface 6 Organization 7 Contents 9 Algorithmic Analysis of a Two-Class Multi-server Heterogeneous Queueing System with a Controllable Cross-connectivity 11 1 Introduction 12 2 Mathematical Model 13 3 MBD Formulation 14 4 Mean Performance Measures 19 5 Maximal Queue Length in a Busy Period 24 6 Conclusion 26 References 26 Queueing Analysis of Cognitive Radio Networks with Finite Number of Secondary Users 28 1 Introduction 28 2 Model Description and Balance Equations 30 3 Stationary System State Distribution 31 3.1 Joint Distribution of the Server State and the Orbit Size 31 3.2 Main Macro-characteristics of the System Performance 35 4 Comparison with the Model with Poisson Input Flow of SUs 39 5 Concluding Remarks 40 References 41 On Reliability of a Double Redundant Renewable System 43 1 Introduction 43 2 The Problem Set. Assumptions and Notations 44 3 Reliability Function 46 4 System Steady State Probabilities 48 5 Investigation of the System Behavior on a Separate Regeneration Period 49 6 Conclusion 50 References 50 Queueing Analysis for a Mixed Model of Carsharing and Ridesharing 52 1 Introduction 52 2 The CRS System 53 2.1 Premise 53 2.2 Station Demand 54 2.3 Movement from the University to the Station 54 2.4 Takeover of the Car at the Station and Car Return 55 3 Modelling 55 3.1 Parameters Used in the Model 55 3.2 Markov Chain and Stability Condition 55 3.3 Performance Measures 58 4 Numerical Examples 59 4.1 Mean Waiting Time for Customers 59 4.2 Capacity of a Bus 61 4.3 Minimum Number of Passengers of a Car 62 4.4 Maximum Number of Passengers of a Car 64 5 Conclusion 65 References 65 An All Geometric Discrete-Time Multiserver Queueing System 67 1 Introduction 67 2 Mathematical Model 68 3 Analysis of System Content 70 4 Delay Analysis 72 4.1 Delay of a Customer with k Customers Ahead 73 4.2 Delay of an Arbitrary Customer 75 4.3 Tail Approximation 76 5 Numerical Examples 76 6 Conclusion 79 References 80 Dealing with Dependence in Stochastic Network Calculus – Using Independence as a Bound 81 1 Introduction 81 2 Definitions and Modeling Assumptions 82 2.1 SNC Background and Notation 82 2.2 Negative Dependence and Acceptable Random Variables 84 3 Independence as a Bound 85 3.1 Diamond Network 85 3.2 The L 87 4 Numerical Evaluation 89 4.1 Quality of the Bounds 89 4.2 Computation Run Time 89 5 Discussion 90 A Appendix 90 A.1 Diamond Network 90 A.2 The L 92 References 93 Map-Reduce Process Algebra: A Formalism to Describe Directed Acyclic Graph Task-Based Jobs in Parallel Environments 95 1 Introduction 95 1.1 Big Data Applications Performance Prediction 96 1.2 Map-Reduce Process Algebra (MRPA) 96 1.3 Originality of the Contribution 97 2 The Four Pillars of the Approach 97 2.1 Apache Spark 97 2.2 Process Algebra 98 2.3 PEPA 99 2.4 The Fork-Join Paradigm 100 3 The Map-Reduce Process Algebra (MRPA) Formalism 100 3.1 DAG Examples 101 3.2 Solution with the dagSim Simulator 104 4 Experiments 105 5 Related Work 107 6 Conclusions 108 References 108 Performance Evaluation of Scheduling Policies for the DRCMPSP 110 1 Introduction 110 2 Methodology 112 2.1 The Problem Setting 112 2.2 Decision State 113 2.3 Action Representation 114 2.4 Transition Function 115 2.5 Profit Representation 116 2.6 Goal Function 116 2.7 Solution by Dynamic Programming 117 3 Results and Comparisons 117 3.1 Genetic Algorithm 118 3.2 Priority Rule (Longest Task First) 118 3.3 Worst Decision Algorithm 119 4 Computational Results 119 4.1 Experimental Setup 119 4.2 Discussion 121 5 Conclusion 122 References 122 An Algorithm for Improved Proportional-Fair Utility for Vehicular Users 125 1 Introduction 125 1.1 Contributions 127 1.2 Organisation 127 2 Problem Formulation 127 2.1 PF-EXP 129 2.2 Predictive Finite-Horizon PF Scheduling ((PF)2S) 129 3 Projected Gradient Approach 130 3.1 Projected Gradient Short Term Objective Algorithm (STO1) 131 3.2 Projected Gradient Short Term Objective Algorithm 2 (STO2) 132 4 Numerical Results 133 4.1 Homogeneous Vehicle Velocities 133 4.2 Comparison with the Upper Bound 134 4.3 Heterogeneous Vehicle Velocities 135 5 Future Work 136 A Projection on Feasible Set D 137 B Modeling as an Optimal Control Problem 137 C Proofs 138 References 139 Method of Asymptotic Diffusion Analysis of Queueing System M|M|N with Feedback 141 1 Introduction 141 2 Statement of the Problem and Mathematical Model 142 3 Kolmogorov Differential Equations 142 4 Asymptotic Diffusion Analysis Method 144 5 Conclusion 152 References 152 Exact Performance Analysis of Retrial Queues with Collisions 154 1 Introduction 154 2 Model 155 3 Analysis 156 4 Extension to Models with Abandonment 162 5 Numerical Results 164 6 Conclusion 166 References 167 Infinite-Server Bulk Queue with MMPP Arrivals 168 1 Introduction 168 2 Mathematical Model 169 3 Dynamic Screening Method 170 4 Asymptotic Analysis 173 5 Simulation and Numerical Examples 178 6 Conclusion 179 References 179 Dissipativity of the Quantum Measurement Model 181 1 Introduction 181 2 Basic Quantum Equations 182 2.1 Markovian Quantum Master Equation 182 2.2 Adjoint Quantum Master Equation 185 3 Kuryshkin-Wodkiewicz Quantum Measurement Model 185 4 Conclusion 189 References 194 Author Index 196 Front Matter ....Pages i-x Algorithmic Analysis of a Two-Class Multi-server Heterogeneous Queueing System with a Controllable Cross-connectivity (Dmitry Efrosinin, Irina Kochetkova, Konstantin Samouylov, Natalia Stepanova)....Pages 1-17 Queueing Analysis of Cognitive Radio Networks with Finite Number of Secondary Users (Velika Dragieva, Tuan Phung-Duc)....Pages 18-32 On Reliability of a Double Redundant Renewable System (Vladimir Rykov)....Pages 33-41 Queueing Analysis for a Mixed Model of Carsharing and Ridesharing (Ayane Nakamura, Tuan Phung-Duc, Hiroyasu Ando)....Pages 42-56 An All Geometric Discrete-Time Multiserver Queueing System (Freek Verdonck, Herwig Bruneel, Sabine Wittevrongel)....Pages 57-70 Dealing with Dependence in Stochastic Network Calculus – Using Independence as a Bound (Paul Nikolaus, Jens Schmitt, Florin Ciucu)....Pages 71-84 Map-Reduce Process Algebra: A Formalism to Describe Directed Acyclic Graph Task-Based Jobs in Parallel Environments (Enrico Barbierato, Marco Gribaudo, Mauro Iacono)....Pages 85-99 Performance Evaluation of Scheduling Policies for the DRCMPSP (Ugur Satic, Peter Jacko, Christopher Kirkbride)....Pages 100-114 An Algorithm for Improved Proportional-Fair Utility for Vehicular Users (Thi Thuy Nga Nguyen, Olivier Brun, Balakrishna J. Prabhu)....Pages 115-130 Method of Asymptotic Diffusion Analysis of Queueing System M|M|N with Feedback (Anatoly Nazarov, Svetlana Paul, Ekaterina Pavlova)....Pages 131-143 Exact Performance Analysis of Retrial Queues with Collisions (Tuan Phung-Duc, Dieter Fiems)....Pages 144-157 Infinite-Server Bulk Queue with MMPP Arrivals (Anna Boyarkina, Svetlana Moiseeva, Michele Pagano, Ekaterina Lisovskaya, Alexander Moiseev)....Pages 158-170 Dissipativity of the Quantum Measurement Model (Alexander V. Zorin, Leonid A. Sevastianov, Nikolay P. Tretyakov)....Pages 171-185 Back Matter ....Pages 187-187 Algorithmic Analysis of a Two-Class Multi-Server HeterogeneousQueueing System with a Controllable Cross-Connectivity -- Queueing Analysis of Cognitive Radio Networks with Finite Number ofSecondary Users -- On Reliability of a Double Redundant Renewable System -- Queueing Analysis for a Mixed Model of Carsharing and Ridesharing -- An All Geometric Discrete-Time Multiserver Queueing System -- Dealing with Dependence in Stochastic Network Calculus { UsingIndependence as a Bound -- Map-Reduce Process Algebra: a Formalism to Describe Directed -- Acyclic Graph Task-Based Jobs in Parallel Environments -- Performance Evaluation of Scheduling Policies for the DRCMPSP -- An Algorithm for Improved Proportional-Fair Utility for Vehicular Users -- Method of Asymptotic Di usion Analysis of Queueing System MjMjNwith feedback -- Exact Performance Analysis of Retrial Queues with Collisions -- In nite-Server Bulk Queue with MMPP Arrivals -- Dissipativity Of The Quantum Measurement Model