無線感測器在當今大數據時代非常重要。在環境中收集的數據需要通過無線感測網路來傳輸。一方面，無線感測器需要能量來完成傳輸服務。另一方面，無線感測器的能量容量受限於小尺寸。為了延長每個無線感測器的壽命，能量收集方法可用於收集可再生能源。我們的研究假設透過能量收集方法來收集太陽能，用於支援無線感測器的傳輸需求。為了提供更好的誤碼率或數據速率，一個封包的能量需求可以是多於一個能量單位。此外，如果超過耐性區間，則封包會由於不耐煩而可能在沒完成服務的情況下離開。在這研究中，我們研究了無線感測器網路的三種情境：一種不耐煩的客戶，兩種不耐煩的客戶，以及多種不耐煩的客戶。在具有一種不耐煩客戶的第一種情境中，每個在佇列中等待的客戶可能變得不耐煩並且只需要一個能量單位來啟動服務。我們使用二維馬可夫鏈來描述第一個系統。在具有兩種不耐煩客戶的第二種情境中，每個客戶必須消耗一個或兩個能量單位來啟動服務。我們使用三維馬可夫鏈來描述第二個系統，因為我們必須確定是否是在佇列中排頭的客戶變得不耐煩。在具有多類不耐煩客戶的第三種情境中，每位不同種類的客戶必須消耗不同的能量單位來啟動服務。我們使用三維馬可夫鏈來描述第三個系統。首先，我們推導出所考慮系統的解析模型。我們利用疊代算法找到穩態機率分佈和感興趣的效能指標。其次，我們提出了一種近似方法來計算完成服務的客戶在佇列中的等待時間。第三，我們研究了不同的系統參數對於感興趣的效能指標的影響。最後但並非最不重要的是，我們利用C語言撰寫相關模型的電腦模擬程式。在研究的大多數情況下，解析結果顯示與模擬結果非常一致。

Wireless sensors are extremely important in today's era of big data. Data collected in the environment needs to be transmitted through the wireless sensor network. On one hand, wireless sensors need energy to complete the transmission service. On the other hand, the energy capacity of a wireless sensor is limited by its small size. To extend the lifetime of each wireless sensor, the energy harvesting method can be utilized to collect renewable energy. Our research assumes that the solar energy is collected via the energy harvesting method to support the transmission needs of wireless sensors. In order to provide better bit error rate or data rate, the energy requirement of a packet may be more than one unit of energy. Furthermore, a packet may leave without finishing the service due to impatience if the patient interval is exceeded. In this work, we study three scenarios for wireless sensor networks: one class of impatient customers, two classes of impatient customers, and multiple classes of impatient customers. In the first scenario with one class of impatient customers, we focus on the cases where each customer waiting in the queue becomes impatient and requires only one energy unit to start the service. We use a two-dimensional Markov chain to describe the first system. In the second scenario with two classes of impatient customers, each customer has to consume one or two energy units to start the service. We use a three-dimensional Markov chain to describe the second system since we have to determine whether the customer becoming impatient is at the head of line in the queue or not. In the third scenario with multiple classes of impatient customers, each customer of different classes has to consume different energy units to start the service. We use a three-dimensional Markov chain to describe the third system. First, we derive the analytical models for the systems considered. An iterative algorithm is utilized to find the steady state probability distribution and performance measures of interest. Second, an approximation method is proposed to calculate the waiting time in the queue for the customers completing the service. Third, the impacts of different system parameters on the performance measures of interest are studied. Last but not least, the computer simulation program is written in C language. In most cases studied, the analytical results are shown to be in good agreement with the simulation results.

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