Problem 16-05 (Algorithmic)
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.
b. What is the probability that in the long run the traffic will
not be in the delay state? If required, round your answers to three
decimal places.
______________________
transition matrix (T) is:
no delay | delay | |
no delay | 0.9 | 0.1 |
delay | 0.25 | 0.75 |
let long term steady state matrix is: X=[x 1-x}
therefore XT=X
or 0.9*x+(1-x)*0.25 =x
x=0.25/0.35 = 0.714
Problem 16-05 (Algorithmic) A major traffic problem in the Greater Cincinnati area involves traffic attempting to...
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probablity of no traffic delay in one perio given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.65. Trafie is classified as having ether a delay or a no-delay state,...