Chapter 8, Problem 15RE

(a)

To determine

The interpretation of the numbers in the second column of the stochastic matrix that describes the day-to-day transitions of the workday traffic conditions on the Baltimore Beltway is characterized as Light, Moderate and Heavy is,

$\begin{array}{l}\begin{array}{ccc}\text{L}& \text{ M}& \text{ H}\end{array}\\ \begin{array}{c}\text{L}\\ \text{M}\\ \text{H}\end{array}\left[\begin{array}{ccc}.70& .20& .10\\ .20& .75& .30\\ .10& .05& .60\end{array}\right]\end{array}$

(b)

To determine

To calculate: The percentage of the workdays that would fall for each category in the long run when the stochastic matrix that describes the day-to-day transitions of the workday traffic conditions on the Baltimore Beltway is characterized as Light, Moderate and Heavy is,

$\begin{array}{l}\begin{array}{ccc}\text{L}& \text{ M}& \text{ H}\end{array}\\ \begin{array}{c}\text{L}\\ \text{M}\\ \text{H}\end{array}\left[\begin{array}{ccc}.70& .20& .10\\ .20& .75& .30\\ .10& .05& .60\end{array}\right]\end{array}$

(c)

To determine

To calculate: The workdays out of 20 workdays in a month when it is expected to have heavy traffic on the Baltimore Beltway when the stochastic matrix that describes the day-to-day transitions of the workday traffic conditions on the Baltimore Beltway is characterized as Light, Moderate and Heavy is,

$\begin{array}{l}\begin{array}{ccc}\text{L}& \text{ M}& \text{ H}\end{array}\\ \begin{array}{c}\text{L}\\ \text{M}\\ \text{H}\end{array}\left[\begin{array}{ccc}.70& .20& .10\\ .20& .75& .30\\ .10& .05& .60\end{array}\right]\end{array}$