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The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.
[1] [2] Such models are often described as M/G/1 type Markov chains because they can describe transitions in an M/G/1 queue. [ 3 ] [ 4 ] The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains.
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.
In probability theory, the matrix geometric method is a method for the analysis of quasi-birth–death processes, continuous-time Markov chain whose transition rate matrices with a repetitive block structure. [1] The method was developed "largely by Marcel F. Neuts and his students starting around 1975." [2]
In probability theory, a transition-rate matrix (also known as a Q-matrix, [1] intensity matrix, [2] or infinitesimal generator matrix [3]) is an array of numbers describing the instantaneous rate at which a continuous-time Markov chain transitions between states.
For a continuous time Markov chain (CTMC) with transition rate matrix, if can be found such that for every pair of states and π i q i j = π j q j i {\displaystyle \pi _{i}q_{ij}=\pi _{j}q_{ji}} holds, then by summing over j {\displaystyle j} , the global balance equations are satisfied and π {\displaystyle \pi } is the stationary ...
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 ...
A Markov decision process is a Markov chain in which state transitions depend on the current state and an action vector that is applied to the system. Typically, a Markov decision process is used to compute a policy of actions that will maximize some utility with respect to expected rewards.