MARKOV ANALYSIS

The personal computer industry is very fast moving and technology provides motivation for customers to upgrade with new computers every few years. Brand loyalty is very important and companies try to do things to keep their customers happy. However, some current customers will switch to a different company. Three particular brands, Doorway, Bell, and Kumpaq, hold the major shares of the market. People who own Doorway computers will buy another Doorway in their next purchase 80% of the time, while the rest will switch to the other companies in equal proportions. Owners of Bell computers will buy Bell again 90% of the time, while 5% will buy Doorway and 5% will buy Kumpaq. About 70% of the Kumpaq owners will make Kumpaq their next purchase while 20% will buy Doorway and the rest will buy Bell. If each brand currently has 200,000 customers who plan to buy a new computer in the next year, how many computers of each type will be purchased?

QUEUING THEORY

13-19 Juhn and Sons Wholesale Fruit Distributors employ one worker whose job is to load fruit on outgoing company trucks. Trucks arrive at the loading gate at an average of 24 per day, or 3 per hour, according to a Poisson distribution. The worker loads them at a rate of 4 per hour, following approximately the exponential distribution in service times. Determine the operating characteristics of this loading gate problem. What is the probability that there will be more than three trucks either being loaded or waiting? Discuss the results of your queuing model computation.