Journal ArticleDOI
Comparative Analysis for the N Policy M/G/1 Queueing System with a Removable and Unreliable Server
TLDR
In this article, the authors analyzed a single removable and unreliable server in the N policy M/G/1 queueing system in which the server breaks down according to a Poisson process and the repair time obeys an arbitrary distribution.Abstract:
In this paper we analyze a single removable and unreliable server in the N policy M/G/1 queueing system in which the server breaks down according to a Poisson process and the repair time obeys an arbitrary distribution. The method of maximum entropy is used to develop the approximate steady-state probability distributions of the queue length in the M/G(G)/1 queueing system, where the second and the third symbols denote service time and repair time distributions, respectively. A study of the derived approximate results, compared to the exact results for the M/M(M)/1, M/E2(E3)/1, M/H2(H3)/1 and M/D(D)/1 queueing systems, suggest that the maximum entropy principle provides a useful method for solving complex queueing systems. Based on the simulation results, we demonstrate that the N policy M/G(G)/1 queueing model is sufficiently robust to the variations of service time and repair time distributions.read more
Citations
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(International Transactions in Operational Research,09(2):195-212)Control Policies of an M/G/1 Queueing System with a Removable and Non-reliable Server
Kuo-Hsiung Wang,J. C. Ke +1 more
TL;DR: A single non-reliable server in the ordinary M/G/1 queueing system whose arrivals form a Poisson process and service times are generally distributed and it is shown that the optimal N policy and the optimal Min(N, T) policy are always superior to the optimal T policy.
Journal ArticleDOI
A maximum entropy approach for the (p,N)-policy M/G/1 queue with a removable and unreliable server
Kuo-Hsiung Wang,Kai-Bin Huang +1 more
TL;DR: A comparative analysis between the derived approximate results with exact analytic results for three different service time and repair time distributions such as exponential, uniform, and gamma shows that the maximum entropy approach is sufficiently accurate for practical use.
Journal ArticleDOI
Maximum entropy approach for batch-arrival queue under N policy with an un-reliable server and single vacation
Jau-Chuan Ke,Chuen-Horng Lin +1 more
TL;DR: It is demonstrated that the maximum entropy approach is efficient enough for practical purpose and is a feasible method for approximating the solution of complex queueing systems.
Journal ArticleDOI
Maximum entropy solutions for batch arrival queue with an un-reliable server and delaying vacations
Jau-Chuan Ke,Chuen-Horng Lin +1 more
TL;DR: This work uses maximum entropy principle to derive the approximate formulas for the steady-state probability distributions of the queue length and demonstrates that the maximum entropy approach is accurate enough for practical purpose and is a useful method for solving complex queueing systems.
Journal ArticleDOI
Mathematical Analysis of Queue with Phase Service: An Overview
TL;DR: An attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations to provide relevant information to system analysts, managers, and industry people interested in using queueing theory to model congestion problems wherein the phase type services are prevalent.
References
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Book
Simulation with Arena
TL;DR: In this article, the authors introduce the subject of simulation using examples from Arena and are designed for the introductory simulation course offered in industrial engineering and business departments Simulation with Arena is the only book to cover the Arena product and it is accompanied by an Arena CD.
Journal ArticleDOI
Queueing Systems with a Removable Service Station
TL;DR: A single-server queueing system with constant Poisson input is considered and the partial elimination of the service station's idle fraction is envisaged by intermittent close-down and set-up.
Journal ArticleDOI
Optimal Operating Policies for M/G/1 Queuing Systems
TL;DR: In this paper, the authors consider the economic behavior of a M/G/1 queuing system operating with the following cost structure: a server start-up cost, a server shut-down cost, and a holding cost per unit time spent in the system for each customer, and prove that for the single server queue there is a stationary optimal policy of the form: Turn the server on when n customers are present, and turn it off when the system is empty.
Journal ArticleDOI
Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server
TL;DR: The paper characterizes an optimal policy for the infinite-horizon discounted problem, offers an optimality proof, and presents a computational algorithm.