Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown

碩士 === 國立中興大學 === 應用數學研究所 === 81 === This thesis studies the optimal control $N$-policy of a $"non- perfect"$ removable service station in the M/M/1 queueing systems with infinite and finite capacities, respectively. A $"non-perfect"$...

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Main Authors: Wen-Far Hsieh, 謝文發
Other Authors: K.-H. Wang
Format: Others
Language:en_US
Published: 1993
Online Access:http://ndltd.ncl.edu.tw/handle/77624968392020714011
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spelling ndltd-TW-081NCHU05070132015-10-13T17:44:44Z http://ndltd.ncl.edu.tw/handle/77624968392020714011 Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown 有限及無限容量之排隊系統單一可移動服務站會故障的最佳控制 Wen-Far Hsieh 謝文發 碩士 國立中興大學 應用數學研究所 81 This thesis studies the optimal control $N$-policy of a $"non- perfect"$ removable service station in the M/M/1 queueing systems with infinite and finite capacities, respectively. A $"non-perfect"$ removable service station means that the removable service station is typically subject to unpredictable breakdown. The form of the $N$-policy is that turn on the service station (i.e. open the service station to provide service) when $N$ customers are present in the system and turn it off when the system is empty (i.e. no customers are in the system), and this cycle is repeated. The service station can break down only when it is turned on and there are at least one customer in the system. First, we develop the steady-state characteristics of the infinite capacity and finite capacity systems, such as the probability distributions of the number of customers in the system, the expected number of customers in the system, and so on. Second, the results of these two systems generalize (i) the $"perfect"$ M/M/1 queue with a removable server; (ii) the $"non-perfect"$ M/M/1 queue; and (iii) the $"standard"$ M/M/1 queue. Finally, we derive the total steady- state expected cost function per unit time, and determine the optimal value of the control parameter $N$, $N^\star$, in order to minimize this function for these two systems. K.-H. Wang 王國雄 1993 學位論文 ; thesis 54 en_US
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language en_US
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description 碩士 === 國立中興大學 === 應用數學研究所 === 81 === This thesis studies the optimal control $N$-policy of a $"non- perfect"$ removable service station in the M/M/1 queueing systems with infinite and finite capacities, respectively. A $"non-perfect"$ removable service station means that the removable service station is typically subject to unpredictable breakdown. The form of the $N$-policy is that turn on the service station (i.e. open the service station to provide service) when $N$ customers are present in the system and turn it off when the system is empty (i.e. no customers are in the system), and this cycle is repeated. The service station can break down only when it is turned on and there are at least one customer in the system. First, we develop the steady-state characteristics of the infinite capacity and finite capacity systems, such as the probability distributions of the number of customers in the system, the expected number of customers in the system, and so on. Second, the results of these two systems generalize (i) the $"perfect"$ M/M/1 queue with a removable server; (ii) the $"non-perfect"$ M/M/1 queue; and (iii) the $"standard"$ M/M/1 queue. Finally, we derive the total steady- state expected cost function per unit time, and determine the optimal value of the control parameter $N$, $N^\star$, in order to minimize this function for these two systems.
author2 K.-H. Wang
author_facet K.-H. Wang
Wen-Far Hsieh
謝文發
author Wen-Far Hsieh
謝文發
spellingShingle Wen-Far Hsieh
謝文發
Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
author_sort Wen-Far Hsieh
title Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
title_short Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
title_full Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
title_fullStr Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
title_full_unstemmed Optimal Control of the Finite Capacity and Infinite Capacity with a Removable Service Station Subject to Breakdown
title_sort optimal control of the finite capacity and infinite capacity with a removable service station subject to breakdown
publishDate 1993
url http://ndltd.ncl.edu.tw/handle/77624968392020714011
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