4.43. 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 1 2 3 1 0 1/4 1/2 2 1/5 0 1/5 3 1/3 1/3 0 In equilibrium what is the probability no one is in the system, i.e., 1(0,0,0).
4.43. 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 1 2 3 1 0 1/4 1/2 2 1/5 0 1/5 3 1/3 1/3 0 In equilibrium what is the probability no one is in the system, i.e., 1(0,0,0).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:4.43. 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
1
2
3
0 1/4 1/2
2 1/5 0 1/5
3 1/3 1/3 0
1
In equilibrium what is the probability no one is in the system, i.e., 7(0,0,0).
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