Steady stateAnalysis of the initial transient problem of Monte Carlo steady state simulation motivates the following question for Markov chains: when does there exist a deterministic T such that P(x(T) = y-bar-(0) = x) = pi(y), where pi is the stationary distribution of X. We show ...
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 ...
Let e be the n-vector of all 1's, and b be the (n+1)-vector with a 1 in position n+1 and 0 elsewhere. 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...
We prove new iterative algorithms to provide component-wise bounds of the steady-state distribution of an irreducible and aperiodic Markov chain. These bounds are based on simple properties of (max,+) and (min,+) sequences. The bounds are improved at each iteration. Thus, we have a clear ...
Using the matrix analytic method, we identify the necessary and sufficient condition for both Markov chains to be positive recurrent. For the GI/M/1 type chain, we derive a matrix-geometric solution for its steady-state distribution and for the M/G/1 type chain, we develop a simple linear...
Steady-State Theory refers to a mathematical concept associated with stationary Markov processes, characterizing nonequilibrium steady states in terms of time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. AI generated definition based on: Physic...
In a general one-sector model of optimal stochastic growth where the productivity of capital is bounded but may vary widely due to technology shocks, we derive a tight estimate of the slope of the optimal policy function near zero. We use this to derive a readily verifiable condition that ens...
The deterministic quasi-state-state approximation (QSSA) can thus be used to reduce the dimensionality of a system and avoid stiffness in numerical simulations. QSSA has been widely used in both numerical and theoretical studies and its validity condition in deterministic models is well understood ...
The sensitivity analyses focused on the power law exponent (a), parent rate constant, mean jump length, and source boundary condition in order to better understand their effect on plume transport with first-order reac- tions. In addition, the sensitivity of the number of simulated particles on ...
A Markov chain method for estimating the steady-state error of an extremal systemNot Availabledoi:10.1007/BF01030326N. M. VolchkovKluwer Academic Publishers-Plenum PublishersRadiophysics & Quantum Electronics