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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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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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.
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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 |
work_keys_str_mv |
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