Journal ArticleDOI
On the Optimality of Single-Server Queuing Systems
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This paper considers optimal design models for queuing systems in which the decision variables are the number of servers and the mean rate at which each serves, and it is shown that a single-server system is optimal for a wide class of arrival processes and service-time distributions.Abstract:
This paper considers optimal design models for queuing systems in which the decision variables are the number of servers and the mean rate at which each serves, the total cost per unit time of operating the system is the sum of a service cost per unit time and a waiting cost per unit time, and the optimality criterion is long-run expected average cost per unit time. It is shown that a single-server system is optimal for a wide class of arrival processes and service-time distributions, and for a wide variety of waiting-cost functions.read more
Citations
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Journal ArticleDOI
Optimality of the shortest line discipline
TL;DR: In this paper, the authors considered a queuing system consisting of a finite number of identical exponential servers, each server has its own queue, and upon arrival each customer must be assigned to some server's queue.
Journal ArticleDOI
OR Forum—Perspectives on Queues: Social Justice and the Psychology of Queueing
TL;DR: This speculative paper uses personal experiences, published and unpublished cases, and occasionally “the literature” to begin to organize the thoughts on the important attributes of queueing.
Journal ArticleDOI
Optimal control of batch service queues
Rajat K. Deb,Richard F. Serfozo +1 more
TL;DR: A batch service queue is considered where each batch size and its time of service is subject to control and policies which minimize the expected continuously discounted cost and the expected cost per unit time over an infinite time horizon are shown.
Journal ArticleDOI
Comparing counting processes and queues
TL;DR: In this article, partial orderings of counting processes are introduced and applied to compare stochastic processes in queueing models, where the conditions for the queueing comparisons involve the counting processes associated with the interarrival and service times.
Journal ArticleDOI
A Classified Bibliography of Research on Optimal Design and Control of Queues
TL;DR: In this article, the authors present a classified bibliography organized into six sections-static design models, dynamic control models, models involving queue discipline control, miscellaneous models, tutorial and survey papers, and books that have specific portions devoted to design and control.
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Book
A first course in stochastic processes
Samuel Karlin,Howard M. Taylor +1 more
TL;DR: In this paper, the Basic Limit Theorem of Markov Chains and its applications are discussed and examples of continuous time Markov chains are presented. But they do not cover the application of continuous-time Markov chain in matrix analysis.
Book
Introduction to Operations Research
TL;DR: The Simplex Method duality theory and sensitivity analysis for linear programming has been studied extensively in the field of operations research as mentioned in this paper, including the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.
Book
An introduction to probability theory
TL;DR: The authors introduce probability theory for both advanced undergraduate students of statistics and scientists in related fields, drawing on real applications in the physical and biological sciences, and make probability exciting." -Journal of the American Statistical Association