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Visitors come to a two-server location following a Poisson process with a rate of A. When they arrive, they join a common queue. The next person in line begins service as soon as a server finishes servicing the previous customer. The service times of server i are exponential RVs with rate μi, i=1; 2, where μ₁ + #2 > A. An arrival finding both servers free is equally likely to go to either one. 1. (10 pts) Define an appropriate continuous-time Markov chain for modeling this prob- lem. 2. (15 pts) Write flow balance equations for this CTMC 3. (15 pts) Find the limiting probabilities. Show your calculations.

Visitors come to a two-server location following a Poisson process with a rate of A. When they arrive, they join a common queue. The next person in line begins service as soon as a server finishes servicing the previous customer. The service times of server i are exponential RVs with rate μi, i=1; 2, where μ₁ + #2 > A. An arrival finding both servers free is equally likely to go to either one. 1. (10 pts) Define an appropriate continuous-time Markov chain for modeling this prob- lem. 2. (15 pts) Write flow balance equations for this CTMC 3. (15 pts) Find the limiting probabilities. Show your calculations.

A First Course in Probability (10th Edition)
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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Visitors come to a two-server location following a Poisson process with a rate of A. When they arrive, they join a common queue. The next person in line begins service as soon as a server finishes servicing the previous customer. The service times of server i are exponential RVs with rate μi, i=1; 2, where μ₁ + #2 > A. An arrival finding both servers free is equally likely to go to either one. 1. (10 pts) Define an appropriate continuous-time Markov chain for modeling this prob- lem. 2. (15 pts) Write flow balance equations for this CTMC 3. (15 pts) Find the limiting probabilities. Show your calculations.
Transcribed Image Text:Visitors come to a two-server location following a Poisson process with a rate of A. When they arrive, they join a common queue. The next person in line begins service as soon as a server finishes servicing the previous customer. The service times of server i are exponential RVs with rate μi, i=1; 2, where μ₁ + #2 > A. An arrival finding both servers free is equally likely to go to either one. 1. (10 pts) Define an appropriate continuous-time Markov chain for modeling this prob- lem. 2. (15 pts) Write flow balance equations for this CTMC 3. (15 pts) Find the limiting probabilities. Show your calculations.
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