In the discussion in this section we have

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Unformatted text preview: table goes to the English table with probability 2/5 and to the cashier with probability 3/5. Students who reach the cashier leave the system after they pay. Suppose that the service times for the English table, Math table, and cashier are 25, 30, and 20, respectively. Find the stationary distribution. 4.44. At a local grocery store there are queues for service at the fish counter (1), meat counter (2), and caf´ (3). For i = 1, 2, 3 customers arrive from outside e 157 4.8. EXERCISES 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 1 2 3 1 0 1 /5 1 /3 2 3 1 / 4 1 /2 0 1 /5 1/3 0 In equilibrium what is the probability no one is in the system, i.e., ⇡ (0, 0, 0). 4.45. Three vendors have vegetable stands in a row. Customers arrive at the stands 1, 2, and 3 at rates 10, 8, and 6. A customer visiting stand 1 buys something and leaves with probability 1/2 or visits stand 2 with...
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