物聯網 (IoT) 對社會產生了巨大影響，推動了工業、交通和 5G 通信等各個領域的進步。隨著物聯網的快速發展，機器對機器的通信變得越來越重要。 如何很好地實現機器對機器的通信是一個非常重要的課題。為了減輕傳統主從系統(Client-server system)的壅塞問題，人們提議將發布/訂閱系統(Pub/Sub system)應用於物聯網。發布/訂閱系統包含發布器，中介器(broker)與訂閱器。在我們的研究中，我們聚焦於行動發布/訂閱系統的中介器。為了表徵不同物件之間的時變距離，我們將中介器塑模成為一個具有兩種以上服務狀態的間歇佇列，其中每個服務狀態都有相應的服務速率。為了更接近真實情況，我們假設所有事件可分為二種優先權等級，高優先權和低優先權。另外，為了表達事件的時效性，在佇列等候的事件有不耐煩限制，亦即當事件在佇列中過期時，它會立即離開系統。首先，我們推導出所考慮系統的解析模型。其次，迭代算法被用於尋找穩態概率分佈和感興趣的效能指標。第三，我們研究了系統參數(例如服務狀態數量和到達速率）對我們感興趣的效能指標的影響。最後，我們編寫了模擬程式來驗證解析結果的正確性。

The Internet of Things (IoT) has greatly impacted society, enabling advancements in various fields such as industry, transportation, and 5G communication. With the rapid development of IoT, machine-to-machine communication has become increasingly important. How to well realize the machine-to-machine communication is a very important subject. To alleviate the congestion of the traditional client-server system, the Pub/Sub system is proposed to be applied to the IoT. The Pub/Sub system consists of publisher, broker and subscriber. In our research, we focus on the broker of the mobile Pub/Sub system. Specifically, we model the broker as an intermittent queue with two or more service states to characterize the time-varying distances between different objects. Each service state is associated with a corresponding service rate. To be more realistic, we assume that there are two priority classes of events, high-priority and low-priority. Additionally, to indicate the time effectiveness, each event waiting in the queue has an impatience limit, i.e., the event must leave the system at once the impatience limit expires. First, we derive the analytical model for the considered system. Second, an iterative algorithm is used for finding the steady state probability distribution and the interested performance measures. Third, we study the effects of system parameters, such as the number of service states and arrival rate, on the performance measures of interest to us. Finally, we write the simulation programs to verify the accuracy of the analytical results.

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