臺灣博碩士論文加值系統

本文主要研究在計數過程架構下, 等候系統之服務端為批次服務之問題, 並
結合損失函數評估等候系統之最佳服務器個數。文中以計數過程的等候模型為
基礎, 假設顧客的到達率雖獨立但間隔時間不限定分配的λ(t) = θλ0(t) 之參
數模型, 其中我們假設顧客到達的模型為卜瓦松過程、線性模型和二次式模型,
且利用鞅論的弱收斂性質估計參數θ。
除此之外, 本研究還考慮系統可能有閒置情況。而損失函數方面, 則考慮服
務端會因運行次數產生的損耗所延伸的損失, 與顧客等待時間的損失及架設服
務器個數產生的損失架構損失函數, 並以某醫院的電梯系統為例, 以風險值針
最低為最佳決策, 針對不同的顧客到達率、電梯容量和電梯服務效能之組合分
析。顧客到達率的部份, 我們分為尖峰(ˆθ = 0.6)、普通(ˆθ = 0.3) 和離峰(ˆθ =
0.1) 三種情況; 電梯容量的部分, 分為高承載(m = 19)、一般承載(m=13)
和低承載(m=8) 三種情況; 電梯服務效能則分為效能佳(α = 1.9,β =
60.3)、效能普通(α = 2.3,β = 80.3) 和效能差(α = 2.9,β = 100.3) 三種
情況, 模擬各組合的情況, 並以醫院電梯系統服務環境為例, 由實際的調查知,
醫院電梯最高承載為13人, 在參數估計後電梯效能為α = 2.3、β = 80.3, 此
情況下, 如果面對顧客到達為離峰情況(ˆθ = 0.1), 在顧客到達率卜瓦松過程、
線性模型和二次式模型時, 最佳的電梯數皆為2台; 如果顧客到達為一般的情
況(ˆθ = 0.3), 同樣針對顧客到達為卜瓦松過程、線性模型和二次式模型時最
佳的電梯數分別為5台、4台及5台; 如果顧客到達為尖峰的情況(ˆθ = 0.6),
則在顧客到達的模型為卜瓦松過程、線性模型和二次式模型時, 最佳的電梯數
分別為9台、6台及9台。其餘情況的模擬結果可參見第四章, 供醫院作為決定
最佳電梯個數之參考。

This paper discuss the queuing model with bulk service inder counting
proceses and use loss function to value the optimal number id services.
The Queuing model is based on counting processes. Assume
the distribution of customers arrive indepentlly but the interval arrival
time is not identical, it means that the rate of arrival cahnge with
time. We define the model is λ(t) = θλ0(t) and consider some situtations
such as poisson processes, linear medol and quadratic function.
About the parameter , θ, we will use the property of weak converge
of martingale central limit theory to estimate it.
Beside, we also consider the dormant of service. The aspect of loss
function, the first loss made form the rounds of the machine working,
second is customers’ waiting time and the third is the loss of
machine built-on. We take an elevator system of a hospital for an
example and estimate the parameter of the rate of customers arrive
and elevators interval serve time. The part of customers’ arrival, the
three situations are offpeak (ˆθ=0.1)、averge (ˆθ = 0.3) and peak-hour
(ˆθ = 0.6); the capacity of elevator are hight capacity (m = 19)、normal
capacity (m = 13) and low capacity (m = 8). About the efficiency
of service of elevator, good efficiency (α=1.9,=60.3)、averge efficiency
(α=2.3,β=80.3) and low efficiency (α=2.9,β=100.3) will be considered.
In the hospital case, ˆθ = 0.3, ˆα = 2.3 and ˆ β = 80.3. If the offpeak
(ˆθ = 0.1), the optimal number of service of poisson processes、linear
model and qaudratic function is 2. If the customers arrival rate is
average (ˆθ=0.3), the optimal number of service is 5、4 and 5. If the
customers arrival rate is peak-hour (ˆθ=0.6), the optimal number of
service is 9、6 and 9。Other conclusion of simulation will be displayed
in Ch4.

1 緒論1
1.1 研究動機和目的. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究目的. . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 研究流程. . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 本文架構. . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 文獻探討5
2.1 等候理論. . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 計數過程. . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 決策理論. . . . . . . . . . . . . . . . . . . . . . . . . . 7
3 等候模型與風險函數10
3.1 建立等候模型及風險函數. . . . . . . . . . . . . . . . . . 10
3.2 參數估計. . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 蒙地卡羅模擬15
4.1 損失函數權重. . . . . . . . . . . . . . . . . . . . . . . . 15
4.2 顧客到達率為卜瓦松過程. . . . . . . . . . . . . . . . . . 16
4.3 顧客到達率為線性模式. . . . . . . . . . . . . . . . . . . 24
4.4 顧客到達率為二次函數模式. . . . . . . . . . . . . . . . . 31
5 結論與建議

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