Alice (A), Bob (B) and Chris (C) pass a stochastic models textbook to each other. When B gets

the book, he sets up two independent \alarm clocks," which ring after independent exponentially

distributed times: alarm clock B-A is distributed as EXP(2), i.e. has exponential distribution with

parameter 2 (mean 1/2); alarm clock B-C is distributed as EXP(5). If B-A rings rst, at that

time B passes the book to A; if B-C rings rst, at that time B passes the book to C. When C get

the book, he behaves analogously, except his alarm clocks to pass the book to A or B are EXP(5)

and EXP(3), respectively. Alice (A) behaves dierently. When she gets the book, she sets a rst

independent alarm clock H1 which is distributed as EXP(4). When H1 rings, A with probability

1/4 passes the book to C, and with probability 3/4 sets another independent alarm clock H2 which

is distributed as EXP(4). Finally, when H2 rings, Alice passes the book to either B or C with equal

probabilities 1/2.

Can this process be modeled as a CTMC? If so, what is the state space and transition rates

(the Gij's)?

In the long-run, what is the fraction of time that Alice holds the book?