At the repair facility machines are worked on by a

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 computer left it places an order for 2 more computers. The order takes an exponentially distributed amount of time with mean 1 week to arrive. Of course, while the store is waiting for delivery, sales may reduce the inventory to 1 and then to 0. (a) Write down the matrix of transition rates Qij and solve ⇡ Q = 0 to find the stationary distribution. (b) At what rate does the store make sales? 4.3. Consider two machines that are maintained by a single repairman. Machine i functions for an exponentially distributed amount of time with rate i before it fails. The repair times for each unit are exponential with rate µi . They are repaired in the order in which they fail. (a) Formulate a Markov chain model for this situation with state space {0, 1, 2, 12, 21}. (b) Suppose that 1 = 1, µ1 = 2, 2 = 3, µ2 = 4. Find the stationary distribution. 4.4. Consider the set-up of the previous problem but now suppose machine 1 is much more important than 2, so the repairman will always service 1 if it is broken. (a) Form...
View Full Document

Ask a homework question - tutors are online