Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity

Wang, K.-H.; Hsieh, Wen-Yang

doi:10.1016/0026-2714(95)90085-5

Cited by 11 publications

(2 citation statements)

References 7 publications

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“…No specific realistic cases are taken into account. However, under the assumption that, the arrival rate, batch service rate, individual service rate, startup rate, breakdown rate, repair rate, holding cost, operating cost, startup cost, setup cost, breakdown cost and reward are trapezoidal fuzzy numbers, and they are represented by: ̃ = [2,3,4,5], ̃= [10,11,12,13], ̃= [8,9,10,11], ̃= [3,4,5,6], ̃= [0.2,0.3,0.4,0.5], ̃= [3,4,5,6], ̃ℎ = [5,6,7,8], ̃= [10,15,20,25], ̃= [100, 150, 200, 250], ̃ = [200,250,300,350], ̃ = [50,60,70,80], and ̃ = [30,40,50,60] respectively.…”

Section: Numerical Examplementioning

confidence: 99%

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Sama¹,

Vemuri²,

Boppana³

2021

ISI

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The two-phase service models analyzed by several authors considered only the probabilistic nature of the queue parameters with fixed cost elements. But the queue parameters and cost elements will be in general are of both possibilistic and probabilistic in nature. Analyzing the performance of the queueing systems with fuzzy environment facilitates to investigate for the possibilistic interval estimates to the performance measures of a queueing system rather than point estimates. In this work, it is proposed to construct membership function of the fuzzy cost function to obtain confidence estimates for some performance measures of a controllable two-phase service single server Markovian gated queue with server startups and breakdowns under N-policy in which the queue parameters viz. arrival rate, startup rate, batch service rate, individual service rate, repair rate and cost elements are all defined as fuzzy numbers. Based on Zadeh’s extension principle and the α-cuts, a set of parametric nonlinear programming problems are developed to find the upper and lower bounds of the minimum total expected cost per unit time at the possibility level α. As the analytical solutions of the nonlinear programming problems developed for the proposed model are tedious, considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical results for the lower and upper bounds of the optimal threshold N* and the minimum total expected cost per unit time are computed using the nonlinear programming solver available in MATLAB.

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Section: Numerical Examplementioning

confidence: 99%

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Sama¹,

Vemuri²,

Boppana³

2021

ISI

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“…Recently, Ke and Wang [4] developed analytic steady-state solutions for the N policy G/M/1 queueing system with finite capacity. For a non-reliable server, analytic steady-state solutions of the N policy M/M/1 queueing systems with either finite or infinite capacity were first obtained by Wang and Hsieh [11] and Wang [8], respectively. Wang [9] developed analytic steady-state solutions for the N policy M/E k /1 queueing system.…”

Section: Introductionmentioning

confidence: 99%

Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/H_k/1 Queueing System

Wang

Kao

Chen

2004

Quality Technology & Quantitative Management

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We consider a single removable and non-reliable server in both infinite capacity and finite capacity queueing systems with Poisson arrivals and k-type hyper-exponential distribution for the service times operating under the N policy. The server may be turned on at arrival epochs or off at departure epochs. Breakdown and repair times of the server are assumed to follow a negative exponential distribution. Cost model for infinite capacity queueing system (say cost model 1) is developed to determine the optimal operating policy. Cost model for finite capacity queueing system (say cost model 2) is developed to determine the optimal operating policy and the optimal system capacity, simultaneously. This paper presents the optimal operating policy, the optimal system capacity, the minimum expected cost based on specific values given to the system parameters, as well as to the cost elements. The sensitivity analysis is also investigated.

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Optimizing the Profit of On-Demand Multimedia Service Via a Server-Dependent Queuing System

Lin

2006

Advances in Web-Age Information Management

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Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity

Cited by 11 publications

References 7 publications

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/H_k/1 Queueing System

Optimizing the Profit of On-Demand Multimedia Service Via a Server-Dependent Queuing System

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Optimal control of a removable and non-reliable server in a markovian queueing system with finite capacity

Cited by 11 publications

References 7 publications

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Optimal Control Policy for a Two-Phase M/M/1 Unreliable Gated Queue under N-Policy with a Fuzzy Environment

Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/Hk/1 Queueing System

Optimizing the Profit of On-Demand Multimedia Service Via a Server-Dependent Queuing System

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Optimal Management of a Removable and Non-Reliable Server in an Infinite and a Finite M/H_k/1 Queueing System