Continuous-time Markov chain example

Now, since we have a basic understanding of exponential distributions and the Poisson process, we can move on to the example to build up a continuous-time Markov chain. In this example, we will try to show how the properties of exponential distributions can be used to build up generic continuous-time Markov chains. Let's consider a hotel reception where n receptionists are working in parallel. Also consider that the guests arrive according to a Poisson process, with rate λ, and the service time for each guest is represented using an exponential random variable with learning rate µ. Also, if all the receptionists are busy when a new guest arrives, he/she will depart without getting any service. Now let's ...

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