During the course of a day, the vehicle traffic at a certain location varies randomly, changing among "light", "medium" and "heavy". Imagine a 3-state continuous time Markov process where changes in traffic density are represented by transitions. Assume the only way to get from "light" to "heavy" or vice versa is by way of the "medium" state. The transition times are independent and exponentially distributed, with rate parameters ALM = 5, AML = 4, AH = 2, Ahm= 1. In terms of notation, Alm denotes that transition rate from light to medium. The rates are defined in the unit of hours. a.) Model a continuous time birth-death process that describes the dynamics of traffic state transitions. What are the holding time distributions for each state? b.) If the traffic has been medium for the last 10 minutes, what is the expected length of additional time that it takes to change state? c.) If the traffic has been medium for the last 10 minutes, what is the expected length of additional time that it takes to change state, conditional on that the state is changing to light? d.) Suppose now there is an additional state "blocked", which can be reached only from the state "heavy" with rate hB=1. Starting from state medium, how long in expectation does it take to first change to state "blocked"? e.) Following the statement in part d.), starting from medium, what is the probability that the traffic condition becomes "blocked" before ever becoming "light"?