Continuous-time Markov chain

Definition

A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to the least value of a set of exponential random variables, one for each possible state it can move to, with the parameters determined by the current state.

Related concepts

Adversarial queueing network Arrival theorem BCMP network Balance equation Beneš method Birth process Bulk queue Burke's theorem Buzen's algorithm Competing exponentials Conditional probability D/M/1 queue Data buffer Decomposition method (queueing theory)Diagonal matrix Discrete-time Markov chain Discrete metric Ergodic Erlang (unit)Erlang distribution Eugene Seneta Exponential random variable FIFO (computing and electronics)First-order differential equation Flow-equivalent server method Flow control (data)Fluid limit Fluid queue Fork–join queue G-network G/G/1 queue G/M/1 queue Gordon–Newell theorem Heavy traffic approximation Identity matrix Information system J. L. Doob J. Laurie Snell Jackson network James R. Norris John G. Kemeny Kelly's lemma Kelly network Kendall's notation Kingman's formula Kolmogorov's criterion Kolmogorov backward equations (continuous-time Markov chains)Kolmogorov equations (Markov jump process)LIFO (computing)Layered queueing network Lindley equation Little's law Little-o notation Loss network M/D/1 queue M/D/c queue M/G/1 queue M/G/k queue M/M/1 queue M/M/c queue M/M/∞ queue Main diagonal Markov chain Markov property Markovian arrival process Matrix analytic method Matrix exponential Mean-field theory Mean value analysis Message queue Network congestion Network scheduler Norm (mathematics)Pac-Man Pipeline (software)Poisson point process Pollaczek–Khinchine formula Polling system Probability vector Processor sharing Product-form solution Quality of service Quasireversibility Queueing theory Rational arrival process Reflected Brownian motion Retrial queue Right continuous Round-robin scheduling Scheduling (computing)Semigroup Shortest job next Shortest remaining time Society for Industrial and Applied Mathematics Stationary probability distribution Stochastic matrix Stochastic process Teletraffic engineering Traffic equations Transition-rate matrix Unit vector

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