A taxi alternates between three locations When it reaches location 1 it is equally likely to go next to either 2 or 3 When it reaches 2 it will next go to 1 with probability and to 3 with probability 3. From 3 it always goes to 1 The mean times between locations i and j are t 20, 1330, 123 = 30 (t,, = t,,) ==

(a) What is the (limiting) probability that the taxi's most recent stop was at location i, i = 1, 2, 3

(b) What is the (limiting) probability that the taxi is heading for loca- tion 2

(c) What fraction of time is the taxi traveling from 2 to 3? Note. Upon arrival at a location the taxi immediately departs.