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Applied probability and stochastic processes
Joshua V., Varadhan S., Vishnevsky V., Springer International Publishing, New York, NY, 2020. 521 pp. Type: Book (978-9-811559-50-1)
Date Reviewed: May 16 2023

Natural phenomena are very complicated, and statistical analysis, which is categorized in the stochastic conceptual framework, is an effective tool to formulate, estimate, and predicate their nature, behaviors, and functionalities. Stochastic processes are useful models that are used to imitate the natural and artificial creatures of life. The book offers 30 chosen papers from the 2019 International Conference on Advances in Applied Probability and Stochastic Processes. Thematically it can be divided into three groups: queueing theory, production inventory systems, and other subjects.

The first group encompasses versatile topics related to the Markovian arrival process (MAP) and retrial queueing (Orbit). Included is a technical report about different arrival process methods for evaluating some remarkable topics: the busy periods of servers; an analysis of queue-length distribution at post-vacation termination; post-service completion in a single-server finite-buffer system; a focus on the steady state of a queueing system; single-server finite-buffer length influenced by negative customers: remove the customer at the head (RCH), remove the customer at the end (RCE), or disaster (all customers are removed); an investigation into the asymptotic behavior of single-server systems under heavy loads and long delay limit conditions using the matrix method; steady state featuring a mixed queueing and inventory system where the servers have different duties and service speeds; the stability of a two-stage tandem queueing system; performance analysis of a queueing system; an investigation into the number of customers in high- and low-priority finite queueing systems with a re-sequencing mechanism; and an examination of performant tradeoff between idle time and setup time, while waiting time, mean queue length, and power consumption are the pivotal criteria for numerous servers in data centers.

The second group looks at a continuous review inventory system, a finite capacity production inventory system, and the deterioration rate in an inventory control model.

The third group of papers covers a diversity of subjects. Based on the maximality results of locally compact, second-countable Hausdorff topological groups, one paper discusses the existence of shift coupling. Two papers look at wireless multi-hop networks: one of them investigates the performance characteristics of a linear topology network with a relay or distributed coordination function (DCF) channel, and the other provides a link scheduling algorithm for sustainable quality of service and system coverage with different resource requirements. Standard Brownian motion is briefly discussed in another paper. Using a probabilistic approach, a transient solution for the amount of charge in a finite capacity rechargeable battery is discussed. One paper exposes the characteristics of risk-sensitive costs and rewards for a Collatz-Wielandt formula; it derives dynamic programming equations for a risk-sensitive reward process and provides a controlled version of Donsker-Varadhan formulae. Another paper introduce a new probability distribution to model non-monotonic behavior in real-life phenomena. These are just some of the topics covered.

While the third group’s papers are only loosely linked with the conference subject, most are well-developed works. Unfortunately, a majority of the first and second group’s papers haven’t been fully developed, and for some of them, the relevance of their content with their title is unclear. Due to a lack of novelty and significance, as well as a failure to look at ethical principles, it is hard to recommend this book.

Reviewer:  Mohammad Sadegh Kayhani Pirdehi Review #: CR147590 (2307-0086)
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