Example
Example 5.16 Consider a system in which individuals at any time are classified as being in one of r possible states, and assume that an individual changes states in accordance with a Markov chain having transition probabilities Pij , i, j = 1, … , r. That is, if an individual is in state i during a time period then, independently of its previous states, it will be in state j during the next time period with probability Pij . The individuals are assumed to move through the system independently of each other. Suppose that the numbers of people initially in states 1, 2, … , r are independent Poisson random variables with respective means λ1 , λ2 , … , λr . We