Problem 16-03 (Algorithmic)
The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities:
To | ||
From | Running | Down |
Running | 0.70 | 0.30 |
Down | 0.20 | 0.80 |
(a) If the system is initially running, then the probability of it being down in the next hour is 0.30 from the table, it's obvious.
(b)
1 = 0.7
1 + 0.2
2
Let 2
= 1-
1
1
= 0.7
1
+ 0.2 * (1-
1
)
1
= 0.7
1
+ 0.2 - 0.2 *
1
0.5 1 =
0.2
1 =
0.40
2 = 1 -
0.4 = 0.60
Please leave a like. Thank you.
Problem 16-03 (Algorithmic) The computer center at Rockbottom University has been experiencing computer downtime. Let us...
The computer center at Rockbottom University has been experiencing computer downtime. Let us assume that the trials of an associated Markov process are defined as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities: TO Down From Running Down Running 0.80 0.10 0.20 0.90 a. If the system is initially running, what...
Problem 16-09 (Algorithmic) The purchase patterns for two brands of toothpaste can be expressed as a Markov process with the following transition probabilities: To From MDA Special B 0.80 0.25 Special B MDA 0.20 0.75 a. Which brand appears to have the most loyal customers? Special B Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor. b. What are the projected market shares for the two brands? If required,...
Problem 15-33 (Algorithmic) Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to ten. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.07 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.6 machines per hour. a. Compute the operating characteristics if the...
Problem 15-33 (Algorithmic) Kolkmeyer Manufacturing Company is considering adding two machines to its manufacturing operation. This addition will bring the number of machines to nine. The president of Kolkmeyer asked for a study of the need to add a second employee to the repair operation. The arrival rate is 0.06 machines per hour for each machine, and the service rate for each individual assigned to the repair operation is 0.6 machines per hour, a. Compute the operating characteristics if the...
Problem 15-9 (Algorithmic) Marty's Barber Shop has one barber. Customers have an arrival rate of 2.3 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that no units are in the system? If required, round your answer to four decimal places. P0 = What is the probability that one customer is receiving a haircut and no...
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...
Problem 16-07 (Algorithmic) Baseball's World Series is a maximum of seven games, with the winner being the first team to win four games. Assume that the Atlanta Braves are playing the Minnesota Twins in the World Series and that the first two games are to be played in Atlanta the next three games at the Twins' ballpark, and the last two games, if necessary, back in Atlanta. Taking into account the projected starting pitchers for each game and the home...
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,...
Problem 15-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 9 calls per hour. The arrival rate is 17 calls...
Problem 5-86A (Algorithmic) Accounting for Notes Receivable Yarnell Electronics sells computer systems to small businesses. Yamell engaged in the following activities involving notes receivable a. On November 1, 2019, Yamell sold a $5,000 system to Ross Company. Ross gave Yamella 6-month, 11% note as payment b. On December 1, 2019, Yarnell sold an $8,500 system to Searfoss Inc. Starfoss gave Yarella 9- month, 10% note as payment c. On May 1, 2020, Ross paid the amount due on its note....