Abstract
In this chapter, we discuss the continuous-time Markov chain (CTMC), which is a continuous-time Markov process that has a discrete state space. CTMC is a widely used mathematical model in reliability and availability studies, queueing systems, communication systems, inventory models, and epidemic studies. The distinction between the discrete-time Markov chain (DTMC) and CTMC is that in DTMC there is a “jump” to a new state at times 1,2,…, but in CTMC the “jump” to a new state may occur at any time t>0. The times between successive transitions are independent and exponentially distributed random variables with means that depend only on the state from which the transition is being made.
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