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A taxi alternates between three locations. When it reaches location 1 it is equally likely to go next to either location 2 or location 3. When it reaches location 2 it will next go to location 1 with probability 1/3 and to location 3 with probability 2/3. From location 3 it always goes to location 1. The mean time between locations i and j are t12 = 20, t13 = 30, t23 = 30. Assume exponential service and assume tij = tji.

(a) Find 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 location 2?

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

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Statistics and Probability, Statistics

Category:- Statistics and Probability
Reference No.:- M91581817

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