link: [[notes/C/C strings|C strings]]:string literals 存放於 static storage 中。
1/26/2024在了解 Markov Chain 的定義及其性質之後,這一節要介紹一種 continuous-time Markovian Chain: Birth-Death Processes。 在 Birth-Death Processes 中,state $n$ 只會跳到 state $n-1$ 或者 state $n+1$(state $0$ 只能跳到 state $1$),$n$ 代表 population in the system。 Transition rate 可表示為: $$\begin{cases} \lambda_n,\ n \to n+1 \newline \mu_n,\ n \to n-1\end{cases}$$ 所謂 Birth 就代表有一個 arrival($\lambda$ 對應的箭頭),使整個系統的 size 增加 1,而從一個 birth 到下一個 birth 發生的間隔時間為 exponential random variable。
11/3/2023Markov Processes 不管是 discrete($X(t), t = 0,1,2, \cdots$) or continuous parameter time($X(t), t \gt 0$) 的 Stochastic Process,只要滿足以下式子,即可稱為一個 Markov Process: $$P(X(t_n) \le x_n | X(t_1) = x_1, ..., X(t_{n-1}) = x_{n-1}) = P(X(t_n) \le x_n | X(t_{n-1}) = x_{n-1})$$ :::info a Stochastic Process is best defined as a family of random variables, ${X(t), t \in T}$, defined over some index set or parameter space $T$. The set $T$ is sometimes also called the time range, and $X(t)$ denotes the state of the process at time t. :::
12/26/2022CHAPTER 1 - INTRODUCTION CHAPTER 2 - SIMPLE MARKOVIAN QUEUEING MODELS CHAPTER 3 - ADVANCED MARKOVIAN QUEUEING MODELS CHAPTER 4 - NETWORKS, SERIES, AND CYCLIC QUEUES NTUEE 2020 FALL MIDTERM NTUEE 2020 FALL PRACTICE MIDTERM NTUEE 2021 FALL MIDTERM NTUEE Queueing Theory 2022 FALL PRACTICE MIDTERM NTUEE Queueing Theory 2022 FALL HW1 NTUEE Queueing Theory 2022 FALL HW2
12/22/2022or
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