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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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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