Steady-State Convergence Theorem 只有一个recurrent class并且是非周期性的马尔可夫链,状态 j 以及稳态概率 \pi_j 具有以下特性: \lim_{n \rightarrow \infty}{r_{ij}(n)=\pi_j},\ \ \forall i,j\in R 稳态概率 \pi_j 是以下方程的唯一解: \begin{cases}\pi_j=\sum_{k=1}^m\pi_kp_{...
Recurrent Class: Set of state inA(i)form a recurrent class. States inA(i)are accessible from each other, no states outsideA(j)is accessible from them. For a recurrent statei, we haveA(i)=A(j)ifjbelongs toA(i). And we drived the Markov chain decomposition law: A Markov chain can ...
Markov Chains—Stationary Distributions and Steady StateLet N n(y) denote the number of visits of the Markov chain {X n} to y during times m = 1,…,n. That is, $${N_n}(y) = \\sum\\limits_{m = 1}^n {{I_{\\{ y\\} }}({X_m})}...
In this paper, we develop a continuous-time Markov chain model to describe the radio spectrum usage, and derive the transition rate matrix for this model. In addition, we perform steady-state analysis to analytically derive the probability state vector. The proposed model and derived expressions ...
3)Steady State Distribution(稳态分布) r为行和 IV. NUMERICAL RESULTS 参数意义: CaseⅠ:对照组 CaseⅡ:更高的故障率 CaseⅢ:更高效的检测和补偿 需要更高效的自修复SON函数 一般故障率极大地影响网络的可靠性 关键故障率太低,影响不大 V. UTILITY OF THE DEVELOPED MODEL : FAULT PREDICTION FRAMEWORK (FPF...
To compute the steady state vector, solve the following linear system for Pi, the steady-state vector of the Markov chain: (Q | e)TPi=b Appending e to Q, and a final 1 to the end of the zero-vector on the right-hand side ensures that the solution vector Pi has ...
The concept of communication divides the state space into a number of separate classes. The Markov chain is said to be irreducible if there is only one class, that is, if all states communicate with each other. In other words, it is possible to move from any state to any other ...
PR ] 2 1 Ja n 20 19 STEADY STATE SENSITIVITY ANALYSIS OF CONTINUOUS TIME MARKOV CHAINS In this paper we study Monte Carlo estimators based on the likelihood ratio approach for steady-state sensitivity. We first extend the result of Glynn and ... T Wang,P Plechá - 《Siam Journal on ...
A Markov chain (discrete-time Markov chain or DTMC[1]), named after Andrey Markov, is a random process that undergoes transitions from one state to another on a state space. It must possess a property that is usually characterized as "memoryless": the probability distribution of the next ...