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.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter4: Linear Functions

Section4.3: Fitting Linear Models To Data

Problem 24SE: Table 6 shows the year and the number ofpeople unemployed in a particular city for several years....

See similar textbooks