Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

https://cyberleninka.org/article/n/662470.pdf

Literature review of deteriorating inventory models by key topics from 2012 to 2015

Cloud computing is a recent trend in IT, which has attracted lots of attention. In cloud computing, service reliability and service performance are two important issues. To improve cloud service reliability, fault tolerance techniques such as fault recovery may be used, which in turn has impact on cloud service performance. Such impact deserves detailed research. Although there exist some researches on cloud/grid service reliability and performance, very few of them addressed the issues of fault recovery and its impact on service performance. In this paper, we conduct detailed research on performance evaluation of cloud service considering fault recovery. We consider recovery on both processing nodes and communication links. The commonly adopted assumption of Poisson arrivals of users' service requests is relaxed, and the interarrival times of service requests can take arbitrary probability distribution. The precedence constraints of subtasks are also considered. The probability distribution of service response time is derived, and a numerical example is presented. The proposed cloud performance evaluation models and methods could yield results which are realistic, and thus are of practical value for related decision-makings in cloud computing.

Performance evaluation of cloud service considering fault recovery

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Optimization In Operations Research

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.

Discrete-time GI/Geo/1 queue with multiple working vacations

In this paper, we analyse a multi-server queue with bulk arrivals and finite-buffer space. The interarrival and service times are arbitrarily and exponentially distributed, respectively. The model is discussed with partial and total batch rejections and the distributions of the numbers of customers in the system at prearrival and arbitrary epochs are obtained. In addition, blocking probabilities and waiting time analyses of the first, an arbitrary and the last customer of a batch are discussed. Finally, some numerical results are presented.

Analysis of finite-buffer multi-server queues with group arrivals: GI X /M/c/N

The Markovian arrival process (MAP) is used to represent the bursty and correlated traffic arising in modern telecommunication network. In this paper, we consider a single server finite capacity queue with general bulk service rule in which arrivals are governed by MAP and service times are arbitrarily distributed. The distributions of the number of customers in the queue at arbitrary, post-departure and pre-arrival epochs have been obtained using the supplementary variable and the embedded Markov chain techniques. Computational procedure has been given when the service time distribution is of phase type.

Analysis of the MAP/G a , b /1/N Queue

On the finite-buffer bulk-service queue with general independent arrivals: GI/M[b]/1/N

Impatient customer queue with Bernoulli schedule vacation interruption

This article presents the analysis of a finite buffer M/M/1 queue with multiple and single working vacations. The arriving customers balk (that is do not join the queue) with a probability and renege (that is leave the queue after joining) according to exponential distribution. The inter-arrival times, service times during a regular service period, service times during a vacation period and vacation times are independent and exponentially distributed random variables. Steady-state behavior of the model is considered and various performance measures, some special cases of the model and cost analysis are discussed.

P. Vijaya Laxmi

Papers

Analysis of finite-buffer multi-server queues with group arrivals: GI X /M/c/N

Analysis of the MAP/G a , b /1/N Queue

On the finite-buffer bulk-service queue with general independent arrivals: GI/M[b]/1/N

Impatient customer queue with Bernoulli schedule vacation interruption

Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations