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At a local grocery store there are queues for service at the fish counter (1), meat counter (2),…


At a local grocery store there are queues for service at the fish counter (1), meat counter (2), and café (3). For i = 1, 2, 3 customers arrive from outside the system to station i at rate i, and receive service at rate 4 + i. A customer leaving station i goes to j with probabilities p(I, j) given the following matrix:

At a local grocery store there are queues for service at the fish counter (1), meat counter (2),...

In equilibrium what is the probability no one is in the system, i.e., π(0, 0, 0).