Infosys Science Foundation Series Infosys Science Foundation Series in Mathematical Sciences Series Editors Irene Fonseca, Carnegie Mellon University, Pittsburgh, PA, USA Gopal Prasad, University of Michigan, Ann Arbor, USA Editorial Board Manindra Agrawal, Indian Institute of Technology Kanpur, Kanpur, India Weinan E, Princeton University, Princeton, USA Chandrashekhar Khare, University of California, Los Angeles, USA Mahan Mj, Tata Institute of Fundamental Research, Mumbai, India Ritabrata Munshi, Tata Institute of Fundamental Research, Mumbai, India S. R. S. Varadhan, New York University, New York, USA The Infosys Science Foundation Series in Mathematical Sciences is a sub-series of The Infosys Science Foundation Series. This sub-series focuses on high-quality content in the domain of mathematical sciences and various disciplines of math- ematics, statistics, bio-mathematics, financial mathematics, applied mathematics, operations research, applied statistics and computer science. All content published in the sub-series are written, edited, or vetted by the laureates or jury members of the Infosys Prize. With this series, Springer and the Infosys Science Foundation hope to provide readers with monographs, handbooks, professional books and textbooks of the highest academic quality on current topics in relevant disciplines. Literature in this sub-series will appeal to a wide audience of researchers, students, educators, and professionals across mathematics, applied mathematics, statistics and computer science disciplines. More information about this subseries at http://www.springer.com/series/13817 V. C. Joshua • S. R. S. Varadhan • Vladimir M. Vishnevsky Editors Applied Probability and Stochastic Processes Editors V. C. Joshua S. R. S. Varadhan Department of Mathematics Courant Institute of Mathematical Sciences CMS College New York University Kottayam, India New York, NY, USA Vladimir M. Vishnevsky Institute of Control Sciences Russian Academy of Sciences Moscow, Russia ISSN 2363-6149 ISSN 2363-6157 (electronic) Infosys Science Foundation Series ISSN 2364-4036 ISSN 2364-4044 (electronic) Infosys Science Foundation Series in Mathematical Sciences ISBN 978-981-15-5950-1 ISBN 978-981-15-5951-8 (eBook) https://doi.org/10.1007/978-981-15-5951-8 Mathematics Subject Classification: 60B10, 60J65, 60K20, 60K25, 60K30, 62H99, 68M18, 90B05, 90B15, 91B05 © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface This book is a collection of selected papers presented at the International Conference on Advances in Applied Probability and Stochastic Processes (ICAAP&SP@CMS 2019) held during 7–10 January 2019 at CMS College Kottayam, Kerala, India, in honour of Prof. Dr. A. Krishnamoorthy, Emeritus Professor and Former Head of Department of Mathematics, Cochin University of Science and Technology, Kerala, India. It is the first conference in the series of conferences decided to be conducted biannually, aiming to promote high-quality research in the field of applied probability that would keep pace with the advancements in science and technology. It focuses on applied probability techniques in modelling and analysis of systems evolving in time. Stochastic modelling plays a key role in analysing real-life situations such as queueing theory, reliability, inventory problems, biology, medicine, and finance. The conference was a great success, attracting 145 delegates from 14 countries. Professor S. R. S. Varadhan, FRS (Abel Laureate) delivered the keynote address. It had 9 plenary speakers and 26 invited speakers. It provided a platform to researchers, academicians, practitioners, industrialists, and so on from various countries, interested in the theory and applications of applied probability and stochastic processes to share their views, discuss prospective developments, and pursue collaborations in these areas. The conference had 104 papers for presentation. Out of 104 papers, 30 papers are selected for publication in a book form as Springer proceedings in accordance with the conducted peer reviews. These papers are revelations of strong theoretical as well as practical foundations of probabilistic modelling tools. Its target audience includes researchers and practitioners of probability theory, stochastic process, and mathematical modelling. v vi Preface We thank all the authors for the contributions, reviewers for peer- reviewing, members of the program committee for timely help, and sponsors for financial support. Kottayam, India V. C. Joshua New York, NY, USA S. R. S. Varadhan Moscow, Russia Vladimir M. Vishnevsky January 2020 Contents Shift-Coupling and Maximality ................................................ 1 Hermann Thorisson Diffusion Approximation Analysis of Multihop Wireless Networks: Quality-of-Service and Convergence of Stationary Distribution............ 15 K. S. Ashok Krishnan and Vinod Sharma Analysis of Retrial Queue with Heterogeneous Servers and Markovian Arrival Process ................................................ 29 Liu Mei and Alexander Dudin What is Standard Brownian Motion?.......................................... 51 Krishna B. Athreya Busy Period Analysis of Multi-Server Retrial Queueing Systems .......... 61 Srinivas R. Chakravarthy Steady-State and Transient Analysis of a Single Channel Cognitive Radio Model with Impatience and Balking ................................... 77 Alexander Rumyantsev and Garimella Rama Murthy Applications of Fluid Queues in Rechargeable Batteries .................... 91 Shruti Kapoor and S. Dharmaraja Analysis of BMAP/R/1 Queues Under Gated-Limited Service with the Server’s Single Vacation Policy....................................... 103 Souvik Ghosh, A. D. Banik, and M. L. Chaudhry A Production Inventory System with Renewal and Retrial Demands...... 129 G. Arivarignan, M. Keerthana, and B. Sivakumar A Queueing System with Batch Renewal Input and Negative Arrivals .... 143 U. C. Gupta, Nitin Kumar, and F. P. Barbhuiya vii viii Contents Asymptotic Analysis Methods for Multi-Server Retrial Queueing Systems ................................................................ 159 Ekaterina Fedorova, Anatoly Nazarov, and Alexander Moiseev On the Application of Dynamic Screening Method to Resource Queueing System with Infinite Servers ........................................ 179 Michele Pagano and Ekaterina Lisovskaya “Controlled” Versions of the Collatz–Wielandt and Donsker–Varadhan Formulae ............................................. 199 Aristotle Arapostathis and Vivek S. Borkar An (s, S) Production Inventory System with State Dependant Production Rate and Lost Sales ................................................ 215 S. Malini and Dhanya Shajin Analysis of a MAP Risk Model with Stochastic Incomes, Inter-Dependent Phase-Type Claims and a Constant Barrier .............. 235 A. S. Dibu and M. J. Jacob A PH Distributed Production Inventory Model with Different Modes of Service and MAP Arrivals ........................................... 263 Salini S. Nair and K. P. Jose On a Generalized Lifetime Model Using DUS Transformation ............. 281 P. Kavya and M. Manoharan Analysis of Inventory Control Model for Items Having General Deterioration Rate ............................................................... 293 V. P. Praveen and M. Manoharan A Two-Server Queueing System with Processing of Service Items by a Server ........................................................................ 307 A. Krishnamoorthy and Divya V. A Two-Stage Tandem Queue with Specialist Servers ........................ 335 T. S. Sinu Lal, A. Krishnamoorthy, V. C. Joshua, and Vladimir Vishnevsky The MAP/(PH,PH,PH)/1 Model with Self-Generation of Priorities, Customer Induced Interruption and Retrial of Customers ................. 355 Jomy Punalal and S. Babu Valuation of Reverse Mortgage ................................................ 371 D. Kannan and Lina Ma Stationary Distribution of Discrete-Time Finite-Capacity Queue with Re-sequencing .............................................................. 399 Rostislav Razumchik